MATH 125: Numerical Analysis

Many problems in the natural sciences, social sciences, and engineering can be studied through mathematical models. Typically, these models often require solving mathematical problems, such as solving systems of equations, approximating integrals, and solving differential equations. Numerical Analysis is the field that investigates how these problems can be addressed on computers using finite precision arithmetic. Therefore, this course aims to clearly define the accuracy and efficiency of numerical algorithms and explore these concepts in various contexts. We will systematically examine fundamental concepts of Numerical Analysis, understand standard algorithms, and discuss advanced methods and their applications. 

This course covers topics related to numerical methods for mathematical problems in calculus and linear algebra. We will begin by understanding how computers interpret numbers and perform arithmetic when solving mathematical problems. We will explore methods for finding approximate numerical solutions to various mathematical problems, emphasizing careful error analysis. A mathematical software package will be utilized to apply iterative techniques for nonlinear equations, polynomial interpolation, integration, and linear algebra tasks such as matrix inversion, eigenvalues, and eigenvectors.