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Introduction to finite element analysis Introduction to finite element analysis

Description

What is finite element analysis (what is it and why do we carry it out? This free course, Introduction to finite element analysis, introduces the essence of finite element analysis. As an example of its use, you will look at the case of FEA of the tub of a racing car. You will also have the opportunity to try out two exercises to carry out a simple analysis of a plate and a square beam. First published on Wed, 23 Mar 2016 as Introduction to finite element analysis. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 What is finite element analysis (what is it and why do we carry it out? This free course, Introduction to finite element analysis, introduces the essence of finite element analysis. As an example of its use, you will look at the case of FEA of the tub of a racing car. You will also have the opportunity to try out two exercises to carry out a simple analysis of a plate and a square beam. First published on Wed, 23 Mar 2016 as Introduction to finite element analysis. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 First published on Wed, 23 Mar 2016 as Introduction to finite element analysis. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 First published on Wed, 23 Mar 2016 as Introduction to finite element analysis. To find out more visit The Open University's Openlearn website. Creative-Commons 2016Subjects

Science | Maths & Technology | Science | Maths & Technology | Engineering and Technology | Engineering and Technology | Design and Innovation | Design and Innovation | T804_1 | T804_1License

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open UniversitySite sourced from

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This course presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element procedures are discussed with their applications to the solution of general problems in solid, structural, and fluid mechanics, heat and mass transfer, and fluid-structure interactions. The governing continuum mechanics equations, conservation laws, virtual work, and variational principles are used to establish effective finite element discretizations and the stability, accuracy, and convergence are discussed. The homework and the student-selected term project using the general-purpose finite element analysis program ADINA are important parts of the course. This course presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element procedures are discussed with their applications to the solution of general problems in solid, structural, and fluid mechanics, heat and mass transfer, and fluid-structure interactions. The governing continuum mechanics equations, conservation laws, virtual work, and variational principles are used to establish effective finite element discretizations and the stability, accuracy, and convergence are discussed. The homework and the student-selected term project using the general-purpose finite element analysis program ADINA are important parts of the course.Subjects

linear static analysis | linear static analysis | solids | solids | structures | structures | nonlinear static analysis | nonlinear static analysis | heat transfer | heat transfer | fluid flows | fluid flows | finite element methods | finite element methods | ADINA | ADINA | student work | student work | beams | beams | plates | plates | shells | shells | displacement | displacement | conduction | conduction | convection | convection | radiation | radiation | Navier-Stokes | Navier-Stokes | incompressible fluids | incompressible fluids | acoustic fluids | acoustic fluidsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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Includes audio/video content: AV lectures. Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study. Includes audio/video content: AV lectures. Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.Subjects

finite element method | finite element method | statics | statics | dynamics | dynamics | linear analysis | linear analysis | nonlinear analysis | nonlinear analysis | computer modeling | computer modeling | engineering design | engineering design | solids | solids | structures | structures | wave propagation | wave propagation | vibration | vibration | collapse | collapse | buckling | buckling | Lagrangian formulation | Lagrangian formulation | truss | truss | beam | beam | plate | plate | shell | shell | elastic materials | elastic materials | plastic materials | plastic materials | creep | creep | ADINA | ADINA | numerical integration methods | numerical integration methods | mode superposition | mode superpositionLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element procedures are discussed with their applications to the solution of general problems in solid, structural, and fluid mechanics, heat and mass transfer, and fluid-structure interactions. The governing continuum mechanics equations, conservation laws, virtual work, and variational principles are used to establish effective finite element discretizations and the stability, accuracy, and convergence are discussed. The homework and the student-selected term project using the general-purpose finite element analysis program ADINA are important parts of the course. This course presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element procedures are discussed with their applications to the solution of general problems in solid, structural, and fluid mechanics, heat and mass transfer, and fluid-structure interactions. The governing continuum mechanics equations, conservation laws, virtual work, and variational principles are used to establish effective finite element discretizations and the stability, accuracy, and convergence are discussed. The homework and the student-selected term project using the general-purpose finite element analysis program ADINA are important parts of the course.Subjects

