Advanced Numerical Analysis (MATH 269A), Fall 2024.

This is the primary course website for Advanced Numerical Analysis (MATH 269A), Fall 2024.

Announcements

Homework

There will be several assignments involving both theoretical and computational exercises. Submit through Bruin Learn.

  1. Homework 1, Due 10/11.
  2. Homework 2, Due 10/21.
  3. Homework 3, Due 10/30.
  4. Homework 4, Due 12/02.
  5. Homework 5, Due 12/09.

Lecture Plans

Course Information

Instructor

Ernest K. Ryu, Mathematical Sciences 7619B,
Office hours: Wednesday 12:00–1:30pm

Photo of Ernest Ryu

Teaching Assistant

Zheng Tan
Office hours: Tuesday and Thursday 3:00–4:00pm

Lectures

Monday, Wednesday, and Friday 4:00–4:50pm at Mathematical Sciences 5118.

Discussion Section

Tuesday 4:00–4:50pm at Mathematical Sciences 5118. Run by the TA

Exams

This class will have in-person closed-book hand-written (no computers) midterm and final exams.

  • Midterm exam: 11/04, 4:00–5:00pm, Mathematical Sciences 5118.
  • Final exam: 12/11, 8:00–11:00am, Mathematical Sciences 5118.

Grading

Homework 30%, midterm exam 30%, final exam 40%.

Course Overview

Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved "by hand" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations. In 269A, the principle goals consist of identifying, analyzing, and implementing the most commonly used numerical techniques to construct approximate solutions of systems of ordinary differential equations (ODE's). A variety of single step and multistep methods will be covered as well as general theoretical aspects that, when understood, help with the tasks of method selection and implementation. Methods for "stiff systems" and adaptive timestepping methods will be covered in the latter part of the quarter.

Prerequisites

For graduate students, it is recommended that the students have taken at least one undergraduate course in numerical analysis, preferably two (e.g. Math 151AB), as well as an upper-division undergraduate course in linear algebra. The assignments will involve programming so an undergraduate course in programming is recommended.

The basic qualification for undergraduates to enroll in 269A, if there is space, is that you have completed 151AB and 131AB, and are maintaining a good GP by showing an unofficial transcript to me.

Textbooks

Ascher and Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998.