| Day |
Date |
Activity |
Assignment (due one week from assignment date, unless otherwise stated) |
| Tue | 1/13 |
Welcome/Intro |
Homework 1 (for next time):
- read pages xiii-12, and begin Homework problem set 1, p. 11, #1-8
(note these will be due Tuesday, next week).
- See
if you can get Mathematica installed on some machine of
your own, or one you have access to. If not, you'll have
to find a computer on campus where you can use
Mathematica. Once you have access, begin working through
Appendix A: Getting Started with Mathematica.
- Read on into Sections 1.3-1.5, if you're able. (We'll be talking
about it next time.)
- If you get Mathematica up and working, you might give the second
computer problem on p. 11 a try.
|
| Thu | 1/15 |
Sections 1.3-1.5 |
Make sure to finish reading sections 1.3-1.5 by next
time, when we'll wrap up chapter 1, and begin chapter 2.
I hope that you'll have read to p. 43 (through 2.2) by Tuesday next.
Homework problem set 2: p. 14, #3 (you may use the results of #1 and 2, which we
will have done in class); p. 20, #1,2,5-7.
|
| Tue | 1/20 |
Sections 1.5, 2.1-2.2; Homework problem set 1 due. |
Homework set 3 (due Thursday, 1/29):
Homework Problems:
- p. 28, #1, 4, 5, 8, 14
- p. 35, #1 (and what would be the disadvantages?), 3, 8
Computer project #1 (due 2/5): Write computer code that converts
between two arbitrary bases (any integer base between 2 and
10). Demonstrate that your code works on the following examples, and
try a few examples of your own:
- Write
 in base 8.
- Write
 in base 2.
- Write
 in base 10.
If it has some nice interface, all the better! Computer problem
#1, p. 37 describes a procedure for converting from base 10 to
base 2....
I should be able to run your program with examples of my own,
to check it.
Provide a 2-3 page description of your program, including how it
behaves on the examples, what you like about it, etc. These projects
will be posted on a website for others to view, and try.
|
| Thu | 1/22 |
Homework problem set 2 due. |
Homework set 4 (Due Tue, 2/3 -- note: I've moved the p. 54
problems to later):
- p. 42, #1, 3, 5
- p. 48, #1bcd, 2, 5, 6
|
| Tue | 1/27 |
Continuing with Chapter 2 |
No new assignment - you've got enough! |
| Thu | 1/29 |
|
Homework Set 5 (due 2/10):
- p. 54, #3, 5, 12
- p. 68, #1, 2, 3, 7, 12, 13
|
| Tue | 2/3 |
Begin Chapter 3. Please read through p. 91. |
|
| Thu | 2/5 |
Bisection and Newton's Method |
Project 1 due |
| Tue | 2/10 |
|
Homework Set 6 (due Thursday, 2/26 -- deadline extended):
- p.77 #1; use bisection to find the m=4 root.
- p.80 #1
- p.88 #2,4,7,8
|
| Thu | 2/12 |
root-finding |
|
| Tue | 2/17 |
root-finding |
|
| Thu | 2/19 |
Cold day! |
|
| Tue | 2/24 |
Exam 1 |
|
| Thu | 2/26 |
The end of root-finding |
Please read into chapter 5: pp. 169-185. Homework #7 (due
Thursday, 3/5): derive Muller's method, which generalizes the Secant
method. Given }) , we seek a root  such that =0}) .
- Given three initial guesses,
 ,  , and  ; find the unique quadratic that
passes through the three points )}) .
- Find the zeros of this quadratic (use a sensible choice of formula
for finding the roots).
- Make a sensible choice of root to replace "the oldest guess" .
- Describe how to iterate (Do it again!).
- Illustrate the method graphically, and numerically, for the
function
{=}e^x-\frac{1}{x^{2}}}) .
- Explain how Muller's method will allow us to find complex roots
with an example (e.g.
=x^4+1}) ).
|
| Tue | 3/3 |
Interpolation |
|
| Thu | 3/5 |
|
|
| Tue | 3/10 |
Spring Break |
|
| Thu | 3/12 |
Spring Break |
|
| Tue | 3/17 |
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| Thu | 3/19 |
|
Project 2 was scheduled to be due (new due date: 3/24).
Homework: due Thursday, 3/26:
- p. 178, #2, 3
- p. 181, #6
- p. 190, #1, 2, 8
- p. 221, #7, 10
|
| Tue | 3/24 |
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| Thu | 3/26 |
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| Tue | 3/31 |
|
Please read this description of Bezier splines; I'll say more about your project next time.
Homework: due Tuesday, 4/7:
- On the computer: Follow the lead of my Mathematica file
to create a Hermite cubic spline (stitched together with three
cubics) to
{=}ln(x+1)}) over the
interval  . Choose equally
spaced  values.
- Plot the difference between
 and the Hermite spline on the domain.
- Compute the approximation at
 and  and
- Use the appropriate divided difference to bound the error on each of the sub-intervals.
- p. 179, #8
- p. 190, #4, 7
- p. 221, #9, 17
|
| Thu | 4/2 |
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| Tue | 4/7 |
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|
| Thu | 4/9 |
Exam 2 |
|
| Tue | 4/14 |
Leading up to adaptive quadrature |
Homework (due 4/21):
- p. 264, #1, 3
- p. 281, #1, but do it for all three methods; 2, 15
- p. 293, #1, 4a (I'm not sure about b!), 5
|
| Thu | 4/16 |
We'll finish numerical integration with adaptive quadrature |
Please read the introductory section for ODEs (chapter 8). It's really
quite a nice introduction (reminder) about why we're interested in
solving ODEs, how to solve them analytically in a few cases, and a
history of numerical solutions (dating back to the mid 1700s).
Homework (due Thursday, 4/23):
Break my adaptive integration
code.
- What makes it fail?
- How can you improve it?
Write up very explicit problems, and suggest solutions. Two pages, typed.
|
| Tue | 4/21 |
Euler's method |
Please read 8.4 for next time. |
| Thu | 4/23 |
Taylor methods |
Please read 8.5 for next time. |
| Tue | 4/28 |
Runge-Kutta methods |
|
| Thu | 4/30 |
Review |
Project 3 due (revised due date);
Assignment for final:
Given the Initial Value Problem
- Find the exact solution.
- Approximate the solution numerically on the interval [0,1],
creating a table of estimates at each step using
 for each of the following methods:
- Euler's method
- Taylor 2
- RK-2
- Taylor 4
- RK-4
- Create a similar table, but for the absolute errors each method is making
at each step (compare to the exact solution).
- Repeat the process for
 (half the step-size).
- Use the results to estimate the order of accuracy of each
method. Do they seem to be in line with what's expected?
This will be due and handed in at the time of the final.
|
| Tue | 5/5 |
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| Thu | 5/7 |
Final Exam: 1:00-3:00 pm |
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