# Methods in Applied Math -- 2950

## Textbook

Principles of Applied Mathematics, James Keener.

#### Missing pages from book Errata Hints to the exercises

The grades are based on the homework which will be given roughly weekly. It is usually due the Friday a week after it was assigned.

## Syllabus

• Week 1 Chapter 1.1,1.2,1.3
• Homework 1 Due Sept 6 1.1:1,2,3,6,9c; 1.2:3,4;1.4:4
• Here is the list of problems from the new edition of the book

• Week 2 Chapter 1.4,1.5 Homework 2 Due Sept 13 Here it is!
• Week of Sept 9: Chapter 2.1 (no measure thy, though), Chapt 2.2.1,2.2.3,2.2.4,3.1
• Homework 3 Due Friday sept 27
• 2.2 3 Find a polynomial whose Fourier representation on x in [0,2 pi] has coefficients that decay like 1/n^3
• 2.2 4 Find the best L1 linear approximation of exp(x) on [0,1]...(see the rest in Keener)
• 2.2 8 b (about Cheyshev polys)
• 2.2 9 (orthonormal poly)
• 2.2 14 (convolution theorem)
• 3.1 1
• 3.2 3abc
• Week of Sept 16. There will be no class Friday 9/20. We will do Chapt 3.2 and 3.3
• Week of Sept 23. More Chapter 3
• Week of Oct 7 Chapter 4.2,4.3. There will be no class on Wednesday Oct 12
• Week of Oct 14 Rest of Chapt 4, 5.1,5.2
• HOMEWORK 4 Due Oct 18
• chapter 3.4 1a,2 abcd,6
• 3.6 2,3,5
• chapter 4.1 1a,2,3,5,6,9
• suppose f(x) is continuous and differentiable at 0 and f'(0) is nonzero. evaluate delta(f(x)) in terms of delta(x) in the sense of distributions. Suppose that the same about f(x) but that it is also C^2. Compute delta'(f(x)) is the sense of distributions.
• Homework 5 DUE NOV 1
• 4.2: 1,3,4
• 4.3: 1,3,5,9,10
• 5.1: 1,2,9,10,12
• 5.2: 7,8
• Homework 6 DUE NOV 8
• Week of November 4:Chapt 11.3-11.4
• Week of November 11:Chapt 11.5,12.1
• Week of November 18 Finish chapt 11 and start chapt 12
• Homework due on November 22: 11.3:2,5,6,7a ,11.4:3a,5, 11.5: 1,3 (Only find conditions for the linearized part Hopf - dont do the nonlinear calcs.

Find parameters A,B,C such that there is more than one periodic solution to :

u'' + epsilon u' [ A + B u^2 + C u^4] + u = 0

• Week of November 25: No classes
• Week of December 2: Chapter 12
• Week of December 9: Chapt 12 and 10.3
• Last Homework Due Friday Dec 13 12.1 3,5; 12.2 5; Try this singular perturbation problem.

eps y'' + y' + y(1-y) =0

y(0)=y(1)=1/2