Lecture Outlines
- Overview, Introduction to floating point arithmetic
Reading: Chapters 1,2,5 in Greenbaum/Chartier text
Additional reading: Chapter 2 in Bindel/Goodman text - Nonlinear equations in one variable
Bisection, Newton's method, secant method, fixed point iteration
Reading: Chapter 4 in Greenbaum/Chartier text
Additional reading: Chapter 2 in Bindel/Goodman text - More on nonlinear equations in one variable, numerical linear algebra
Reading: Chapters 6,7 in Greenbaum/Chartier text
Additional reading: Chapters 3-5 in Bindel/Goodman text - Dense matrix methods in linear algebra
LU and Cholesky factorizations, matrix norms, condition number, stability analysis
Reading: Chapters 7,12 in Greenbaum/Chartier text
Additional reading: Chapters 3-5 in Bindel/Goodman text - Dense matrix methods in linear algebra
QR and SVD factorizations, least squares problems
Reading: Chapters 7,8,12 in Greenbaum/Chartier text
Additional reading: Chapters 3-5,7 in Bindel/Goodman text - Polynomial interpolations, Hermite interpolation, Splines
Numerical differentiation, Richardson extrapolation
Reading: Chapters 8,9 in Greenbaum/Chartier text
- Numerical integration (quadrature)
Trapezoidal and midpoint rules, Newton-Cotes, Gaussian and adaptive quadrature
Reading: Chapter 10 in Greenbaum/Chartier text
- The Euler-MacLaurin formula, infinite intervals,
singular integrals, periodic functions, trigonometric interpolation
Reading: Chapter 10 in Greenbaum/Chartier text
- The Fast Fourier transform, filtering, and convolution
Reading: supplemental notes
- Ordinary differential equations
Existence/uniqueness, Euler's method, Runge-Kutta methods, linear multistep methods, stability theory
Reading: Chapter 11 in Greenbaum/Chartier text