Lecture: Polynomial Fits and Splines

Lecture: Least-Squares Fitting Methods

Lecture: Data Fitting with Matlab

Lecture: Eigen-decompositions and Iterations

Lecture: Eigenvalues and Eigenvectors

Lecture: Iteration Methods for Ax-b

Lecture: Unconstrained Optimization (Derivative-Free Methods)

Lecture: Linear Programming and Genetic Algorithms

Lecture: Theory of the Fourier Transform

Lecture: Unconstrained Optimization (Derivative Methods)

Lecture: Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)

Lecture: Ordinary Differential Equations and Time-stepping

Lecture: Numerical Differentiation Methods

Supplement: Mean Value Theorem

Lecture: Higher-order Integration Schemes

Lecture: FFT and Image Compression

Lecture: Higher-order Accuracy Schemes for Differentiation and Integration

Supplement: Using ODE45 & Runge-Kutta methods

Lecture: Vectorized Time-step Integrators

Lecture: Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum

Lecture: Error and Stability of Time-stepping Schemes

Lecture: Application of Runge-Kutta to Lorenz Equation

Lecture: General Time-stepping and Runge-Kutta Schemes

Supplement: Indexing equations

Lecture: Principal Componenet Analysis (PCA)

Supplement: Big systems of ODEs

Lecture: The Singular Value Decomposition (SVD)

Supplement: Vector fields and phase-planes

Supplement: Discrete Fourier Transform

Lecture: PCA for Face Recognition