Lectures: MWF 11:00-11:50am, MS 5137 Instructor: Jianlin Xia Email: Office: Math Sciences 7370 Office Hours: MW 12-1pm, or by appointment Discussion Section: T 11:00-11:50am, MS 5137 Teaching Assistant: Aleka McAdams Email: Office: Math Sciences 3973 Office Hours:
| HW Assignments | Due date | Solutions and codes | |
| 1 | p.255: 1(d); p.263: 1(b,c), 11, 12, 15 | Wed, Jan 16 | hw1sol, hw1codes |
| 2 | HW2 | Wed, Jan 23 | hw2sol, hw2codes |
| 3 | p.341: 7(b), 10, 15(a); p.301, 6(a), 12. | Wed, Jan 30 | hw3sol, hw3codes |
| 4 | p.323: 2(a), 3(b); p.333, 1, 2, 4(a)(d), 8 | Wed, Feb 6 | hw4sol, hw4codes |
| 5 | p.334: 7; p.661, 3(a,c) (write Aw=b only) | Wed, Feb 13 | hw5sol |
| 6 |
p.667: 1(write the nonlinear system & formulas for Newton's method only); p.427, 1(a,c), 2(a,c) 4(c), 7, 9(a, c) |
Wed, Feb 20 | hw6sol (updated: 3/13) |
| 7 | p.449: 2(c), 4(c), 9(a), 17(a,c), 21(b)(apply to Exercise 2(c), not 1), 22 | Wed, Feb 27 | hw7sol |
| 8 | HW8 (one problem moved to HW9: 10:45am, Mon, 3/3) | Wed, Mar 5 | hw8sol |
| 9 | HW9 (updated: Wed, 3/5) | Wed, Mar 12 | hw9sol |
| Week |
Date |
Section
|
Topics
|
| 1 | 1/7 |
.
|
General course overview
|
| 1/9 |
5.1
|
Background for programming projects. Introduction to
the solution of initial value problems.
|
|
| 1/11 |
5.2
|
Derivations of Euler's method. Definition of
convergence. |
|
| 2 | 1/14 |
5.2, 5.3
|
Error bounds and asymptotic error estimate for
Euler's method. Local truncation error, global
error. |
| 1/16 |
5.2, 5.3, 5.4
|
Convergence proof for Euler's method. Derivation of
Runge-Kutta methods. |
|
| 1/18 |
5.4
|
Runge-Kutta methods cont. Derivation of the general
second order Runge-Kutta methods. |
|
| 3 | 1/21 | Holiday | |
| 1/23 |
AS
|
Timestep estimation. Model problem analysis;
intervals of absolute stability. |
|
| 1/25 |
AS
|
Timestep estimation for general equations.
|
|
| 4 | 1/28 |
5.11
|
Implicit methods (Trapezoidal rule, Backward Euler).
Comparison of ODE methods. |
| 1/30 |
5.11
|
Implicit methods. Solving the implicit equations.
Stiff differential equations. |
|
| 2/1 |
5.6
|
Overview of multistep methods.
|
|
| 5 | 2/4 |
5.9
|
Numerical methods for systems of ODE's.
|
| 2/6 |
5.9
|
Results on numerical methods for systems;
convergence results, error bounds, asymptotic error
estimates. Regions of absolute stability.
|
|
| 2/8 |
11.3
|
Two point boundary value problems. Finite difference
approximation. |
|
| 6 | 2/11 |
7.1, 11.3
|
Review of vector and matrix norms. Error estimates
for linear two-point boundary value problem.
|
| 2/13 |
.
|
Midterm
|
|
| 2/15 |
11.4
|
Midterm discussion. Programming considerations for
two point boundary value problems. |
|
| 7 | 2/18 | Holiday | |
| 2/20 |
7.3
|
Iterative methods for the solution of linear systems
of equations. Gauss-Jacobi. |
|
| 2/22 |
7.3
|
Iterative methods cont. Gauss-Seidel. Error analysis
for iterative methods. |
|
| 8 | 2/25 |
7.1, 7.3, 7.4
|
Error analysis for iterative methods cont.
Relationship between error and the residual.
Stopping criterion. |
| 2/27 |
7.3, 7.4
|
Convergence results for iterative methods. Condition
number. |
|
| 2/29 |
8.1
|
Discrete least squares approximation. Construction
of the normal equations. |
|
| 9 | 3/3 |
8.1, DLS
|
Derivation of the normal equations. Matrix/vector
formulation of the discrete least squares problem.
|
| 3/5 |
DLS
|
Using the QR decomposition to solve normal
equations. Relation of QR to Gram-Schmidt.
|
|
| 3/7 |
8.5
|
Introduction to discrete Fourier approximation.
|
|
| 10 | 3/10 |
8.5
|
Fourier approximation cont. Complex form of the
discrete Fourier approximation. |
| 3/12 |
8.6
|
The fast Fourier transform.
|
|
| 3/14 |
.
|
Review
|
|
| 3/20 | Final (Thursday, March 20, 2008, 3:00 PM - 6:00 PM) |
