Research Assistant Professor, Department of Mathematics, Pennsylvania State University

MATH/CMPSC 455 (Fall 2011)

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

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.

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

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

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

Grading Policy

- Homework & Computer projects (50 %);
- Midterm exam (20 %);

- Final exam (30 %).

Office Hours

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

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

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

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