Introduction to Numerical Analysis
Revised: July 2009 (Erin McNelis)
Course Description & Topics
This first semester introduction to the field of numerical analysis will investigate numerical techniques in:
- solving equations in one variable (a.k.a. root finding)
- interpolation and polynomial approximation
- numerical differentiation and integration
- solving ordinary differential equations
and the errors associated with each of these techniques. There will be a significant component of the class the comes from implementing or using these methods to complete homework projects.
Objectives
To develop students' understanding of computing in a finite precision environment, to familiarize students with types of problems where numerical methods are used to approximate solutions, to cover the basic algorithms of numerical analysis in these areas, and to provide an understanding of the mathematical analysis behind the numerical methods discussed.
Required Text
Burden & Faires, Numerical Analysis (8th Ed.), Thompson Brooks/Cole Publishing.
Prerequisites
MATH 255, CS 150 or CS 340.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
-
Preliminaries (Chapter 1) [4 days]
o Round-off Errors
o Floating Point Arithmetic -
Solutions of Equations in One Variable (Chapter 2) [10 days]
o Bisection Method
o Fixed-Point Iteration
o Newton's Method
o Müller's Method -
Polynomial Interpolation (Chapter 3) [6 days]
o Lagrange Polynomial
o Divided Differences
o Cubic Spline Interpolation -
Numerical Differentiation and Integration (Chapter 4) [11 days]
o Numerical Differentiation
o Simple Quadrature Methods
o Composite Methods
o Adaptive Quadrature Methods -
Initial Value Problems for Ordinary Differential Equations (Chapter 5) [14 days]
o Euler's Method
o Higher-Order Taylor Methods
o Runge-Kutta Methods
o Multistep Methods
o Higher Order Equations and Systems