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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc. This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule | single variable calculus | single variable calculus | mathematical applications | mathematical applications | function | function | graphing | graphing | rates | rates | approximations | approximations | definite integration | definite integration | indefinite integration | indefinite integration | geometry | geometry | science | science | elementary functions | elementary functions | definite integrals | definite integrals

License

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18.01SC Single Variable Calculus (MIT) 18.01SC Single Variable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics. Includes audio/video content: AV lectures. This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Subjects

differentiation of functions | differentiation of functions | integration of functions | integration of functions | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite integration | definite integration | indefinite integration | indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'Hôpital's rule | l'Hôpital's rule

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.htm

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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This introductory calculus course covers differentiation and integration of functions of one variable, with applications. Includes audio/video content: AV lectures. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule

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.htm

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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

This introductory calculus course covers differentiation and integration of functions of one variable, with applications. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule

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.htm

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18.01 Single Variable Calculus (MIT)

Description

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc.

Subjects

differentiation and integration of functions of one variable | limits | continuity | differentiation rules | extremum problems | definite and indefinite integration | fundamental theorem of calculus | elementary | techniques of integration | approximation of definite integrals | improper integrals | l'H?pital's rule | single variable calculus | mathematical applications | function | graphing | rates | approximations | definite integration | indefinite integration | geometry | science | elementary functions | definite integrals

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 https://ocw.mit.edu/terms/index.htm

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18.01SC Single Variable Calculus (MIT)

Description

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Subjects

differentiation of functions | integration of functions | limits | continuity | differentiation rules | extremum problems | definite integration | indefinite integration | fundamental theorem of calculus | techniques of integration | approximation of definite integrals | improper integrals | pital's rule

License

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

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2.29 Numerical Marine Hydrodynamics (13.024) (MIT) 2.29 Numerical Marine Hydrodynamics (13.024) (MIT)

Description

Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects

License

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2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods. This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.

Subjects

numerical methods | numerical methods | interpolation | interpolation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | finite difference methods | finite difference methods | boundary integral equation panel methods | boundary integral equation panel methods | numerical lifting surface computations | numerical lifting surface computations | Fast Fourier Transforms | Fast Fourier Transforms | Numerical representation | Numerical representation | deterministic and random sea waves | deterministic and random sea waves | Integral boundary layer equations | Integral boundary layer equations | numerical solutions | numerical solutions

License

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13.024 Numerical Marine Hydrodynamics (MIT) 13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™ This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects | 2.29 | 2.29

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18.304 Undergraduate Seminar in Discrete Mathematics (MIT) 18.304 Undergraduate Seminar in Discrete Mathematics (MIT)

Description

This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computing

License

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18.01 Single Variable Calculus (MIT)

Description

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | limits | continuity | differentiation rules | extremum problems | definite and indefinite integration | fundamental theorem of calculus | elementary | techniques of integration | approximation of definite integrals | improper integrals | l'H?pital's rule

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 https://ocw.mit.edu/terms/index.htm

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18.01 Single Variable Calculus (MIT)

Description

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | limits | continuity | differentiation rules | extremum problems | definite and indefinite integration | fundamental theorem of calculus | elementary | techniques of integration | approximation of definite integrals | improper integrals | l'H?pital's rule

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 https://ocw.mit.edu/terms/index.htm

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THEMIS: Accounting for diversity in Polish migration in Europe: motivation and early integration

Description

Lucinda Platt presents her paper 'Accounting for diversity in Polish migration in Europe' co-authored by Renee Luthra & Justyna Salamonska in Parallel session VI(B) of the conference Examining Migration Dynamics: Networks and Beyond, 24-26 Sept 2013 Research on the decision to migrate overwhelmingly draws from neo-classical and revised economic models of international flows, in which individuals and their families choose migration strategies to maximize and diversify their incomes (Borjas, 1989)and reduce their exposure to financial risks (Taylor, 1999, Stark and Bloom, 1985). Yet these models do little to explain the large amount of remaining variation in the type and size of migration flows across receiving countries after the costs and benefits of migration are accounted for. We also

