Math 4066 - Numerical Differential Equations

Syllabus

Instructor: Xiaoliang Wan

Lecture: TTH 12:00-1:20pm, B016 Lockett Hall

Office Hours: MW 12:30-2:00pm

Course Description: In this course, we will discuss the numerical integration of ordinary differential equations. We will introduce the construction of several typical numerical schemes, including Euler's method, the Taylor series method, the Runge–Kutta method, and multistep methods. We will also develop a mathematical understanding of some key concepts such as stability, consistency, and convergence. In addition, we will briefly address specific issues such as adaptive step-size selection and the numerical integration of stiff problems. Furthermore, we will discuss applications of ODEs in machine learning.

Grade: Your final grade will be based on your performance on homework and exams: Homework (40%), Midterm (30%) and Final exam (30%). You are encouraged to discuss with others about your homework. However, you must prepare you own solutions. No late homework is accepted.

HW 1:	Exercise 1.3, 1.4, 1.5, 2.2, 2.3, 2.4 [Due on 01/29/2026]
HW 2:	Exercise 2.7, 2.8, 2.9, 2.10, 2.13, 2.14 [Due on 02/05/2026]

Instructor:	Xiaoliang Wan
Lecture:	TTH 12:00-1:20pm, B016 Lockett Hall
Office Hours:	MW 12:30-2:00pm
Course Description:	In this course, we will discuss the numerical integration of ordinary differential equations. We will introduce the construction of several typical numerical schemes, including Euler's method, the Taylor series method, the Runge–Kutta method, and multistep methods. We will also develop a mathematical understanding of some key concepts such as stability, consistency, and convergence. In addition, we will briefly address specific issues such as adaptive step-size selection and the numerical integration of stiff problems. Furthermore, we will discuss applications of ODEs in machine learning.
Grade:	Your final grade will be based on your performance on homework and exams: Homework (40%), Midterm (30%) and Final exam (30%). You are encouraged to discuss with others about your homework. However, you must prepare you own solutions. No late homework is accepted.