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MATH 441: Introduction to Numerical Analysis


Revised: November 2006 (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. In addition to homework projects, students will also be responsible for choosing an independent project in a topic related to the course material. They must:
  • choose an appropriate topic for further study,
  • do research on their topic outside of class,
  • implement any computational procedures associated with it,
  • present their work and findings before the class, and
  • submit a written report at the end of the semester.



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

CS 150 or CS 340 or equivalent.


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]
    • Round-off Errors
    • Floating Point Arithmetic
  • Solutions of Equations in One Variable (Chapter 2) [10 days]
    • Bisection Method
    • Fixed-Point Iteration
    • Newton's Method
    • Müller's Method
  • Polynomial Interpolation (Chapter 3) [6 days]
    • Lagrange Polynomial
    • Divided Differences
    • Cubic Spline Interpolation
  • Numerical Differentiation and Integration (Chapter 4) [11 days]
    • Numerical Differentiation
    • Simple Quadrature Methods
    • Composite Methods
    • Adaptive Quadrature Methods
  • Initial Value Problems for Ordinary Differential Equations (Chapter 5) [14 days]
    • Euler's Method
    • Higher-Order Taylor Methods
    • Runge-Kutta Methods
    • Multistep Methods
    • Higher Order Equations and Systems
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