Subjects

THEMIS | migration | poland | integration | THEMIS | migration | poland | integration | 2013-09-26

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Integration of Brits in Turkey and Turks in Britain

Description

Ibrahim Sirkeci explores integration patterns of English-speaking movers in Turkey and those of Turkish-speaking movers in Britain International migration studies have largely focused on movers from the developing countries, or the South. Nevertheless, about one third of the global human mobility happens within the North and from North to South. Hence there is a need for reconsidering our understanding of global human mobility. Despite the hierarchy in the language used in describing these two categories of movers, there are similarities in causes, mechanisms and lived experiences. In this study, integration patterns of English-speaking movers in Turkey and those of Turkish-speaking movers in Britain have been contrasted. Particular attention has been paid to the perceived discrimination a Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

Subjects

mobility | integration | Turkey | UK | mobility | integration | Turkey | UK | 2017-05-03

License

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2.008 Design and Manufacturing II (MIT) 2.008 Design and Manufacturing II (MIT)

Description

This course introduces you to modern manufacturing with four areas of emphasis: manufacturing processes, equipment/control, systems, and design for manufacturing. The course exposes you to integration of engineering and management disciplines for determining manufacturing rate, cost, quality and flexibility. Topics include process physics, equipment design and automation/control, quality, design for manufacturing, industrial management, and systems design and operation. Labs are integral parts of the course, and expose you to various manufacturing disciplines and practices. This course introduces you to modern manufacturing with four areas of emphasis: manufacturing processes, equipment/control, systems, and design for manufacturing. The course exposes you to integration of engineering and management disciplines for determining manufacturing rate, cost, quality and flexibility. Topics include process physics, equipment design and automation/control, quality, design for manufacturing, industrial management, and systems design and operation. Labs are integral parts of the course, and expose you to various manufacturing disciplines and practices.

Subjects

modern manufacturing | modern manufacturing | manufacturing processes | manufacturing processes | equipment/control | equipment/control | systems | systems | design for manufacturing | design for manufacturing | integration of engineering and management disciplines | integration of engineering and management disciplines | manufacturing rate | manufacturing rate | cost | cost | quality | quality | flexibility | flexibility | process physics | process physics | equipment design | equipment design | automation/control | automation/control | industrial management | industrial management | systems design and operation | systems design and operation

License

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16.225 Computational Mechanics of Materials (MIT) 16.225 Computational Mechanics of Materials (MIT)

Description

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is 16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is

Subjects

Computational Mechanics | Computational Mechanics | Computation | Computation | Mechanics | Mechanics | Materials | Materials | Numerical Methods | Numerical Methods | Numerical | Numerical | Nonlinear Continuum Response | Nonlinear Continuum Response | Continuum | Continuum | Deformation | Deformation | Elasticity | Elasticity | Inelasticity | Inelasticity | Dynamics | Dynamics | Variational Formulation | Variational Formulation | Variational Constitutive Updates | Variational Constitutive Updates | Finite Element | Finite Element | Discretization | Discretization | Error Estimation | Error Estimation | Constrained Problems | Constrained Problems | Time Integration | Time Integration | Convergence Analysis | Convergence Analysis | Programming | Programming | Continuum Response | Continuum Response | Computational | Computational | state-of-the-art | state-of-the-art | methods | methods | modeling | modeling | simulation | simulation | mechanical | mechanical | response | response | engineering | engineering | aerospace | aerospace | civil | civil | material | material | science | science | biomechanics | biomechanics | behavior | behavior | finite | finite | deformation | deformation | elasticity | elasticity | inelasticity | inelasticity | contact | contact | friction | friction | coupled | coupled | numerical | numerical | formulation | formulation | algorithms | algorithms | Variational | Variational | constitutive | constitutive | updates | updates | element | element | discretization | discretization | mesh | mesh | generation | generation | error | error | estimation | estimation | constrained | constrained | problems | problems | time | time | convergence | convergence | analysis | analysis | parallel | parallel | computer | computer | implementation | implementation | programming | programming | assembly | assembly | equation-solving | equation-solving | formulating | formulating | implementing | implementing | complex | complex | approximations | approximations | equations | equations | motion | motion | dynamic | dynamic | deformations | deformations | continua | continua | plasticity | plasticity | rate-dependency | rate-dependency | integration | integration

