Course Description for Math 151A: Numerical Analysis

Textbook: Numerical Analysis, by Burden and Faires

This course is the first part of a series of 2 courses (151A and 151B). It will essentially cover the first four chapters and chapter six of the textbook. We will learn some of the important algorithms to numerically solve an equation of the form f(x)=0 (root finding), to interpolate data to a polynomial, to numerically differentiate and integrate a function, and to directly solve systems of linear equations.
This class is not a progamming class; however, some programming skills are required for this course. We will discuss different algorithms for the examples mentioned above. It will than be an integral part of this course to numerically implement these algorithms in a computer code, and solve a number of examples. Many examples will be discussed in class; however, there will also be a numerics homework in all (most) homework assignments.

The general plan for this course is the following:

Weeks 1,2,3:

• Introduction and course overview
• Chapter 2: Solutions of equation of one variable

Week 4:

• Chapter 1: Arithmetics, Roundoffs, and Accuracy

Week 5,6:

• Chapter 3: Interpolation and Polynomial Approximation
• Midterm

Week 7,8:

• Chapter 4: Numerical Differentiation and Integration

Week 9,10:

• Chapter 6: Direct Methods for solving linear systems

Prerequisites:

• Lower division mathematics course sequence

Other Suggested Reading:

• K.E. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1989.
• Numerical Recipes, various versions.