Lecture |
Section |
Topics |
F 9/29 |
. |
General course overview |
M 10/1 |
2.1 |
Background
for programming projects. Introduction to the solution of nonlinear equations. |
W 10/3 |
2.1 |
The bisection
method. |
F 10/5 |
2.1 |
Convergence
estimates for the bisection method. Errors and residuals. |
M 10/8 |
2.3 |
The Newton-Raphson
method. |
W 10/10 |
2.3 |
The secant method. |
F 10/12 |
2.4 |
Error analysis for
Newton-Raphson and the secant method. Rates of convergence. |
M 10/15 |
2.4 |
Stopping criterion.
Relationship between errors and residuals. Comparison of iterative methods.
Global convergence properties. |
W 10/17 |
1.2 |
Computer representation
of numbers. Limitations imposed by integer representation. |
F 10/19 |
1.2 |
Limitations imposed
by floating point representation. Unit roundoff. |
M 10/22 |
1.2 |
Errors in floating
point arithmetic computations; catastrophic cancellation. |
W 10/24 |
3.1 |
Polynomial Interpolation.
Method of undetermined coefficients. (Vandermonde matrix.) |
F 10/26 |
3.2 |
Newton Divided differences. |
M 10/29 |
--- |
MIDTERM 1. |
W 10/31 |
3.1, 3.2 |
Lagrange Interpolation
Formula. Interpolant existence and uniqueness. |
F 11/2 |
3.2 |
Polynomial interpolation
error estimates. (Error estimate for equispaced nodes*.) |
M 11/5 |
3.2 |
Runge phenomenon.
(Derivation of Newton dividend difference formulas.) |
W 11/7 |
4.1 |
Numerical differentiation.
Error estimates for numerical differentiation formula. |
F 11/9 |
4.2 |
Asymptotic error
expansions for numerical differentiation. (Richardson extrapolation.) |
W 11/14 |
4.3, 4.4 |
Numerical integration.
Newton-Cotes formulas. Composite integration formulas. |
F 11/16 |
4.3, 4.4 |
Numerical integration
error estimates. (Aitken estimation of rates of convergence.) |
M 11/19 |
--- |
MIDTERM 2. |
W 11/21 |
4.7 |
Gauss quadrature,
derivation of 2 and 3 point formulas. Error estimates. |
M 11/26 |
6.1 |
Solving linear systems
of equations. Review of Gaussian elimination. |
W 11/28 |
6.5 |
Equivalence of Gaussian
elimination and LU factorization. |
F 11/30 |
6.2 |
Construction of
the LU factorization. Pivoting. Use of the LU factorization. |
M 12/3 |
6.1 |
Operation counts
for Gaussian elimination (LU factorization). |
W 12/5 |
6.6 |
(Special type of
matrices. Band solvers, Choleski factorization.) |
F 12/7 |
. |
Review |