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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.
Course readings.
| 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 |
|