Research Assistant Professor, Department of Mathematics, Pennsylvania State University

MATH/CMPSC 456 (Spring 2012)

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

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.

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

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.

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

Grading Policy

- Homework & Computer projects (50 %);
- Midterm exam (20 %): March 2;

- Final exam (30 %).

Office Hours

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

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

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

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 ...

Coming soon ...