MATH/CMPSC 455 (Fall 2011)

Introduction to Numerical Analysis I, M W F 12:20 pm - 1:10 pm, 112 Engineering Unit B

Course Brief Description

This course is an introduction to basic and classical numerical algorithms. We will describe numerical algorithms for floating point computation, rootfinding, solving linear systems, interpolation and quadrature. 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.

Recommended Reference

• Homework & Computer projects (50 %);
• Midterm exam (20 %);
• Final exam (30 %).
Homework & Computer projects will be assigned every 2 or 3 sections. The lowest grade will be dropped. Details about midterm and final exam will be announced later.

Office Hours

Tuesday & Thursday, 1:30 pm - 2:30 pm, or by appointment.

Syllabus

Lecture Notes & Slides

0.0 Introduction: slides
0.1 Evaluating a Polynomial: Notes & Slides
0.2 Binary Numbers: Notes & Slides
0.3 Floating Point Representation: Notes (updated) & Slides (updated)
0.4 Loss of Significance: Notes & Slides
1.1 Bisection Method: Notes & Slides
1.2 Fixed Point Iteration: Notes & Slides
1.3 Newton's Method: Notes & Slides
1.4 Root Finding without Derivatives: Notes & Slides
2.1 Gaussian Elimination: Notes & Slides
2.2 LU factorization: Notes & Slides
2.3 Source of Error: Notes
2.4 PA=LU: Notes & Slides
2.5 Iterative Method: Notes & Slides
2.6 Conjugate Gradient Method: Notes & Slides
3.1 Interpolation: Notes & Slides
3.2 Interpolation Error: Notes & Slides
3.4 Splines: Notes & Slides
5.2 Numerical Integration: Notes & Slides
5.3 Romberg Integration: Notes & Slides
5.5 Gauss Quadrature: Notes & Slides
6    Ordinary Differential Equations: Notes & Slides

Homework & Computer Projects

Homework 1 (Due Sep. 16, 2011)