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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams | constant coefficients | constant coefficients | complex numbers | complex numbers | exponentials | exponentials | eigenvalues | eigenvalues | eigenvectors | eigenvectors

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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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams | constant coefficients | complex numbers | exponentials | eigenvalues | eigenvectors

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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Mathematical Methods II Mathematical Methods II

Description

This course consists of a introduction to linear algebra. This course consists of a introduction to linear algebra.

Subjects

Bachelor in Statistics and Business | Bachelor in Statistics and Business | Algebra | Algebra | Prerequisites | Prerequisites | Systems of linear equations | Systems of linear equations | Eigenvalues and eigenvectors | Eigenvalues and eigenvectors | General information | General information | Orthogonality and least-square problems | Orthogonality and least-square problems | Singular value decomposition | Singular value decomposition | ística y Empresa | ística y Empresa | Real vector spaces | Real vector spaces | Matrices and determinants | Matrices and determinants | Diagonalization | Diagonalization | 2012 | 2012

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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3.016 Mathematics for Materials Scientists and Engineers (MIT) 3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site. The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | energetics | materials structure and symmetry: applied fields | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | mechanics and physics of solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalues | eigenvalues | eigenvectors | eigenvectors | quadratic forms | quadratic forms | tensor operations | tensor operations | symmetry operations | symmetry operations | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walks | random walks | mathematical technicques | mathematical technicques | materials science | materials science | materials engineering | materials engineering | materials structure | materials structure | symmetry | symmetry | applied fields | applied fields | materials response | materials response | solids mechanics | solids mechanics | solids physics | solids physics | soft materials | soft materials | multi-variable calculus | multi-variable calculus | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | applied mathematics | applied mathematics | mathematical techniques | mathematical techniques

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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18.03SC Differential Equations (MIT) 18.03SC Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

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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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

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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RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT) RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT)

Description

Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos w Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos w

Subjects

differential equations | differential equations | ODE | MATLAB | ODE | MATLAB | first order equations | first order equations | second order equations | second order equations | matrices | matrices | Laplace transform | Laplace transform | linear algebra | linear algebra | eigenvalues | eigenvalues | eigenvectors | eigenvectors | Fourier series | Fourier series | Runge-Kutta | Runge-Kutta | Tumbling box | Tumbling box | predator-prey equations | predator-prey equations | Lorenz Attractor | Lorenz Attractor

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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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods Matrix systems | Laplace transform methods Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams

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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18.03SC Differential Equations (MIT)

Description

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

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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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

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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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

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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Linear Algebra II

Description

Linear Algebra is both rich in theory and full of interesting applications; in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 212)

Subjects

sets | functions | fundamental theorem | matrices | row operations | factorization | linear programming | spectral theory | eigenvalues | eigenvectors | vector spaces | markov chains | inner product spaces | self-adjoint operators | numerical methods | differential equations | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT)

Description

Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos were produced by The MathWorks® and are

Subjects

differential equations | ODE | MATLAB | first order equations | second order equations | matrices | Laplace transform | linear algebra | eigenvalues | eigenvectors | Fourier series | Runge-Kutta | Tumbling box | predator-prey equations | Lorenz Attractor

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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3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | linear algebra | orthonormal basis | eigenvalues | eigenvectors | quadratic forms | tensor operations | symmetry operations | calculus | complex analysis | differential equations | theory of distributions | fourier analysis | random walks | mathematical technicques | materials science | materials engineering | materials structure | symmetry | applied fields | materials response | solids mechanics | solids physics | soft materials | multi-variable calculus | ordinary differential equations | partial differential equations | applied mathematics | mathematical techniques

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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18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.

Subjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams

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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