Math 467 Numerical Analysis Spring 2009
Some General Links for the Text:
Post Exam 2
- Week 12
- Mon, Apr 20 Differentiation (5.1)
NOTE: We're skipping Chapter 4.
MATLAB NOTE: Skip Section 5.1.4, we do not have the symbolic toolbox for Matlab
Homework:
- p. 251-252: 1, 2, 7, 8*, 9*, 13*
- p. 253 (Matlab) 1* (Turn in a plot of the result)
(Update Apr 28: Delete problem 13. Problems 12 and 15 are
more like what we need to be able to do.)
- Wed, Apr 22: Finished Section 5.1.
- Fri, Apr 24: HW 6 DUE
- Week 13: This week: Finish up integration
- Mon, Apr 27: For HW 7:
- Write a Matlab function (diffvec.m) to differentiate a vector of function
values, . Assume they are sampled at a fixed rate h.
- p. 263: 5*, 6*, 7, 8, 10
- p. 264: 3(c,d)*, 4(c,d)*, and: Approximate the derivative
of the integrand using your Matlab code diffvec.m using 16 and 32
points on [0, pi] respectively(*).
- p. 273: Use the text's code to do exercise 8(*).
- Wed, Apr 29
- Fri, May 1: HW 7 DUE
Using Matlab's QUAD function (and perhaps an intro to ODEs)
- Week 14: Solving Differential Equations
- Mon, May 4: Intro to IVPs (Chapter 6). HW:
- Matlab's Quad routine (see previous handout)
- 1(c), p. 295
- 1(c), p. 306
- 1(c), using Runge Kutta order 4 (See below for code)
- Wed, May 6: Matlab code for IVPs
- Fri, May 8 (No homework due- Discuss any problems with homework)
Post Exam 1
- Week 7
- Wed, Mar 4: Vector and matrix norms, introduce Condition Number
- Fri, Mar 6: Finish the norms, LU decomp. and swamping.
- Week 8
- Mon, Mar 9: Using iterations to solve Ax=b; Jacobi (Section 2.5)
Homework to turn on Friday: Set 1: 1, 5, 6 (from the vector
handout), Set 2: 1, 5, 6 (matrix norm handout), Set 3: 1, 3 (condition
number handout)
- Wed, Mar 11: Jacobi and Gauss-Seidel iterations
Matlab file to split the matrix A=(D+L+U)
for Jacobi iteration (SplitMatrix.m)
You should also see Programs 2.1
and 2.2 from the text (linked above).
Example of a driver for the Jacobi iterations (JacobiExample.m)
- Fri, Mar 13: Finish Gauss-Seidel, briefly talk about multidimensional
Newton's Method to finish the material we will cover from Chapter 2.
- (Spring Break)
- Week 9
- Mon, Mar 30: Finish Newton's Method, start Interpolation. Homework
for Friday (only turn in the starred problems):
- p 99-100: 1(a), 2(a), 5*, 13(a)*, 14(a)
- p. 121-122: 1(a), 2(a)
- p. 124: 1*
- p. 137: 1(a), 2(a), 3(a)*, 4(a)
- Wed, Apr 1: Newton's Method (finish up), start Interpolation. For
homework, use Newton's Method to solve the optimization problem given
below. We will set it up in class:
(*) Maximize x+y+z subject to x^2-y^2=z and x^2+z^2=4
Code from class for the homework:
- Fri, Apr 3: HW 4 DUE. You don't need to turn in the Matlab
code, but summarize your answer on your paper with the other solutions.
- Week 10
- Mon, Apr 6: Today in-class, we discussed the error in
using the Lagrange interpolating polynomial, and began discussing
Newton's Divided Difference formulas. We ended the class by
looking at the following code:
Code from class for Section 3.1:
Homework for Section 3.1/3.2: (Turn in starred problems only)
- page 151-152: 1(a, b), 2(a,b), 3*, 9, 10* (in Matlab- plot the data and
the interpolating polynomial).
- page 153: Computer Problem 1*
- page 159: 1, 2*, 4
- Wed, Apr 8: We'll finish Newton's Divided Differences, and begin
a little in Chebyshev Polynomials if time.
Computer Code from today's session:
- Fri, Apr 10: HW 5 DUE
Here are the new
Review Questions for Exam 2 and here are Review Set 2 SOLUTIONS
Homework that was posted:
- p. 160, Exercises 5, 6
- p. 169, Exercises 1(d), 2(d), 6
- p. 170, Exercise 1 (Matlab)
- Make a piecewise defined polynomial using Matlab:
P(x)=3x-5x^2 if 0<=x<=1, 5x-x^3 if 1<=x<=2
- Week 11
- Mon, Apr 13: Matlab with Cubic Splines
- Wed, Apr 15: EXAM 2 (In-class portion, Take Home posted and Due on Monday)
- Fri, Apr 17: Finished Cubic splines- Applications to
parametric curves and antiderivatives.
Handouts from Class
Materials for Exam 1
Chapter 1
Homework heads up: Stewart Platform (Project at the end of Chapter 1).
Here is a movie of what we're talking about: Link to movie is here now