احتمال و محاسبات عددی می شود و سپس مباحثی نظیر معادلات دیفرانسیل، لاپلاس، سری فوریه، تبدیل فوریه
گسسته و … را پوشش می دهد. بخش اول فیلم های آموزشی کلاس های درس دانشگاه MIT شامل ۳۲
قسمت می شود که عبارتند از:
Lecture 1: Positive definite matrices K = A’CA
Lecture 2: One-dimensional applications: A = difference matrix
Lecture 3: Network applications: A = incidence matrix
Lecture 4: Applications to linear estimation: least squares
Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu” + Ku = F(t
Lecture 6: Underlying theory: applied linear algebra
Lecture 7: Discrete vs. continuous: differences and derivatives
Lecture 8: Applications to boundary value problems: Laplace equation
Lecture 9: Solutions of Laplace equation: complex variables
Lecture 10 : Delta function and Green’s function
Lecture 11: Initial value problems: wave equation and heat equation
Lecture 12: Solutions of initial value problems: eigenfunctions
Lecture 13: Numerical linear algebra: orthogonalization and A = QR
Lecture 14: Numerical linear algebra: SVD and applications
Lecture 15: Numerical methods in estimation: recursive least squares and covariance matrix
Lecture 16: Dynamic estimation: Kalman filter and square root filter
Lecture 17: Finite difference methods: equilibrium problems
Lecture 18: Finite difference methods: stability and convergence
Lecture 19: Optimization and minimum principles: Euler equation
Lecture 20: Finite element method: equilibrium equations
Lecture 21: Spectral method: dynamic equations
Lecture 22: Fourier expansions and convolution
Lecture 23: Fast fourier transform and circulant matrices
Lecture 24: Discrete filters: lowpass and highpass
Lecture 25: Filters in the time and frequency domain
Lecture 26: Filter banks and perfect reconstruction
Lecture 27: Multiresolution, wavelet transform and scaling function
Lecture 28: Splines and orthogonal wavelets: Daubechies construction
Lecture 29: Applications in signal and image processing: compression
Lecture 30: Network flows and combinatorics: max flow = min cut
Lecture 31: Simplex method in linear programming
Lecture 32: Nonlinear optimization: algorithms and theory
لازم به ذکر است هر بخش مشتمل بر ۵ قسمت از این ویدئوی آموزشی می باشد . شما می توانید هر بخش را جداگانه بدون نیاز به سایر قسمت ها دانلود نمایید . فایل های فشرده به هم مربوط نیستند و برای خارج کردن از حالت فشرده نیاز به سایر بخش ها نمی باشد .لینک های دانلود بروز رسانی شدند .Lecture 2: One-dimensional applications: A = difference matrix
Lecture 3: Network applications: A = incidence matrix
Lecture 4: Applications to linear estimation: least squares
Lecture 5: Applications to dynamics: eigenvalues of K, solution of Mu” + Ku = F(t
Lecture 6: Underlying theory: applied linear algebra
Lecture 7: Discrete vs. continuous: differences and derivatives
Lecture 8: Applications to boundary value problems: Laplace equation
Lecture 9: Solutions of Laplace equation: complex variables
Lecture 10 : Delta function and Green’s function
Lecture 11: Initial value problems: wave equation and heat equation
Lecture 12: Solutions of initial value problems: eigenfunctions
Lecture 13: Numerical linear algebra: orthogonalization and A = QR
Lecture 14: Numerical linear algebra: SVD and applications
Lecture 15: Numerical methods in estimation: recursive least squares and covariance matrix
Lecture 16: Dynamic estimation: Kalman filter and square root filter
Lecture 17: Finite difference methods: equilibrium problems
Lecture 18: Finite difference methods: stability and convergence
Lecture 19: Optimization and minimum principles: Euler equation
Lecture 20: Finite element method: equilibrium equations
Lecture 21: Spectral method: dynamic equations
Lecture 22: Fourier expansions and convolution
Lecture 23: Fast fourier transform and circulant matrices
Lecture 24: Discrete filters: lowpass and highpass
Lecture 25: Filters in the time and frequency domain
Lecture 26: Filter banks and perfect reconstruction
Lecture 27: Multiresolution, wavelet transform and scaling function
Lecture 28: Splines and orthogonal wavelets: Daubechies construction
Lecture 29: Applications in signal and image processing: compression
Lecture 30: Network flows and combinatorics: max flow = min cut
Lecture 31: Simplex method in linear programming
Lecture 32: Nonlinear optimization: algorithms and theory
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