MAT 410: Numerical Analysis
Undergraduate course, Southern Virginia University, 2026
How to get a computer to solve mathematical problems approximately, and how to know whether to trust the answer: root-finding, interpolation, differentiation, integration, differential equations, and linear systems.
About the course
Numerical analysis surveys methods for approximating solutions to problems that cannot be solved exactly. For each algorithm we care about three things: where it comes from, where it breaks down, and how efficient it is.
This is a scientific computing course as much as a mathematics course. Our language is Julia, run in Jupyter notebooks, and no prior Julia experience is assumed. Homework is light, with a written part and a short notebook. Projects are the heart of the course: code projects on root-finding and on a topic of the student’s choosing, and a final project, a parameter-optimization problem built on an initial-value problem, documented in a self-contained notebook and presented.
In Fall 2026 the course runs as an independent study with a weekly check-in.
Textbook: Numerical Analysis, 9th edition, by Richard L. Burden and J. Douglas Faires.
Prerequisites: MAT 343: Linear Algebra and MAT 344: Elementary Differential Equations.
Syllabus (Fall 2026)
Helpful resources
- Julia and the Julia documentation. Free and open source. The manual’s “Getting Started” and “Functions” sections cover most of what we use.
- Jupyter. The notebook environment we work in.
- Fundamentals of Numerical Computation (Julia edition) by Driscoll and Braun. A free online textbook covering the same topics with working Julia code. A good second explanation when Burden and Faires is terse.