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2.75 Precision Machine Design (MIT) 2.75 Precision Machine Design (MIT)

Description

Intensive coverage of precision engineering theory, heuristics, and applications pertaining to the design of systems ranging from consumer products to machine tools. Topics covered include: economics, project management, and design philosophy; principles of accuracy, repeatability, and resolution; error budgeting; sensors; sensor mounting; systems design; bearings; actuators and transmissions; system integration driven by functional requirements, and operating physics. Emphasis on developing creative designs, which are optimized by analytical techniques applied via spreadsheets. This is a projects course with lectures consisting of design teams presenting their work and the class helping to develop solutions; thereby everyone learning from everyone's projects. Intensive coverage of precision engineering theory, heuristics, and applications pertaining to the design of systems ranging from consumer products to machine tools. Topics covered include: economics, project management, and design philosophy; principles of accuracy, repeatability, and resolution; error budgeting; sensors; sensor mounting; systems design; bearings; actuators and transmissions; system integration driven by functional requirements, and operating physics. Emphasis on developing creative designs, which are optimized by analytical techniques applied via spreadsheets. This is a projects course with lectures consisting of design teams presenting their work and the class helping to develop solutions; thereby everyone learning from everyone's projects.

Subjects

precision engineering theory | precision engineering theory | heuristics | heuristics | systems design | systems design | economics | economics | project management | project management | design philosophy | design philosophy | error budgeting | error budgeting | bearings | bearings | actuators | actuators | transmissions | transmissions | system integration | system integration | functional requirements | functional requirements | operating physics | operating physics

License

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18.100C Real Analysis (MIT) 18.100C Real Analysis (MIT)

Description

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.   The three options for 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginni This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.   The three options for 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginni

Subjects

mathematical analysis | mathematical analysis | Archimedean principle | Archimedean principle | decimal expansion | decimal expansion | Cauchy-Schwarz | Cauchy-Schwarz | metric spaces | metric spaces | open subsets | open subsets | Euclidean space | Euclidean space | convergent sequences | convergent sequences | subsequential limits | subsequential limits | inverse functions | inverse functions | Stone-Weierstrass theorem | Stone-Weierstrass theorem | theory of integration | theory of integration | Riemann-Stjeltjes integral | Riemann-Stjeltjes integral | Fourier series | Fourier series

License

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18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integration

License

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15.912 Technology Strategy (MIT) 15.912 Technology Strategy (MIT)

Description

This course provides a series of strategic frameworks for managing high-technology businesses. The emphasis throughout is on the development and application of conceptual models which clarify the interactions between competition, patterns of technological and market change, and the structure and development of internal firm capabilities. The course covers much of the same conceptual material as 15.351 and 15.393, and students should not take 15.912 if they have taken (or intend to take) either alternative.This is not a course in how to manage product or process development. The main focus is on the acquisition of a set of powerful analytical tools which are critical for the development of a technology strategy as an integral part of business strategy. These tools can prov This course provides a series of strategic frameworks for managing high-technology businesses. The emphasis throughout is on the development and application of conceptual models which clarify the interactions between competition, patterns of technological and market change, and the structure and development of internal firm capabilities. The course covers much of the same conceptual material as 15.351 and 15.393, and students should not take 15.912 if they have taken (or intend to take) either alternative.This is not a course in how to manage product or process development. The main focus is on the acquisition of a set of powerful analytical tools which are critical for the development of a technology strategy as an integral part of business strategy. These tools can prov

Subjects

disruptive technology | disruptive technology | strategy | strategy | models | models | analysis | analysis | competition | competition | change | change | organizational competence | organizational competence | vertical integration | vertical integration

