Numerical-Methods

Numerical Linear Algebra

Notes

Practical matrix computations and numerical realities.

Numerical Recipes: The Art of Scientific Computing

Notes

Broad coverage of numerical algorithms in science and engineering. Classic cross-topic numerical algorithms.

Solving Ordinary Differential Equations I & II

Notes

Definitive reference on modern ODE solvers and stiff systems.

Differentiation: Three Ways

Three approaches to computing derivatives—forward-mode AD, reverse-mode AD, and finite differences—each with different trade-offs. Understanding when to use each is essential for numerical computing and machine learning.

Numerical Integration with Generic Concepts

Numerical integration demonstrates both classical numerical analysis and Stepanov's philosophy: by identifying the minimal algebraic requirements, our quadrature routines work with dual numbers for automatic differentiation under the integral.

Numerical Differentiation

The art of numerical differentiation lies in choosing step size h wisely—small enough that the approximation is good, but not so small that floating-point errors dominate.

STAT 575 - Computational Statistics - SIUe - Summer 2021

This is a problem set for STAT 575 - Computational Statistics at SIUe. These problem sets were given by Dr. Qiang Beidi, a professor in the Department of Mathematics and Statistics at Southern Illinois University Edwardsville (SIUe) during the Summer …