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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations | linear algebra | linear algebra | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks

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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13.002J Introduction to Numeric Analysis for Engineering (MIT) 13.002J Introduction to Numeric Analysis for Engineering (MIT)

Description

An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

digital computing | digital computing | algorithm accuracy | algorithm accuracy | error propagation | error propagation | linear equations | linear equations | iterative techniques | iterative techniques | roots of equations | roots of equations | systems of equations | systems of equations | numerical interpolation | numerical interpolation | differentiation | differentiation | integration | integration | finite-difference solutions | finite-difference solutions | differential equations | differential equations | 10.002J | 10.002J | 13.002 | 13.002 | 10.002 | 10.002

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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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc. Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations

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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18.06SC Linear Algebra (MIT) 18.06SC Linear Algebra (MIT)

Description

Includes audio/video content: AV lectures. This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra. Includes audio/video content: AV lectures. This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Subjects

matrix theory | matrix theory | linear algebra | linear algebra | systems of equations | systems of equations | vector spaces | vector spaces | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | positive definite matrices | positive definite matrices | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks | Fourier transforms | Fourier transforms | Markov processes | Markov processes

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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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

Includes audio/video content: AV special element video, AV lectures. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Includes audio/video content: AV special element video, AV lectures. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | matrix theory | linear algebra | linear algebra | systems of equations | systems of equations | vector spaces | vector spaces | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | positive definite matrices | positive definite matrices | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks | Fourier transforms | Fourier transforms | Markov processes | Markov processes

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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2.993J Introduction to Numerical Analysis for Engineering (13.002J) (MIT) 2.993J Introduction to Numerical Analysis for Engineering (13.002J) (MIT)

Description

This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering

Subjects

digital computing | digital computing | algorithm accuracy | algorithm accuracy | error propagation | error propagation | linear equations | linear equations | iterative techniques | iterative techniques | roots of equations | roots of equations | systems of equations | systems of equations | numerical interpolation | numerical interpolation | differentiation | differentiation | integration | integration | finite-difference solutions | finite-difference solutions | differential equations | differential equations | convergence analysis | convergence analysis

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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18.335J Introduction to Numerical Methods (MIT) 18.335J Introduction to Numerical Methods (MIT)

Description

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems. The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.

Subjects

linear algebra | linear algebra | ordinary differential equations | ordinary differential equations | linear systems of equations | linear systems of equations | least square problems | least square problems | eigenvalue problems | eigenvalue problems | singular value problems | singular value problems

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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2.993J Introduction to Numerical Analysis for Engineering (13.002J) (MIT)

Description

This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering

Subjects

digital computing | algorithm accuracy | error propagation | linear equations | iterative techniques | roots of equations | systems of equations | numerical interpolation | differentiation | integration | finite-difference solutions | differential equations | convergence analysis

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Linear algebra | Algebra | Universal | Mathematical analysis | Calculus of operations | Line geometry | Topology | matrix theory | systems of equations | vector spaces | systems determinants | eigen values | positive definite matrices | Markov processes | Fourier transforms | differential equations | linear algebra | determinants | eigenvalues | similarity | least-squares approximations | stability of differential equations | networks

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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13.002J Introduction to Numeric Analysis for Engineering (MIT)

Description

An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

digital computing | algorithm accuracy | error propagation | linear equations | iterative techniques | roots of equations | systems of equations | numerical interpolation | differentiation | integration | finite-difference solutions | differential equations | 10.002J | 13.002 | 10.002

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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18.06 Linear Algebra (MIT)

Description

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Generalized spaces | Linear algebra | Algebra | Universal | Mathematical analysis | Calculus of operations | Line geometry | Topology | matrix theory | systems of equations | vector spaces | systems determinants | eigen values | positive definite matrices | Markov processes | Fourier transforms | differential equations

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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2.993J Introduction to Numerical Analysis for Engineering (13.002J) (MIT)

Description

This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering

Subjects

digital computing | algorithm accuracy | error propagation | linear equations | iterative techniques | roots of equations | systems of equations | numerical interpolation | differentiation | integration | finite-difference solutions | differential equations | convergence analysis

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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18.06SC Linear Algebra (MIT)

Description

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

matrix theory | linear algebra | systems of equations | vector spaces | determinants | eigenvalues | similarity | positive definite matrices | least-squares approximations | stability of differential equations | networks | Fourier transforms | Markov processes

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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18.335J Introduction to Numerical Methods (MIT)

Description

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.

Subjects

linear algebra | ordinary differential equations | linear systems of equations | least square problems | eigenvalue problems | singular value problems

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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