License

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13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | interpolation | differentiation | integration | systems of linear equations | differential equations | numerical integration | partial differential | boundary integral equation panel methods | deterministic and random sea waves | Fast Fourier Transforms | finite difference methods | Integral boundary layer equations | numerical lifting surface computations | Numerical representation | numerical solutions | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | calculus | complex numbers | root finding | curve fitting | numerical differentiation | numerical errors | panel methods | oscillating rigid objects | 2.29

License

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15.070J Advanced Stochastic Processes (MIT) 15.070J Advanced Stochastic Processes (MIT)

Description

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models. This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Subjects

analysis | analysis | modeling | modeling | stochastic processes | stochastic processes | theoretic probability | theoretic probability | martingales | martingales | filtration | filtration | stopping theorems | stopping theorems | large deviations theory | large deviations theory | Brownian motion | Brownian motion | reflected Brownian motion | reflected Brownian motion | stochastic integration | stochastic integration | Ito calculus | Ito calculus | functional limit theorems | functional limit theorems | applications | applications | finance theory | finance theory | insurance | insurance | queueing | queueing | inventory models | inventory models

License

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14.54 International Trade (MIT) 14.54 International Trade (MIT)

Description

This course is an introduction to the theory of international trade and finance with applications to current policy issues. In this course we will cover the basic tools to understand what determines the flow of goods across countries, i.e. international trade, and what determines the flow of savings and investments from one country to another, i.e. international finance. We will also cover applications to a number of topics of current interest, including the debate on globalization, free trade agreements, the U.S. current account deficit, the medium run prospects for exchange rates, European integration, and the debate on global financial architecture following the financial crises in East Asia and Argentina. This course is an introduction to the theory of international trade and finance with applications to current policy issues. In this course we will cover the basic tools to understand what determines the flow of goods across countries, i.e. international trade, and what determines the flow of savings and investments from one country to another, i.e. international finance. We will also cover applications to a number of topics of current interest, including the debate on globalization, free trade agreements, the U.S. current account deficit, the medium run prospects for exchange rates, European integration, and the debate on global financial architecture following the financial crises in East Asia and Argentina.

Subjects

theory of international trade | theory of international trade | finance | finance | policy | policy | flow of goods | flow of goods | flow of savings and investments | flow of savings and investments | globalization | globalization | free trade agreements | free trade agreements | the US current account deficit | the US current account deficit | exchange rates | exchange rates | European integration | European integration | global financial architecture | global financial architecture | financial crises | financial crises | East Asia | East Asia | Argentina | Argentina

License

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HST.921 Information Technology in the Health Care System of the Future (MIT) HST.921 Information Technology in the Health Care System of the Future (MIT)

Description

The healthcare system in the US has been in the midst of a rapid transition in response to changing trends and patterns of care. The growing emphasis on evidence-based medical practice, continuous quality improvement, clinical and cost-effectiveness, and risk management have led to a sea change in medical practice that has been stressful for clinicians, patients, and administrators. As care becomes more tightly managed, it becomes a challenge for clinicians, administrators, and patients to balance time, money, resources, and clinical outcomes. Can emerging technologies help solve these complex problems? How has the demise of the dot.com industry effected these trends and slowed the proliferation of potential solutions?This innovative, trans-faculty course will teach the student how informa The healthcare system in the US has been in the midst of a rapid transition in response to changing trends and patterns of care. The growing emphasis on evidence-based medical practice, continuous quality improvement, clinical and cost-effectiveness, and risk management have led to a sea change in medical practice that has been stressful for clinicians, patients, and administrators. As care becomes more tightly managed, it becomes a challenge for clinicians, administrators, and patients to balance time, money, resources, and clinical outcomes. Can emerging technologies help solve these complex problems? How has the demise of the dot.com industry effected these trends and slowed the proliferation of potential solutions?This innovative, trans-faculty course will teach the student how informa

Subjects

information technology | information technology | health care system | health care system | economy of scale | economy of scale | technical efficiency | technical efficiency | patient education | patient education | self-care | self-care | network integration | network integration | decision support tool | decision support tool | internet | internet | web | web | disease managment | disease managment | health economics | health economics | clinical effectiveness | clinical effectiveness | trials design | trials design | software | software

License

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