Department of Mathematics Generic Syllabus
Boise State University Updated Fall 1998

Math 465
Numerical Analysis
4 semester credits

Catalog Description

M 465 NUMERICAL ANALYSIS (4-0-4)(S). The application of numerical methods to the interpretation and analysis of data, solution of equations, general iterative methods, approximation of functions, error analysis. PREREQ: M 301 or M 333 and competence in programming in at least one of the languages BASIC, Fortran, C, or Pascal. Offered spring of odd-numbered years, subject to sufficient demand.

Prerequisites

M301 or M333: The rationale for this prerequisite is to ensure that students have adequate background and theoretical knowledge of a variety of mathematical problems that will be studied from a numerical perspective.

Competence in BASIC, Fortran, C, or Pascal: The rational for this prerequisite is to ensure that students have adequate computational experience so that they can understand the purposes and limitations of numerical programs as well as program numerical procedures themselves.

Jurisdiction

This course is not currently controlled by a departmental committee.

Learning Objectives

As an applied mathematics course, the objectives of M 465 reflect three of the Department's teaching goals: that students be able to give examples of nontrivial applications of mathematics to various (non-mathematical) fields, that students be able to use suitable mathematical tools, and that students use mathematics as a language. M 465 does not stress the aesthetic side of mathematics or the idea of mathematics as the study of patterns.

Upon completion of this course, students should:

  1. be able to identify the type of problems that require numerical techniques for their solution;
  2. be able to explain how, why and when modern approximation techniques can be expected to work;
  3. be able to accurately approximate the solutions of some problems that cannot be solved exactly; and
  4. be able to determine the type of error that can be expected with the various approximation techniques.

Assessment of Learning Objectives

Problems based on the learning objectives will be assigned on a regular basis and may appear in a variety of contexts:

· Classroom discussion provides an indication of the students' understanding of newly presented topics, of old material, and of their ability to relate new topics to old ones.

· Homework problem sets serve as both learning and assessment tools for understanding how numerical methods work and for their theoretical underpinnings.

· Programming assignments are designed to assess the students' ability to synthesize the ideas discussed in class by writing programs that solve problems for which numerical solution has clear advantages over analytical techniques. The analysis of the output of these programs will give students the opportunity to compare the accuracy of their implementation of numerical schemes to theoretical bounds.

· Exams may be in-class, take-home or both. In-class exams give students the opportunity to demonstrate their ability to work simple problems and to demonstrate their understanding of fundamental concepts. Take-home exams provide the opportunity for students to delve more deeply into the subject, to work more complicated problems, and thus arrive at a more profound understanding of the material.

Topics and Approximate Timeline

The following table is based on a typical semester schedule-60 class meetings of 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.

Number of
Topic Meetings
Introduction 1
Solutions of Equations in One Variable 7
Interpolation and Polynomial Approximation 7
Numerical Differentiation and Integration 8
Initial Value Problems for Ordinary Differential Equations 10
Direct and Iterative Methods for Solving Linear Systems 12
Approximation of Eigenvalues 5
Boundary Value Problems for Ordinary Differential Equations 5
Approximation Theory 3
Exams 2

Text

Numerical Analysis, R.L. Burden and J.D. Faires, 5th edition, PWS-Kent, 1993.

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion; the instructor chooses the appropriate mix. Homework is an important part of the course (where simple numerical work is done to illustrate concepts and justification for the ideas behind the methods is investigated) as well as computer assignments (where much of the actual numerical computational work is done) and writing assignments (which are given to help the students learn to communicate the ideas behind the computations). The exams are used to determine whether the student understands the concepts behind the methods. The instructor chooses the exact grading scheme, but a typical distribution would be:

Homework 200
Computer Assignments 200
Writing Assignments 100
2 Exams 200
Final Exam 200
Total 900

Letter grades are usually based on a standard scale in which 90% of the total possible points guarantees an A , 80% a B, and 70% a C, with the instructor having the discretion to lower these cut-offs if warranted.

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