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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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18.03SC 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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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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18.03 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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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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Logarithms - Manipulation - Practice Test

Description

Ten question test on manipulating logs.

Subjects

graphing | exponential growth | exponential decay | maths | medics | x axis | y axis | Biological Sciences | Medicine and Dentistry | Biological sciences | dentistry | C000 | A000

License

Attribution-Share Alike 2.0 UK: England & Wales Attribution-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-sa/2.0/uk/ http://creativecommons.org/licenses/by-sa/2.0/uk/

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6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT) 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT)

Description

Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions). Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Subjects

NP-completeness | NP-completeness | 3SAT | 3SAT | 3-partition | 3-partition | Hamiltonicity | Hamiltonicity | PSPACE | PSPACE | EXPTIME | EXPTIME | EXPSPACE | EXPSPACE | games | games | puzzles | puzzles | computation | computation | Tetris | Tetris | Nintendo | Nintendo | Super Mario Bros. | Super Mario Bros. | The Legend of Zelda | The Legend of Zelda | Metroid | Metroid | Pokémon | Pokémon | constraint logic | constraint logic | Sudoku | Sudoku | Nikoli | Nikoli | Chess | Chess | Go | Go | Othello | Othello | board games | board games | inapproximability | inapproximability | PCP theorem | PCP theorem | OPT-preserving reduction | OPT-preserving reduction | APX-hardness | APX-hardness | vertex cover | vertex cover | Set-cover hardness | Set-cover hardness | Group Steiner tree | Group Steiner tree | k-dense subgraph | k-dense subgraph | label cover | label cover | Unique Games Conjecture | Unique Games Conjecture | independent set | independent set | fixed-parameter intractability | fixed-parameter intractability | parameter-preserving reduction | parameter-preserving reduction | W hierarchy | W hierarchy | clique-hardness | clique-hardness | 3SUM-hardness | 3SUM-hardness | exponential time hypothesis | exponential time hypothesis | counting problems | counting problems | solution uniqueness | solution uniqueness | game theory | game theory | Existential theory of the reals | Existential theory of the reals | undecidability | undecidability

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

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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18.755 Introduction to Lie Groups (MIT) 18.755 Introduction to Lie Groups (MIT)

Description

This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces. This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

Subjects

Manifolds | Manifolds | Lie groups | Lie groups | exponential mapping | exponential mapping | Lie algebras | Lie algebras | Homogeneous spaces | Homogeneous spaces | transformation groups | transformation groups | Adjoint representation | Adjoint representation | Covering groups | Covering groups | Automorphism groups | Automorphism groups | Invariant differential forms | Invariant differential forms | cohomology of Lie groups | cohomology of Lie groups | homogeneous spaces. | homogeneous spaces. | Lie Groups | Lie Groups | Exponential Mapping | Exponential Mapping | Lie Algebras | Lie Algebras | Homogeneous Spaces | Homogeneous Spaces | Transformation Groups | Transformation Groups | Covering Groups | Covering Groups | Automorphism Groups | Automorphism Groups | Invariant Differential Forms | Invariant Differential Forms | Cohomology of Lie Groups | Cohomology of Lie Groups | Homogeneous Spaces. | Homogeneous Spaces.

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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18.440 Probability and Random Variables (MIT) 18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | Probability spaces | random variables | random variables | distribution functions | distribution functions | Binomial | Binomial | geometric | geometric | hypergeometric | hypergeometric | Poisson distributions | Poisson distributions | Uniform | Uniform | exponential | exponential | normal | normal | gamma and beta distributions | gamma and beta distributions | Conditional probability | Conditional probability | Bayes theorem | Bayes theorem | joint distributions | joint distributions | Chebyshev inequality | Chebyshev inequality | law of large numbers | law of large numbers | And central limit theorem | And central limit theorem

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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18.440 Probability and Random Variables (MIT) 18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | Probability spaces | random variables | random variables | distribution functions | distribution functions | Binomial | Binomial | geometric | geometric | hypergeometric | hypergeometric | Poisson distributions | Poisson distributions | Uniform | Uniform | exponential | exponential | normal | normal | gamma and beta distributions | gamma and beta distributions | Conditional probability | Conditional probability | Bayes theorem | Bayes theorem | joint distributions | joint distributions | Chebyshev inequality | Chebyshev inequality | law of large numbers | law of large numbers | and central limit theorem | and central limit theorem

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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2.087 Engineering Math: Differential Equations and Linear Algebra (MIT) 2.087 Engineering Math: Differential Equations and Linear Algebra (MIT)

Description

Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

Subjects

differential equations | differential equations | linear algebra | linear algebra | linear differential equations | linear differential equations | ordinary | ordinary | partial | partial | vector space | vector space | first order | first order | second order | second order | Heaviside | Heaviside | delta | delta | Dirac | Dirac | exponential | exponential | sinusoid | sinusoid | real | real | complex | complex | forced oscillations | forced oscillations | Laplace transform | Laplace transform | graph | graph | nonlinear | nonlinear | source | source | sink | sink | saddle | saddle | spiral | spiral | Euler | Euler | linearization | linearization | Guassian | Guassian | matrix | matrix | mechanical engineer | mechanical engineer | eigenvector | eigenvector | eigenvalue | eigenvalue | exponentiation | exponentiation | least squares | least squares

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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18.440 Probability and Random Variables (MIT) 18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | Probability spaces | random variables | random variables | distribution functions | distribution functions | Binomial | Binomial | geometric | geometric | hypergeometric | hypergeometric | Poisson distributions | Poisson distributions | Uniform | Uniform | exponential | exponential | normal | normal | gamma and beta distributions | gamma and beta distributions | Conditional probability | Conditional probability | Bayes theorem | Bayes theorem | joint distributions | joint distributions | Chebyshev inequality | Chebyshev inequality | law of large numbers | law of large numbers | central limit theorem | central limit theorem

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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MAS.160 Signals, Systems, and Information for Media Technology (MIT) MAS.160 Signals, Systems, and Information for Media Technology (MIT)

Description

Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ. Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ.

