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MATH/CMPSC 456 (Spring 2012)

Introduction to Numerical Analysis II, M W F 11:15 am - 12:05 pm, 271 Willard Bldg

Course Brief Description

This course is a continuation of MATH/CMPSC 455.  We will describe numerical algorithms for solving nonlinear equations, approximation functions and data, numerical integration,  solving linear systems, Eigenvalue problems, Solving ordinary differential equations and boundary-value problems.  We will also discuss the underlying mathematical principles and theories of these numerical methods and their implementations.

Some knowledge of either MATLAB, Octave, Fortran, C, or C++ is strongly recommended. MATLAB is used for exposition of algorithms during the class. You can choose any computer language as a platform for homework and projects.

Prerequisite
MATH 220, MATH 230 or MATH 231, MATH/CMPSC 451 or MATH/CMPSC 455

Recommended Reference
Numerical Analysis, Timothy Sauer, published by Addison Wesley, ISBN 0-321-26898-9.

Grading Policy

Details about midterm and final exam will be announced later.

Office Hours

Tuesday & Thursday, 1:00 pm - 2:00 pm, or by appointment.

Syllabus

Download Syllabus

Lecture Notes & Slides

0.   Introduction: slides
1.1 Newton' Method: slides
1.2 Quasi-Newton Methods: slides
1.3 FPI and Aitken Acceleration: slides 1 & slides 2
2.1 Polynomial Interpolation: slides
2.2 Trigonometric Interpolation: slides
2.3 Piecewise Interpolation: slides
2.4 Least Square Method: slides
3.1 Adaptive Quadrature: slides
4.2 Basic Linear Iterative Methods: slides
4.3 Krylov Subspace Method: slides
5.   Eigenvalue Problems: slides
6.1 Ordinary Differential Equations: slides
7.1 Finite Difference Method: slides
7.2 Finite Element Method: slides

Homework & Computer Projects

Coming soon ...