Due date: November 16!
Due date: December 2.
Due Date: December 16.
Outline of Contents:
Chapter 0. Introduction and overview (Notes)
Chapter 1. Interpolation and approximation(Notes)
Polynomial interpolation (Lagrange, Newton, Remainder theorem)
piecewise polynomial approximation, splines (curve fitting),
orthogonal polynomials, L^2 approximation
Chapter 2. Numerical integration and differentiation (Notes)
central, forward, and backward difference, accuracy, extrapolation
Trap rule, Euler-Maclaurin formula, Simpson's rule
Chapter 3. Iteration and convergence (Notes)
solving linear and nonlinear equations,
Jacobi, GS, steepest decent,
Newton's iteration, etc.
Chapter 4. linear algebra and MATLAB (Notes)
tridiagonal matrix, LU and QR decomposition
power method, QR iteration for eigenvalues
Chapter 5. elementary probablility and sampling
elementary prob, conditional prob,
expectations, moments, variance,
random number generators,
illustration of law of large numbers and CLT
simple Monte Carlo, variance, and variance reduction
Chapter 6. asymptotic analysis
dominated balance, Laplace integrals, oscillatory integrals,
Stirling formula, Gamma function,
power series solutions of ODEs,
matched asymptotics, removing secular terms
Zhang and Li, Numerical Analysis
Conte and de Boor, Elementary Numerical Analysis
Quarteroni and Saleri, Scientific Computing with MATLAB
Bender and Orszag, Advanced mathematical methods for scientists and engineers.
Nayfeh's book, and other books on asymptotics, Cole's book
MATLAB User's Guide