MATH 342 Fall 2009
Differential Equations with Linear Algebra II Due September 11, 2009
Homework 1
Section 5.1 1. Page 301, number 2 2. Page 301, number 5 3. Page 302, number 9 4. Page 302, number 14 5. Page 302, number 29 6. Page 302, number 37 7. Comput
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due September 25, 2009
Homework 3
Section 6.1 (Edwards and Penney) 1. Page 381, number 5 2. Page 382, number 16 3. Page 382, number 24 4. Consider the system = (a) (b) X
Sketch the phase
MATH 342 Fall 2009
Differential Equations with Linear Algebra II Due October 2, 2009
Homework 4
Section 4.2 1. Page 197, number 3 2. Page 197, number 7 3. Page 199, number 14, except use the bases [x2/2, 1-x, 1] and [x, 1]. For parts (a)(d), use the matri
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due October 9, 2009
Homework 5
Edwards and Penney Section 7.1 1. Calculate the Laplace transform of the following functions. Use the definition, not the table. (a) coswt (b) sinwt (c) ts
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due October 16, 2009
Homework 6
Edwards and Penney Section 7.4 1. Page 481, numbers 17 and 20 Section 7.5 2. Page 491, number 22 3. (a) Find the Laplace transform of (t 1)2u2(t). (b) Fin
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due October 26, 2009
Homework 7
Edwards and Penney Section 8.1 1. Page 516, numbers 4, 5 2. Page 516, number 14 3. Page 516, numbers 16 and 17 4. Page 516, number 22 5. Page 516, number
MATH 342 Fall 2009
Differential Equations with Linear Algebra II Due November 2, 2009
Homework 8
Section 8.2 1. Page 527, number 26 2. Page 527, number 27 3. Page 527, number 30 4. The equation y" - 2xy' + y = 0 - < x <
where is a constant, is known as t
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due November 9, 2009
Homework 9
Edwards and Penney Section 8.3 1. Page 543, number 34 2. Page 543, number 35 Section 8.4 3. Page 559, number 4 4. Find the first four non-zero terms of th
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due November 23, 2009
Homework 11
Leon Section 5.4 1. Page 252, number 2 2. Page 254, number 17 3. Page 254, number 29 4. Which of the following are inner product spaces? (a) (b) (c) Rn
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due November 30, 2009
Homework 12
Leon Section 5.6 1. Page 281, number 3 2. Page 282, number 5 3. Page 282, number 12 4. Construct a QR decomposition for the given matrix: A= 5. Use the
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due December 9, 2009
Homework 13
Edwards and Penney Section 9.2 1. Page 594, number 5 2. Page 594, number 11 3. Find the Fourier series for the given function and sketch the graph for th
MATH 342-010 Fall 2009
Differential Equations with Linear Algebra II Due December 2, 2009 Project
(Least Squares Circle) The parametric equations for a circle with center (3, 1) and radius 2 are x = 3 + 2cost y = 1 + 2Sint Set t = 0: .5: 6 and use MATLAB
MATH 342 010 Differential Equations with Linear Algebra, October 28, 2009
Series solutions
Consider the equation y - y=0
The solution y1 with y1 (0) = 1, y1 (0) = 0 is cosh x The first three approximations to the series are given by y1 1 y1 1 + x2 /2 y1 1
MATH 342-010 Differential Equations with Linear Algebra, November 29, 2009 Fourier Series
The Fourier series for the function f(x)=(x L)2(x + L)2 is given by
f(x)= 8L4/15 48L
4
/4
= =1
1 ncos(nx/L)
Note that f(x)is smooth in its domain.
Above are plotted
MATH 342-010 Dierential Equations with Linear Algebra Oct. 9, 2009
Dirac Forcing
Consider the equation d2V/dt2 + (dV/dt)/5 + V = (t 10) V(0) = 0, dV/dt (0) = 15 Here is a graph of the solution
V(t)vs. t. Note the extra kick the system receives at t = 10.
MATH 342-010 Sep 16 2009
Dierential Equations with Linear Algebra II Sep
Phase Plane: Real Eigenvalues
For the system
= the solution is
x
x = c1e5t
+ c2e
5t
Since we have one positive and one negative eigenvalue, we have a saddle point, as shown below. No
MATH 342-010 Dierential Equations with Linear Algebra II 2009
October 7,
Simple Step Forcing
Here is a graph of the solution for (t 0, 4) of d2y/dt2 + y = f(t), y(0)= dy/dt (0) = 0.
Here is a graph of dy/dt vs. t for the same range. Again, there are no di
MATH 342-010 Fall 2009 Edwards and Penney
Differential Equations with Linear Algebra II Due September 18, 2009
Homework 2
Section 5.2 1. Page 316, number 33 2. Find all eigenvalues and eigenvectors of the given matrix
3. Page 317, number 41 4. Show that t
Homeworks (Math 342)
L: Linear Algebra, by S. Leon (8th Edition)
E: Dierential Equations, by Edwards & Penney (4th Edition)
Note: Detail your work to receive full credit
Homework#1: (due Wed Sep 21)
Sec. 3.1 (L): 10, 13 (list axioms which fail to hold)