MATH/CS 375 — Introduction to Numerical Computing
University of New Mexico
An introduction to numerical methods and scientific computing, with computational experiments in MATLAB.
Curriculum and lecture slides
The lectures are organized by topic below. Each link opens the corresponding lecture slides as a PDF.
1. Foundations of numerical computing
- Lecture 00 — Course introduction
- Lecture 01 — Taylor series and convergence
- Lecture 02A — Introduction to floating-point numbers
- Lecture 02B — Floating-point arithmetic (continued)
2. Numerical differentiation and nonlinear equations
- Lecture 03A — Numerical differentiation
- Lecture 03B — Extrapolation
- Lecture 04A — Nonlinear equations and the bisection method
- Lecture 04B — Nonlinear equations (continued)
- Lecture 04C — Secant method
3. Numerical linear algebra and linear systems
- Lecture 05A — Linear algebra fundamentals
- Lecture 05B — Counting operations and solving special systems
- Lecture 06A — Gaussian elimination
- Lecture 06B — Gaussian elimination (continued)
- Lecture 06C — Numerical stability
- Lecture 07A — LU factorization
- Lecture 07B — LDL and Cholesky factorizations
- Lecture 08A — Stationary iterative methods
- Lecture 08B — Sparsity and iterative methods
- Lecture 08C — Iterative methods (continued)
4. Interpolation and splines
- Lecture 09A — Polynomial interpolation
- Lecture 09B — Newton interpolation
- Lecture 09C — Interpolation error
- Lecture 10A — Splines
- Lecture 10B — Interpolation, splines, and data visualization in MATLAB
5. Numerical integration
- Lecture 11A — Numerical integration
- Lecture 11B — Newton–Cotes formulas
- Lecture 12A — Gaussian quadrature
- Lecture 12B — Generalized Gaussian quadrature
6. Eigenvalue methods and least squares
- Lecture 13A — Power method
- Lecture 13B — Markov chains
- Lecture 14A — Least-squares methods
- Lecture 14B — Least squares