linear static analysis | linear static analysis | solids | solids | structures | structures | nonlinear static analysis | nonlinear static analysis | heat transfer | heat transfer | fluid flows | fluid flows | finite element methods | finite element methods | ADINA | ADINA | student work | student work | beams | beams | plates | plates | shells | shells | displacement | displacement | conduction | conduction | convection | convection | radiation | radiation | Navier-Stokes | Navier-Stokes | incompressible fluids | incompressible fluids | acoustic fluids | acoustic fluidsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results. This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.Subjects

finite element methods | finite element methods | solids | solids | structures | structures | fluid mechanics | fluid mechanics | heat transfer | heat transfer | equilibrium equations | equilibrium equations | direct integration | direct integration | mode superposition | mode superposition | eigensolution techniques | eigensolution techniques | frequencies | frequencies | mode shapes | mode shapes | statics | statics | dynamics | dynamics | nonlinear systems | nonlinear systems | wave propagation | wave propagationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.002 Circuits and Electronics (MIT) 6.002 Circuits and Electronics (MIT)

Description

Includes audio/video content: AV lectures. 6.002 is designed to serve as a first course in an undergraduate electrical engineering (EE), or electrical engineering and computer science (EECS) curriculum. At MIT, 6.002 is in the core of department subjects required for all undergraduates in EECS. The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. 6.002 is worth 4 Engineering Design Poin Includes audio/video content: AV lectures. 6.002 is designed to serve as a first course in an undergraduate electrical engineering (EE), or electrical engineering and computer science (EECS) curriculum. At MIT, 6.002 is in the core of department subjects required for all undergraduates in EECS. The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. 6.002 is worth 4 Engineering Design PoinSubjects

Fundamentals of the lumped circuit abstraction | Fundamentals of the lumped circuit abstraction | Resistive elements and networks | Resistive elements and networks | independent and dependent sources | independent and dependent sources | switches and MOS devices | switches and MOS devices | digital abstraction | digital abstraction | amplifiers | amplifiers | and energy storage elements | and energy storage elements | Dynamics of first- and second-order networks | Dynamics of first- and second-order networks | design in the time and frequency domains | design in the time and frequency domains | analog and digital circuits and applications | analog and digital circuits and applicationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataAstrophysics (MIT) Astrophysics (MIT)

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Includes audio/video content: AV selected lectures. Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature of spacetime near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the semester is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advanced Includes audio/video content: AV selected lectures. Study of physical effects in the vicinity of a black hole as a basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature of spacetime near rotating and nonrotating centers of attraction; trajectories and orbits of particles and light; elementary models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the semester is reserved for collaborative research projects on topics such as the Global Positioning System, solar system tests of relativity, descending into a black hole, gravitational lensing, gravitational waves, Gravity Probe B, and more advancedSubjects

black hole | black hole | general relativity | general relativity | astrophysics | astrophysics | cosmology | cosmology | Energy and momentum in flat spacetime | Energy and momentum in flat spacetime | the metric | the metric | curvature of spacetime near rotating and nonrotating centers of attraction | curvature of spacetime near rotating and nonrotating centers of attraction | trajectories and orbits of particles and light | trajectories and orbits of particles and light | elementary models of the Cosmos | elementary models of the Cosmos | Global Positioning System | Global Positioning System | solar system tests of relativity | solar system tests of relativity | descending into a black hole | descending into a black hole | gravitational lensing | gravitational lensing | gravitational waves | gravitational waves | Gravity Probe B | Gravity Probe B | more advanced models of the Cosmos | more advanced models of the Cosmos | spacetime curvature | spacetime curvature | rotating centers of attraction | rotating centers of attraction | nonrotating centers of attraction | nonrotating centers of attraction | event horizon | event horizon | energy | energy | momentum | momentum | flat spacetime | flat spacetime | metric | metric | trajectories | trajectories | orbits | orbits | particles | particles | light | light | elementary | elementary | models | models | cosmos | cosmos | spacetime | spacetime | curvature | curvature | flat | flat | GPS | GPS | gravitational | gravitational | lensing | lensing | waves | waves | rotating | rotating | nonrotating | nonrotating | centers | centers | attraction | attraction | solar system | solar system | tests | tests | relativity | relativity | general | general | advanced | advancedLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project. This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent StructuresLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.002 Circuits and Electronics (MIT) 6.002 Circuits and Electronics (MIT)

