Lecture Details

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