Beginning Scientific Computing by Steve L. Brunton and ?

source: AMATH 301     2016年2月19日

1 49:34 Higher-order Integration Schemes: Higher-order numerical integration schemes are considered along the classic schemes of trapezoidal rule and Simpson’s rule.
2 46:59 Ordinary Differential Equations and Time-stepping
3 39:15 Data Fitting with Matlab
4 57:09 Linear Programming and Genetic Algorithms
5 47:10 Numerical Differentiation Methods
6 43:51 Eigenvalues and Eigenvectors
7 48:56 Unconstrained Optimization (Derivative Methods)
8 47:22 Iteration Methods for Ax-b
9 9:01 Supplement: Using ODE45 & Runge-Kutta methods
10 48:03 PCA for Face Recognition
11 48:55 Eigen-decompositions and Iterations
12 44:39 Least-Squares Fitting Methods
13 44:00 Polynomial Fits and Splines
14 45:21 Higher-order Accuracy Schemes for Differentiation and Integration
15 45:35 Unconstrained Optimization (Derivative-Free Methods)
16 44:49 Error and Stability of Time-stepping Schemes
17 43:40 FFT and Image Compression
18 45:16 General Time-stepping and Runge-Kutta Schemes
19 48:39 Theory of the Fourier Transform
20 48:03 Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
21 44:36 The Singular Value Decomposition (SVD)
22 51:13 Principal Componenet Analysis (PCA)
23 4:40 Supplement: Big systems of ODEs
24 10:10 Supplement: Indexing equations
25 7:45 Supplement: Discrete Fourier Transform
26 5:53 Supplement: Mean Value Theorem
27 29:51 Application of Runge-Kutta to Lorenz Equation
28 41:07 Vectorized Time-step Integrators
29 49:30 Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum
30 6:07 Supplement: Vector fields and phase-planes
31 41:56 Vectors & Matrices
32 39:25 Logic, Loops, and Iterations
33 41:56 Vectors & Matrices
34 50:59 LU Matrix Decomposition for Ax=b
35 39:40 Gaussian Elimination for Ax=b
36 42:10 Linear Systems of Equations