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home > course - Mathematical Methods for Engineers I- MIT course (Fall 2005)


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Mathematical Methods for Engineers I- MIT course (Fall 2005)

Basic Information

level: Intermediate
created on: February 13, 2008
tags: education ,  math ,  mathematics ,  engineering ,  linear algebra ,  calculus ,  differential equations ,  laplace's equation ,  fourier series


Course Description

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.



Course Videos
Math for Engineers, 01. Positive Definite Matrices K = A
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Math for Engineers, 01. Positive Definite Matrices K = A'CA
02. One-dimensional Applications: a = Difference Matrix
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02. One-dimensional Applications: a = Difference Matrix
03. Network Applications: a = Incidence Matrix
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03. Network Applications: a = Incidence Matrix
04. Applications to Linear Estimation: Least Squares
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04. Applications to Linear Estimation: Least Squares
05. Applications to Dynamics: Eigenvalues of K, Solution of Mu
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05. Applications to Dynamics: Eigenvalues of K, Solution of Mu'' + Ku = F(t)
06. Underlying Theory: Applied Linear Algebra
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06. Underlying Theory: Applied Linear Algebra
07. Discrete vs. Continuous: Differences and Derivatives
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07. Discrete vs. Continuous: Differences and Derivatives
08. Applications to Boundary Value Problems: Laplace Equation
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08. Applications to Boundary Value Problems: Laplace Equation
11. Initial Value Problems: Wave Equation and Heat Equation
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11. Initial Value Problems: Wave Equation and Heat Equation
12. Solutions of Initial Value Problems: Eigenfunctions
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12. Solutions of Initial Value Problems: Eigenfunctions
13. Numerical Linear Algebra: Orthogonalization and a = QR
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13. Numerical Linear Algebra: Orthogonalization and a = QR
14. Numerical Linear Algebra: SVD and Applications
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14. Numerical Linear Algebra: SVD and Applications
15. Numerical Methods in Estimation: Recursive Least Squares and Covariance Matrix
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15. Numerical Methods in Estimation: Recursive Least Squares and Covariance Matrix
16. Dynamic Estimation: Kalman Filter and Square Root Filter
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16. Dynamic Estimation: Kalman Filter and Square Root Filter
18. Finite Difference Methods: Stability and Convergence
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18. Finite Difference Methods: Stability and Convergence
19. Optimization and Minimum Principles: Euler Equation
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19. Optimization and Minimum Principles: Euler Equation
20. Finite Element Method: Equilibrium Equations
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20. Finite Element Method: Equilibrium Equations
21. Spectral Method: Dynamic Equations
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21. Spectral Method: Dynamic Equations
22. Fourier Expansions and Convolution
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22. Fourier Expansions and Convolution
23. Fast Fourier Transform and Circulant Matrices
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23. Fast Fourier Transform and Circulant Matrices
24. Discrete Filters: Lowpass and Highpass
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24. Discrete Filters: Lowpass and Highpass
25. Filters in the Time and Frequency Domain
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25. Filters in the Time and Frequency Domain
26. Filter Banks and Perfect Reconstruction
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26. Filter Banks and Perfect Reconstruction
27. Multiresolution, Wavelet Transform and Scaling Function
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27. Multiresolution, Wavelet Transform and Scaling Function
28. Splines and Orthogonal Wavelets: Daubechies Construction
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28. Splines and Orthogonal Wavelets: Daubechies Construction
29. Applications in Signal and Image Processing: Compression
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29. Applications in Signal and Image Processing: Compression
30. Network Flows and Combinatorics: max flow = min cut
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30. Network Flows and Combinatorics: max flow = min cut
31. Simplex Method in Linear Programming
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31. Simplex Method in Linear Programming
32. Nonlinear Optimization: Algorithms and Theory
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32. Nonlinear Optimization: Algorithms and Theory
10. Delta Function and Green
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10. Delta Function and Green's Function
17. Finite Difference Methods: Equilibrium Problems
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17. Finite Difference Methods: Equilibrium Problems
09. Solutions of Laplace Equation: Complex Variables
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09. Solutions of Laplace Equation: Complex Variables


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