Homework
Assignments: Note the
changes due to missing class 1/21.
Assignments are due by 5:00 PM of the day they are due. If it is an
exam day, then the assignment should be completed before the exam. The
exercises are on the linked pages below and several pages are grouped
together fro each assigned due date. Problems should be neat and in
order. Any changes will be noted. Do not wait to begin assignments the
night before they are due.
| HW # |
Page |
Exercises |
Due |
|
1 |
Floating-point numbers |
1, 2,
4 |
01/19 |
| |
Problems and conditioning |
1, 2,
7 |
|
|
2 |
Algorithms |
2, 3 |
01/28 |
| |
Stability |
1, 2, 4 |
|
| |
Interpolation |
1, 3 |
|
|
3 |
Computing with matrices |
1, 2,
5 |
02/07 |
| |
Linear systems |
2, 3,
4 |
|
| |
LU
factorization |
1, 2,
3 |
|
| |
Efficiency of matrix computations |
1, 2,
4, 5 |
|
| |
Row pivoting |
1, 2 |
|
|
4 |
Vector and matrix norms |
1, 2, 6 |
02/14 |
| |
Conditioning of linear systems |
1, 5 |
|
| |
Exploiting matrix structure |
1 |
|
| |
Fitting functions to data |
1, 2, 5 |
|
| |
The normal equations |
1 |
|
| |
The QR factorization |
7 |
|
|
5 |
The
rootfinding problem |
1 |
02/23 |
| |
Fixed
point iteration |
1, 6 |
|
| |
Newton’s method in one variable |
2*, 4 |
|
| |
Project 1 - World on a String |
|
03/02 |
|
6 |
Interpolation-based methods |
2, 4, 7 |
02/28 |
| |
Newton for nonlinear systems |
1, 6 |
|
| |
Quasi-Newton methods |
2 |
|
|
7 |
Nonlinear least squares |
1, 3 |
03/04 |
| |
The
interpolation problem |
2 |
|
| |
Piecewise linear interpolation |
1a, 3 |
|
|
8 |
Cubic
splines |
1a, 2a |
03/25 |
|
|
Finite differences |
2, 3 |
|
| |
Convergence of finite differences |
2, 3 |
|
| |
Numerical integration |
1c, 4, 6c |
|
|
9 |
Basics of IVPs |
1bc, 3, 4, 7 |
04/04 |
| |
Euler’s method |
1ab, 2ab |
|
|
10 |
Systems of differential equations |
1ab, 2ab, 3b |
04/11 |
| |
Runge–Kutta methods |
2a, 7b, 8 |
|
| |
Adaptive Runge–Kutta |
2 |
|
| |
Implementation of multistep methods |
1ab |
|
|
11 |
Eigenvalue Problems |
1-6 |
04/20 |
| |
Project 2 - Applications of Systems of
ODES |
|
04/25 |
|
12 |
Miscellaneous Problems
- Note change in 7 |
7-15 |
04/29 |
* Also apply the Bisection Method to this problem. Top
|