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