MATH 434

MATH 434: Numerical Analysis I

Credit hours (3)

Prerequisites: MATH 271; MATH 260; MATH 261; and one of CS 109, CS 118, CS 120, or INSY 275; or permission of instructor.

Introduction to scientific computing and numerical methods for nonlinear equations, linear algebra problems, interpolating data sets, numerical differentiation, and numerical integration. Both the implementation of the methods and the underlying analysis of how and why they work are considered.

Detailed Description of Course

The course covers the numerical methods for the types of problems listed below. It
includes both implementations of the approximation methods and analysis of the error
of the methods.

Nonlinear equations, including the bisection method, fixed point iteration, and Newton’s method.
Linear algebra, including solving linear systems and eigenvalues and eigenvectors
Nonlinear systems of equations, including multivariate Newton’s method
Interpolation
Numerical differentiation, including finite-difference approximation
Numerical integration, including Newton-Cotes formulas, adaptive quadrature, and Gaussian quadrature
Random number generators and Monte Carlo simulation.

The course also includes the basic computer programming skills needed to implement
the methods listed above, including if-then statements and for and while loops. The
effects of floating-point arithmetic and roundoff error in calculations are also included.

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

Understand methods for approximately solving equations, including how the error of the approximation behaves.
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.

Assessment Measures

The assessment measures will vary among instructors and may include exams, homework assignments, computer 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. MATH 434 is also beneficial to students in statistics.

Review and Approval

May 10, 2024
November 7, 2017
November 17, 2015
March 2009
September 2001