Description

6.002 is designed to serve as a first course in an undergraduate electrical engineering (EE), or electrical engineering and computer science (EECS) curriculum. At MIT, 6.002 is in the core of department subjects required for all undergraduates in EECS. The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. 6.002 is worth 4 Engineering Design Points. The 6.002 content was created collabora 6.002 is designed to serve as a first course in an undergraduate electrical engineering (EE), or electrical engineering and computer science (EECS) curriculum. At MIT, 6.002 is in the core of department subjects required for all undergraduates in EECS. The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. 6.002 is worth 4 Engineering Design Points. The 6.002 content was created collaboraSubjects

Fundamentals of the lumped circuit abstraction | Fundamentals of the lumped circuit abstraction | Resistive elements and networks | Resistive elements and networks | independent and dependent sources | independent and dependent sources | switches and MOS devices | switches and MOS devices | digital abstraction | digital abstraction | amplifiers | amplifiers | and energy storage elements | and energy storage elements | Dynamics of first- and second-order networks | Dynamics of first- and second-order networks | design in the time and frequency domains | design in the time and frequency domains | analog and digital circuits and applications | analog and digital circuits and applicationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.29 Numerical Fluid Dynamics (MIT) 2.29 Numerical Fluid Dynamics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs). This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent StructuresLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for theSubjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent StructuresLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.014 Calculus with Theory I (MIT) 18.014 Calculus with Theory I (MIT)

Description

18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site. 18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site.Subjects

axioms for the real numbers | axioms for the real numbers | the Riemann integral | the Riemann integral | limits | limits | theorems on continuous functions | theorems on continuous functions | derivatives of functions of one variablethe fundamental theorems of calculus | derivatives of functions of one variablethe fundamental theorems of calculus | Taylor's theorem | Taylor's theorem | infinite series | infinite series | power series | power series | rigorous treatment of the elementary functions | rigorous treatment of the elementary functionsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.093 Computer Methods in Dynamics (MIT) 2.093 Computer Methods in Dynamics (MIT)

Description

Formulation of finite element methods for analysis of dynamic problems in solids, structures, fluid mechanics, and heat transfer. Computer calculation of matrices and numerical solution of equilibrium equations by direct integration and mode superposition. Effective eigensolution techniques for calculation of frequencies and mode shapes. Digital computer coding techniques and use of an existing general purpose finite element analysis program. Modeling of problems and interpretation of numerical results. Formulation of finite element methods for analysis of dynamic problems in solids, structures, fluid mechanics, and heat transfer. Computer calculation of matrices and numerical solution of equilibrium equations by direct integration and mode superposition. Effective eigensolution techniques for calculation of frequencies and mode shapes. Digital computer coding techniques and use of an existing general purpose finite element analysis program. Modeling of problems and interpretation of numerical results.Subjects

finite element methods | | finite element methods | | solids | | solids | | structures | | structures | | fluid mechanics | | fluid mechanics | | heat transfer | | heat transfer | | equilibrium equations | | equilibrium equations | | direct integration | | direct integration | | mode superposition | | mode superposition | | eigensolution techniques | | eigensolution techniques | | frequencies | | frequencies | | mode shapes. | mode shapes.License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.72 Elements of Mechanical Design (MIT) 2.72 Elements of Mechanical Design (MIT)

Description

This course provides an advanced treatment of machine elements such as bearings, springs, gears, cams, and mechanisms. Analysis of these elements includes extensive application of core engineering curriculum including solid mechanics and fluid dynamics. The course offers practice in skills needed for machine design such as estimation, drawing, and experimentation. Students work in small teams to design and build machines that address real-world challenges. This course provides an advanced treatment of machine elements such as bearings, springs, gears, cams, and mechanisms. Analysis of these elements includes extensive application of core engineering curriculum including solid mechanics and fluid dynamics. The course offers practice in skills needed for machine design such as estimation, drawing, and experimentation. Students work in small teams to design and build machines that address real-world challenges.Subjects

machine design | machine design | hardware | hardware | project | project | machine element | machine element | design process | design process | design layout | design layout | prototype | prototype | mechanism | mechanism | engineering | engineering | fabrication | fabricationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata12.479 Trace-Element Geochemistry (MIT) 12.479 Trace-Element Geochemistry (MIT)

