Cape Breton University

 

Numerical Analysis

 

Math 307 (Fall 2010) Course Outline

 

Instructor: Dr. George Chen

Textbook: Numerical Analysis, 9th edition, 2010, by Richard Burden and Douglas Faires

Prerequisite: Math115 or Math226, Math187 and Math122, Math 257 recommended

Exclusion: Credit cannot be obtained for both Math 307 and Math 252/Chem 302

 

Objectives:

Students will learn how to solve applied problems which will guide their exploration of the field of engineering and other applied sciences.  They will also learn how to use computational tools, such as MATLAB or MAPLE to numerically solve those problems. Topics will generally include: the analysis of various numerical integration, differentiation, numerical solution of ordinary differential equations (ODEs), finding roots of nonlinear equations, the solution of linear and non-linear of equations, and their error analysis. The basic concepts and information needed to solve these problems will be provided during lecture and lab time but students will be expected to carry out research to find ways to solve these problems.

 

Outline:

  • Number systems, errors and algorithms

Representation of numbers; error propagation and estimation; iterative algorithms.

  • Numerical Methods for finding roots and solving equations

Bisection, secant method, Newton's method; fixed point iteration and acceleration.

  • Linear and nonlinear systems

Direct method - factorization, pivoting, inverse calculation; fixed precision arithmetic and iteration method.

  • Interpolation and Approximation

Interpolating polynomial, Lagrange form, error formula; cubic spline interpolation;

trigonometric interpolation.

  • Differentiation and Integration

Finite-difference approximation; Numerical quadrature-Romberg scheme; composite rules; Gaussian quadrature; Simpson’s rules.

  • Ordinary Differential Equations - Initial Value Problems

Euler's method, Runge-Kutta and Adams methods; Multistep methods; convergence and stability; stiff equations.

                

Marking Scheme:

               Assignments             25%

               Midterm/projects      30%

               Final                         45%