This course is organized around a collection of interesting applications. Examples from recent years are:
  • Interpolation
  • Finite difference approximations
  • Least Squares
  • Fourier series
  • Graphs and Networks
  • FFT
  • JPEG compression
  • Power method
  • Recursion relations
  • The Anderson tight binding model
  • Markov chains
  • Google PageRank

Outline (please see the lecture notes also):
Chapter 1: Linear Equations
Topics: Solving linear equations, vector and matrix norms, condition number.
Applications: Lagrange interpolation, splines, finite difference approximation.
Chapter 2: Subspaces, Basis and Dimension
Topics: Vector spaces, subspaces, basis, dimension, basis for N(A), R(A), N(A^T) and R(A^T)
Applications: Chemical systems, Graphs and resistor networks
Chapter 3: Orthogonality
Topics: Orthonormal bases and orthogonal matrices, Complex vector spaces
Applications: Least squares
Chapter 4: Eigenvalues and Eigenvectors
Topics: Eigenvalues and Eigenvectors
Applications: Effective resistance, Power method, Markov chains, Anderson tight binding model, Google pagerank, Singular value decomposition (SVD)