MATH 435

MATH 435: Numerical Analysis II

Credit hours (3)

Prerequisites: MATH 434 
Pre- or Corequisites: MATH 346 

Introduction to numerical methods for solving ordinary and partial differential equations and numerical optimization. Usage of these techniques in the context of applied mathematics is emphasized.

Note(s): Applied Learning designated course.

Detailed Description of Course

This course continues the Numerical Analysis sequence begun in MATH 434 and includes implementation and error analysis of the following topics.

1. Numerical methods for initial value problem ordinary differential equations
   1. Euler's method
   2. Runge-Kutta methods
   3. Implicit methods
2. Numerical methods for boundary value problem ordinary differential equations
   1. The Shooting Method
   2. Finite difference methods
3. Introduction to partial differential equations and numerical methods for them
4. Numerical methods for optimization
5. Selected other topics, such as the Fast Fourier transform or stochastic differential equations, given time and student interest.
6. In addition to the methods for solving these equations, the course focuses on modeling different real-world problems in the way that an applied mathematician would approach them.

Detailed Description of Conduct of Course

This course contains an introduction to scientific computing. While the particular software used may vary among instructors, the course contains a significant amount of computer programing, both in class and on homework assignments. Instructors may use in-class lectures or video lectures, and students may be expected to present their work to the class.

Goals and Objectives of the Course

Students will 

1. Understand methods for approximately solving ordinary differential equations, including how the error of the approximation behaves.
2. Be able to write computer programs that implement these methods to solve problems too complex to solve with the pencil-and-paper methods from previous courses.
3. Apply these methods to real-world modeling problems that an applied mathematician would see. 

Assessment Measures

The assessment measures will vary among instructors and may include in-class examinations, homework assignments, computer projects, presentation of projects, and performance in class and in laboratory activities.

 

Other Course Information

Students who plan to work in an applied science need exposure to and hands-on experience with methods and computer software that is applicable to many of the general problems they will encounter.  MATH 434:435 is intended to be the sequence that provides this exposure and experience.

 

Review and Approval

November 17, 2015

March 2009

September 2001

March 01, 2021