| Week |
Lecture |
Subject |
reading |
Week0 |
Lecture1 (9/23) |
General course overview, Background for programming projects. |
1.1 |
| Week1 |
Lecture2 (9/26) |
Computer representation of numbers. Limitations imposed by floating point representation. |
1.2 |
| |
Lecture3 (9/28) |
Errors in floating point arithmetic computations |
1.2 |
| |
Lecture4 (9/30) |
Introduction to the solution of nonlinear equations.The bisection method. |
2.1 |
| Week2 |
Lecture5 (10/3) |
Convergence estimates for the bisection method. Errors and residuals. |
2.1 |
|
Lecture6 (10/5) |
The fixed point iteration1 |
2.2 |
| |
Lecture7 (10/7) |
The fixed point iteration2 |
2.3 |
| Week3 |
Lecture8 (10/10) |
The Newton-Raphson method. |
2.3 |
| |
Lecture9 (10/12) |
The secant method. The method of false position. Rates of convergence. |
2.3, 2.4 |
| |
Lecture10 (10/14) |
Error analysis for Newton-Raphson and the secant method.
| 2.4 |
| Week 4 |
Lecture11 (10/17) |
Multiple roots of a function. Comparison of iterative methods. Global convergence properties. |
2.4 |
| |
Lecture12 (10/19) |
Polynomial Interpolation. Method of undetermined coefficients. (Vandermonde matrix.) |
3.1 |
| |
Lecture13 (10/21) |
Newton Divided differences. |
3.3 |
| Week5 |
Lecture14 (10/24) |
Midterm |
|
| |
Lecture15 (10/26) |
Lagrange Interpolation Formula. Interpolant existence and uniqueness. |
3.1 |
|
|
Lecture16 (10/28) |
Polynomial interpolation error estimates. (Error estimate for equispaced nodes*.) |
3.1, 3.2 |
| Week6 |
Lecture17 (10/31) |
Runge phenomenon. Neville's method.
|
3.2 |
| |
Lecture18 (11/2) |
Neville's method. Numerical differentiation. |
3.2, 4.1 |
|
Lecture19 (11/4) |
Error estimates for numerical differentiation formula. Asymptotic error expansions for numerical differentiation. |
4.1 |
| Week7 |
Lecture20 (11/7) |
Richardson extrapolation. |
4.2 |
| |
Lecture21 (11/9) |
Numerical integration. Newton-Cotes formulas. |
4.3 |
|
Lecture22 (11/11) |
Veterans Day holiday |
|
| Week8 |
Lecture23 (11/14) |
Composite integration formulas. Numerical integration error estimates. (Aitken estimation of rates of convergence.) |
4.3, 4.4 |
| |
Lecture24 (11/16) |
Composite integration formulas.Gauss quadrature. |
4.4, 4.7 |
| |
Lecture25 (11/18) |
Gauss quadrature., derivation of 2 and 3 point formulas. Error estimates. |
4.7 |
| Week9 |
Lecture26 (11/21) |
Solving linear systems of equations. Review of Gaussian elimination. |
6.1, 6.5 |
|
Lecture27 (11/23) |
Equivalence of Gaussian elimination and LU factorization. |
6.5 |
| |
Lecture28 (11/25) |
Thanksgiving holiday |
|
| Week10 |
Lecture29 (11/28) |
Construction of the LU factorization. Pivoting. Use of the LU factorization.Operation counts for Gaussian elimination (LU factorization). |
6.2, 6.6 |
|
Lecture30 (11/30) |
(Special type of matrices. Band solvers, Choleski factorization.) |
6.6 |
| |
Lecture31 (12/2) |
Review |
|
| Final |
12/8 (Thursday) |
8:00AM-11:00AM at TBA |
|
