AMS 326, Numerical Analysis
Catalog Description: Direct and indirect methods for the solution of linear and nonlinear equations.
Computation of eigenvalues and eigenvectors of matrices. Quadrature, differentiation,
and curve fitting. Numerical solution of ordinary and partial differential equations.
Prerequisite: CSE 101; AMS 161; basic skills in using a high-level programming language (C, C++, or Java).
Note: Students who do not have the CSE 101 prerequisite, but have the basic programming skills as stated in the Undergraduate Bulletin should contact either the AMS Department's Undergraduate Program Director or Coordinator for permission to enroll in AMS 326
Advisory prerequisite: AMS 210 or MAT 211
NOTE: AMS 326 may not be taken for credit in addition to CIV 350 or MEC 320
3 credits
Textbook for spring 2024 (optional):
"Numerical Analysis" by Timothy Sauer; 3rd edition, 2017, Pearson Publishing; ISNB:
978-0134696454
SYLLABUS
1. Definition and analysis of errors.
2. Direct and indirect numerical methods for the solution of linear and nonlinear algebraic equations.
3. Computation of eigenvalues and eigenvectors of matrices.
4. Quadrature, differentiation, and curve fitting.
5. Numerical solution of simple ordinary differential equations.
6. Optimizations.
7. Fast Fourier transforms
Learning Outcomes for AMS 326, Numerical Analysis
1) Demonstrate knowledge of the foundational notions of numerical analysis, including basic computer science on storing and manipulating numbers, on finite precision of arithmetic calculations, on the definition of errors and condition number.
2) Demonstrate knowledge of interpolating data using polynomials or trigonometric functions and applying those interpolations to estimate, differentiate, and integrate functions.
3) Demonstrate knowledge of solving systems of algebraic equations using a variety of methods, including iterative ones, leveraging the methods on numerical linear algebra.
4) Demonstrate proficient knowledge of solving ordinary differential equations and their systems, both as initial value problems and as boundary value problems.
5) Demonstrate basic understanding of numerical optimizations and of simple Monte Carlo methods.
6) Demonstrate basic understanding of the numerical aspects of Fourier transforms.