Subjects

Basic math concepts | Basic math concepts | Notation | Notation | Vocabulary | Vocabulary | Representation of systems | Representation of systems | Complex exponentials | Complex exponentials | Spectrum plots | Spectrum plots | AM | AM | Fourier series | Fourier series | FM | FM | Definition of orthogonality | Definition of orthogonality | Walsh functions and other basis sets | Walsh functions and other basis sets | Sampling theorem | Sampling theorem | Aliasing | Aliasing | Reconstruction | Reconstruction | Signal processing | Signal processing

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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18.440 Probability and Random Variables (MIT) 18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | Probability spaces | random variables | random variables | distribution functions | distribution functions | Binomial | Binomial | geometric | geometric | hypergeometric | hypergeometric | Poisson distributions | Poisson distributions | Uniform | Uniform | exponential | exponential | normal | normal | gamma and beta distributions | gamma and beta distributions | Conditional probability | Conditional probability | Bayes theorem | Bayes theorem | joint distributions | joint distributions | Chebyshev inequality | Chebyshev inequality | law of large numbers | law of large numbers | and central limit theorem. | and central limit theorem.

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.

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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18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | random variables | distribution functions | Binomial | geometric | hypergeometric | Poisson distributions | Uniform | exponential | normal | gamma and beta distributions | Conditional probability | Bayes theorem | joint distributions | Chebyshev inequality | law of large numbers | central limit theorem

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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Using Logs and Exponential Equations

Description

A pdf document that describes how to use logs and exponential equations.

Subjects

use logs | exponential equations | multiply | divide | maths | medics | logs | Biological Sciences | Medicine and Dentistry | Biological sciences | dentistry | C000 | A000

License

Attribution-Share Alike 2.0 UK: England & Wales Attribution-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-sa/2.0/uk/ http://creativecommons.org/licenses/by-sa/2.0/uk/

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MAS.160 Signals, Systems, and Information for Media Technology (MIT)

Description

Fundamentals of signals and information theory with emphasis on modeling audio/visual messages and physiologically-derived signals, and the human source or recipient. Linear systems, difference equations, Z-transforms, sampling and sampling rate conversion, convolution, filtering, modulation, Fourier analysis, entropy, noise, Shannon's fundamental theorems. Additional topics may include data compression, filter design, and feature detection. Meets with graduate subjects MAS.510, MAS.511 but assignments differ.

Subjects

Basic math concepts | Notation | Vocabulary | Representation of systems | Complex exponentials | Spectrum plots | AM | Fourier series | FM | Definition of orthogonality | Walsh functions and other basis sets | Sampling theorem | Aliasing | Reconstruction | Signal processing

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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18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | random variables | distribution functions | Binomial | geometric | hypergeometric | Poisson distributions | Uniform | exponential | normal | gamma and beta distributions | Conditional probability | Bayes theorem | joint distributions | Chebyshev inequality | law of large numbers | And central limit theorem

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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DG4H 33 Maths for Engineering

Description

skills to carry out operations involving complex numbers.

Subjects

Argand diagrams | logarithmic functions | DG4H 33 | DG4H33 | indices | scientific notation | exponential functions | simultaneous equations | complex numbers | trigonometric functions | quadratic equations | RB: Mathematics | R: Sciences and Mathematics | SCQF Level 7

License

Licensed to colleges in Scotland only Licensed to colleges in Scotland only http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 Scottish Qualifications Authority Scottish Qualifications Authority

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18.440 Probability and Random Variables (MIT)

Description

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Subjects

Probability spaces | random variables | distribution functions | Binomial | geometric | hypergeometric | Poisson distributions | Uniform | exponential | normal | gamma and beta distributions | Conditional probability | Bayes theorem | joint distributions | Chebyshev inequality | law of large numbers | and central limit theorem

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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6.0002 Introduction to Computational Thinking and Data Science (MIT)

Description

6.0002 is the continuation of 6.0001 Introduction to Computer Science and Programming in Python and is intended for students with little or no programming experience. It aims to provide students with an understanding of the role computation can play in solving problems and to help students, regardless of their major, feel justifiably confident of their ability to write small programs that allow them to accomplish useful goals. The class uses the Python 3.5 programming language.

Subjects

Python 3.5 | Python | machine learning | knapsack problem | greedy algorithm | optimization | weights | models | computational thinking | data science | dynamic programming | recursion | exponential time | stochastic | random | probability | independent variables | dependent variables | monte carlo simulation | simulation | population sampling | law of large numbers | variance | confidence interval | empirical rule | standard deviation | central limit theorem | bias | error distribution | sampling | error bars | numpy | scipy | matplotlib | pylab | python | plotting | graphing | supervised learning | computer modelling | signal-to-noise | feature vectors | classification model | regression model | classification | classifier | nearest neighbors | feature scaling | decision trees | entropy | training data | clustering | cluster analysis | unsupervised learning | objective function | dendogram | statistical fallacy | systematic errors | correlation and causation | misleading statistics | GIGO | axis truncating | extrapolation | data enhancement | Texas Sharpshooter Fallacy

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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