Readings

Assigned readings are sections in the course textbook: Mathews, J. H., and K. D. Fink. Numerical Methods Using MATLAB®. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1998. ISBN: 9780132700429.

LEC # TOPICS READINGS

1

Introduction

Computer Architecture

Number Representations

Recursion

Sections 1.1-1.2

2

Error Propagation

Error Estimation

Condition Numbers

Sections 1.2-1.3

3

Linear Systems of Equations: Cramer's Rule

Gaussian Elimination

Section 1.3

4

Linear Systems: Gaussian Elimination

Pivoting

LU Factorization

Error Analysis

Sections 3.1-3.2

5

Linear Systems: Tri-Diagonal Systems

Special Matrices

Sections 3.3-3.4 and 3.6

6

Linear Systems: Iterative Methods

Convergence of Iterative Schemes

Section 3.4

7

Roots of Non-linear Equations: Bisection

Newton-Ralphson Iteration

Section 3.7

8

Interpolation of Functions by Polynomials

Lagrange Interpolation

Triangular Family

Sections 2.1-2.4

9

Numerical Differentiation and Integration

Error Estimates

Sections 4.1-4.4

10

Ordinary Differential Equations

Initial Value Problems: Euler and Runge-Kutta Methods

Sections 6.1-6.2 and 7.1-7.3

11

Ordinary Differential Equations (cont.)

Boundary Value Problems: Finite Difference Methods

Sections 9.1-9.2 and 9.4-9.5

12

Minimization Problems

Least Square Approximation

Optimization