Topic for Fall 2026: Numerical Analysis

This course is an introduction to the mathematical foundations and computational techniques of numerical analysis, the study of algorithms for solving problems of continuous mathematics using discrete approximations. Numerical analysis is one of the oldest and most influential areas of mathematics. It offers powerful tools for approximations and simulations of complex systems. The course will focus on both the theory and practice of numerical methods, their accuracy, efficiency, and limitations. The first part of the course will cover continuous problems, including solving nonlinear equations, numerical differentiation and integration, and polynomial interpolation. Numerical linear algebra topics will follow, including Gaussian elimination, LU decomposition, and iterative methods for large systems. The final part of the course will introduce numerical methods for differential equations: Euler's and Runge-Kutta methods. Throughout the course, we will analyze the stability, convergence, and computational complexity of algorithms. We will also apply them to practical problems using software such as MATLAB.

Units: 1

Max Enrollment: 15

Prerequisites: MATH 206 or permission of the instructor.

Distribution Requirements: MM - Mathematical Modeling and Problem Solving

Typical Periods Offered: Fall

Semesters Offered this Academic Year: Fall; Not Offered; Spring

Notes: This is a topics course and can be taken more than once for credit as long as the topic is different each time.