Home Schedule Optional Activities Office Hours Homework Archive

UW–Madison Math/CS 714 (Fall 2025)

Methods of Computational Mathematics I

Introduction

Math/CS 714 and Math/CS 715 are concerned with the development and the analysis of numerical methods for solving elliptic, parabolic, and hyperbolic partial differential equations (PDEs). In particular, Math/CS 714 will focus on a class of numerical schemes known as finite difference methods (although finite volume and spectral methods will also be covered). For each type of PDE we will develop numerical schemes from physical and mathematical intuition, analyze these schemes, consider improvements, and discuss issues related to the implementation of these methods into computer code.

An important aspect of accurately and efficiently solving PDEs via numerical methods is the ability to solve large linear systems. Therefore, in addition to the basic numerical methods, this course will include discussions of simple iteration methods for solving large linear systems. Homework assignments will involve problems on theoretical (analyzing methods) and practical (implementing methods into computer code) aspects of numerical analysis.

Quick links

Teaching team

Yue
Yue Sun

Lead instructor

Ann
Ann Bigelow

Grader

Course information

A more detailed description of this information can be found in the course syllabus.

Lectures
Tuesday & Thursday 11:00am–12:15pm CT in B135 Van Vleck Hall
Textbook
Finite Difference Methods for Ordinary and Partial Differential Equations, by Randall J. LeVeque (required)
Finite Volume Methods for Hyperbolic Problems, by Randall J. LeVeque (optional)
Homework
There will be five homework assignments. The first is due on Friday September 26th, and the remainder are due at roughly 2–3 week intervals. Homework assignments will be due at 5pm CT on the course Canvas site. In addition, an introductory homework assignment 0 is provided, which is ungraded but designed for you to refresh your mathematical and programming skills.
Academic integrity policy
Discussion and the exchange of ideas are essential to doing academic work. For assignments in this course, you are encouraged to consult with your classmates as you work on problem sets. However, after discussions with peers, make sure that you can work through the problem yourself and ensure that any answers you submit for evaluation are the result of your own efforts. You must list the names of students with whom you have collaborated on problem sets.
In addition, you must cite any books, articles, websites, lectures, etc. that have helped you with your work using appropriate citation practices. Using homework solutions from previous years is forbidden.
Use of generative AI tools (such as ChatGPT, Copilot, etc.) is not allowed for the writeup and code. Please refer to the course syllabus for details on the academic integrity and AI statements.
Grades
The final letter grade will be based on homework assignments (55%), group activities (5%), and the final project (40%).
Final project
This document contains logistical details about the final project organization. In general, the final project will be completed in groups of two or three students. Multi-person (≥4) projects are also allowed with instructor permission. Each group will propose a project topic drawn from an application area of interest. The project should make use of concepts covered in the course. The project should be roughly equivalent in scope to a section of a published research article. You will be required to write software to solve your problem, and to submit a report that includes a mathematical discussion of your methodology in relation to the theory covered in the course. Projects will be assessed based on a written report (20%), the quality and correctness of software (12%), and the final presentation (8%). Code should be well-documented and should be organized so that figures submitted in the report can be easily reproduced by the teaching staff.