Description

The emphasis of this course is to use Trace Element Geochemistry to understand the origin and evolution of igneous rocks. The approach is to discuss the parameters that control partitioning of trace elements between phases and to develop models for the partitioning of trace elements between phases in igneous systems, especially between minerals and melt. Subsequently, published papers that are examples of utilizing Trace Element Geochemistry are read and discussed. The emphasis of this course is to use Trace Element Geochemistry to understand the origin and evolution of igneous rocks. The approach is to discuss the parameters that control partitioning of trace elements between phases and to develop models for the partitioning of trace elements between phases in igneous systems, especially between minerals and melt. Subsequently, published papers that are examples of utilizing Trace Element Geochemistry are read and discussed.Subjects

trace element geochemistry | trace element geochemistry | igneous rocks | igneous rocks | mineral | mineral | melt | melt | partition coefficient | partition coefficient | simple melt-solid systems | simple melt-solid systemsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail. The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.007 Design and Manufacturing I (MIT) 2.007 Design and Manufacturing I (MIT)

Description

Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering. See this MIT News story for more background, a photo gallery, and videos about this course. Includes audio/video content: AV special element video. Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.From its beginnings in 1970, the 2.007 final project competition has grown into an Olympics of engineering. See this MIT News story for more background, a photo gallery, and videos about this course.Subjects

engineering design | engineering design | synthesis | synthesis | analysis | analysis | robustness | robustness | manufacturability | manufacturability | active learning | active learning | idea generation | idea generation | estimation | estimation | materials selection | materials selection | visual thinking | visual thinking | kinematics | kinematics | machine elements | machine elements | robotics | robotics | mechanical engineering | mechanical engineering | student work | student work | contest | contestLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata21M.303 Writing in Tonal Forms I (MIT) 21M.303 Writing in Tonal Forms I (MIT)

Description

Includes audio/video content: AV special element audio, AV special element video, AV special element audio. Written and analytic exercises based on 18th- and 19th-century small forms and harmonic practice found in music such as the chorale preludes of Bach; minuets and trios of Haydn, Mozart, and Beethoven; and the songs and character pieces of Schubert and Schumann. Musicianship laboratory is required. Includes audio/video content: AV special element audio, AV special element video, AV special element audio. Written and analytic exercises based on 18th- and 19th-century small forms and harmonic practice found in music such as the chorale preludes of Bach; minuets and trios of Haydn, Mozart, and Beethoven; and the songs and character pieces of Schubert and Schumann. Musicianship laboratory is required.Subjects

composition | composition | composing | composing | listening | listening | form | form | structure | structure | harmony | harmony | melody | melody | rhythm | rhythm | motif | motif | theme | theme | voicing | voicing | chord | chord | scale | scale | cadence | cadence | tonality | tonality | tonal music | tonal music | phrasing | phrasing | canon | canon | classical music | classical music | chamber music | chamber music | aesthetics | aesthetics | musical analysis | musical analysis | romantic music | romantic music | romantic poetry | romantic poetry | lieder | lieder | string quartet | string quartetLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata1.105 Solid Mechanics Laboratory (MIT) 1.105 Solid Mechanics Laboratory (MIT)

Description

This course introduces students to basic properties of structural materials and behavior of simple structural elements and systems through a series of experiments. Students learn experimental technique, data collection, reduction and analysis, and presentation of results. Students generally take this subject during the same semester as 1.050, Solid Mechanics. This course introduces students to basic properties of structural materials and behavior of simple structural elements and systems through a series of experiments. Students learn experimental technique, data collection, reduction and analysis, and presentation of results. Students generally take this subject during the same semester as 1.050, Solid Mechanics.Subjects

properties of structural materials | properties of structural materials | structural elements | structural elements | structural systems | structural systems | experimental technique | experimental technique | data collection | data collection | reduction | reduction | analysis | analysis | presentation | presentation | properties | properties | structural materials | structural materials | structural behavior | structural behavior | simple structural elements | simple structural elements | simple structural systems | simple structural systems | laboratory experiments | laboratory experiments | data reduction | data reduction | data analysis | data analysis | solid mechanics | solid mechanics | loading | loading | observation | observation | measurement | measurement | force | force | displacement | displacement | stiffness | stiffness | failure modes | failure modes | failure mechanisms | failure mechanisms | instrumentation | instrumentation | resolution | resolution | range | range | transducer response | transducer response | signal conditioning | signal conditioning | experimental design | experimental design | report writing | report writingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.72 Elements of Mechanical Design (MIT) 2.72 Elements of Mechanical Design (MIT)

Description

This is an advanced course on modeling, design, integration and best practices for use of machine elements such as bearings, springs, gears, cams and mechanisms. Modeling and analysis of these elements is based upon extensive application of physics, mathematics and core mechanical engineering principles (solid mechanics, fluid mechanics, manufacturing, estimation, computer simulation, etc.). These principles are reinforced via (1) hands-on laboratory experiences wherein students conduct experiments and disassemble machines and (2) a substantial design project wherein students model, design, fabricate and characterize a mechanical system that is relevant to a real world application. Students master the materials via problems sets that are directly related to, and coordinated with, the deliv This is an advanced course on modeling, design, integration and best practices for use of machine elements such as bearings, springs, gears, cams and mechanisms. Modeling and analysis of these elements is based upon extensive application of physics, mathematics and core mechanical engineering principles (solid mechanics, fluid mechanics, manufacturing, estimation, computer simulation, etc.). These principles are reinforced via (1) hands-on laboratory experiences wherein students conduct experiments and disassemble machines and (2) a substantial design project wherein students model, design, fabricate and characterize a mechanical system that is relevant to a real world application. Students master the materials via problems sets that are directly related to, and coordinated with, the delivSubjects

biology | biology | chemistry | chemistry | synthetic biology | synthetic biology | project | project | biotech | biotech | genetic engineering | genetic engineering | GMO | GMO | ethics | ethics | biomedical ethics | biomedical ethics | genetics | genetics | recombinant DNA | recombinant DNA | DNA | DNA | gene sequencing | gene sequencing | gene synthesis | gene synthesis | biohacking | biohacking | computational biology | computational biology | iGEM | iGEM | BioBrick | BioBrick | systems biology | systems biology | machine design | machine design | hardware | hardware | machine element | machine element | design process | design process | design layout | design layout | prototype | prototype | mechanism | mechanism | engineering | engineering | fabrication | fabrication | lathe | lathe | precision engineering | precision engineering | group project | group project | project management | project management | CAD | CAD | fatigue | fatigue | Gantt chart | Gantt chartLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata5.310 Laboratory Chemistry (MIT) 5.310 Laboratory Chemistry (MIT)

Description

Laboratory Chemistry (5.310) introduces experimental chemistry for students requiring a chemistry laboratory who are not majoring in chemistry. Students must have completed general chemistry (5.111) and have completed or be concurrently enrolled in the first semester of organic chemistry (5.12). The course covers principles and applications of chemical laboratory techniques, including preparation and analysis of chemical materials, measurement of pH, gas and liquid chromatography, visible-ultraviolet spectrophotometry, infrared spectroscopy, kinetics, data analysis, and elementary synthesis. NOTE: The Staff for this course would like to acknowledge that the experiments include contributions from past instructors, course textbooks, and others affiliated with course #5.310. Since the Laboratory Chemistry (5.310) introduces experimental chemistry for students requiring a chemistry laboratory who are not majoring in chemistry. Students must have completed general chemistry (5.111) and have completed or be concurrently enrolled in the first semester of organic chemistry (5.12). The course covers principles and applications of chemical laboratory techniques, including preparation and analysis of chemical materials, measurement of pH, gas and liquid chromatography, visible-ultraviolet spectrophotometry, infrared spectroscopy, kinetics, data analysis, and elementary synthesis. NOTE: The Staff for this course would like to acknowledge that the experiments include contributions from past instructors, course textbooks, and others affiliated with course #5.310. Since theSubjects

lab | lab | chemistry | chemistry | laboratory | laboratory | experiment | experiment | pH | pH | gas chromatography | gas chromatography | liquid chromatography | liquid chromatography | visible-ultraviolet spectrophotometry | visible-ultraviolet spectrophotometry | infrared spectroscopy | infrared spectroscopy | kinetics | kinetics | data analysis | data analysis | elementary synthesis | elementary synthesis | amino acid | amino acid | ferrocene | ferrocene | essential oil | essential oil | potentiometric titration | potentiometric titration | techniques | techniques | measurement | measurement | materials | materials | data | data | analysis | analysis | elementary | elementary | synthesis | synthesis | amino | amino | acid | acid | essential | essential | oil | oil | gas | gas | chromatography | chromatography | infrared | infrared | spectroscopy | spectroscopy | liquid | liquid | potentiometric | potentiometric | titration | titration | visible | visible | ultraviolet | ultraviolet | spectrophotometry | spectrophotometryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataDibujo Industrial II Dibujo Industrial II

Description

Asignatura obligatoria de primer curso perteneciente a los programas de estudios de Ingeniero Industrial e Ingeniero Químico. Son conceptos fundamentales a lo largo de todo el curso: Funcionamiento del conjunto o del mecanismo. En las pruebas evaluatorias se requiere que se entienda cómo funciona un conjunto o qué función cumplen determinadas piezas. Los temas de tolerancias geométricas y dimensionales también se ven reforzados aquí ya que se exige, por ejemplo, determinar si un ajuste es juego o aprieto en base al funcionamiento correcto del conjunto. El porqué de cada elemento y de la forma de este elemento, haciendo ver que una pieza aislada no tiene sentido si no se ve acoplada en su correspondiente conjunto, donde cada forma y dimensión depende de las demás piezas que est Asignatura obligatoria de primer curso perteneciente a los programas de estudios de Ingeniero Industrial e Ingeniero Químico. Son conceptos fundamentales a lo largo de todo el curso: Funcionamiento del conjunto o del mecanismo. En las pruebas evaluatorias se requiere que se entienda cómo funciona un conjunto o qué función cumplen determinadas piezas. Los temas de tolerancias geométricas y dimensionales también se ven reforzados aquí ya que se exige, por ejemplo, determinar si un ajuste es juego o aprieto en base al funcionamiento correcto del conjunto. El porqué de cada elemento y de la forma de este elemento, haciendo ver que una pieza aislada no tiene sentido si no se ve acoplada en su correspondiente conjunto, donde cada forma y dimensión depende de las demás piezas que estSubjects

Expresión Gráfica en la Ingeniería | Expresión Gráfica en la Ingeniería | Ingeniería Mecánica | Ingeniería Mecánica | engranajes | engranajes | elementos normalizados | elementos normalizados | tolerancias | tolerancias | ejes | ejes | Diseño | Diseño | rodamientos | rodamientos | Proyectos de Ingeniería | Proyectos de Ingeniería | fabricacion | fabricacion | Ingeniería de los Procesos de Fabricación | Ingeniería de los Procesos de Fabricación | croquis | croquis | chavetas | chavetas | Dibujo | Dibujo | CAD | CADLicense

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See all metadata12.479 Trace-Element Geochemistry (MIT) 12.479 Trace-Element Geochemistry (MIT)

Description

The emphasis of this course is to use Trace Element Geochemistry to understand the origin and evolution of igneous rocks. The approach is to discuss the parameters that control partitioning of trace elements between phases and to develop models for the partitioning of trace elements between phases in igneous systems, especially between minerals and melt. Subsequently, published papers that are examples of utilizing Trace Element Geochemistry are read and discussed. The emphasis of this course is to use Trace Element Geochemistry to understand the origin and evolution of igneous rocks. The approach is to discuss the parameters that control partitioning of trace elements between phases and to develop models for the partitioning of trace elements between phases in igneous systems, especially between minerals and melt. Subsequently, published papers that are examples of utilizing Trace Element Geochemistry are read and discussed.Subjects

trace element geochemistry | trace element geochemistry | igneous rocks | igneous rocks | mineral | mineral | melt | melt | partition coefficient | partition coefficient | simple melt-solid systems | simple melt-solid systemsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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