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
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)
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Aug. 28, 2013
Circuit Theory Review
I1 , V1
I3 , V3
I2 , V2
A
Kirchoffs First Law states that the current into a node mus
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Sept. 6, 2013
Conservative Systems
We also examined the case where
x = y
=
y = V 0 (x)
H = V (x) +
y2
+ C.
2
In this case
MATH 342-010
Prof. D. A. Edwards
Dierential Equations with Linear Algebra II
Nov. 11, 2013
The Hessian Matrix
We derived in class that the origin was a local minimum for
f (x, y) = sin(x2 + 3y 2 ).
He
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Sept. 9, 2013
The Hopf Bifurcation
In class, we discussed the solutions of the following system:
x = x y x(x2 + y 2 ),
y
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Oct. 16, 2013
Bessel Functions
Two linearly independent solutions to the Bessel equation of order
z2
dy
d2 y
+z
+ (z 2 2
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Nov. 18, 2013
Fourier Series
We derived in class that the Fourier series for the function
f (x) = (x L)2 (x + L)2
is give
MATH 342-010
Prof. D. A. Edwards
Dierential Equations with Linear Algebra II
Nov. 11, 2013
Quadratic Forms
The quadratic form
Q(x) = 3x21 + 2x1 x2 + 3x22
can be written as
Q(y) =
4y12
+
2y22 ,
y = [x]
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Oct. 21, 2013
Proof Techniques
In this class, you will be asked to prove facts about vectors and matrices. Providing
an e
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Sept. 30, 2013
Simple Step Forcing
Graphed below is the forcing function f (t) = 1 2u (t) for t [0, 2].
f
1
0.5
t
0
1
2
3
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Oct. 9, 2013
Series Solutions
Consider the equation
y 00 y = 0.
The solution y1 with y1 (0) = 1, y10 (0) = 0 is cosh x, w
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Oct. 4, 2013
Dirac Forcing
Consider the equation
V
V
+ + V = (t 10),
10
5
V (0) = 0,
V (0) = 15.
Here is a graph of the s
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Nov. 20, 2013
Sine and Cosine Series
We derived in class that the Fourier cosine series for the function
f (x) = x2 cos x
MATH 342-010
Prof. D. A. Edwards
Differential Equations with Linear Algebra II
Sept. 6, 2013
Hamiltonian Systems
In class, we discussed the solutions of the following system:
H
,
y
H
y =
,
x
and note
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
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
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 th
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
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
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
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.
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)
N
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 approxima
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
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 se
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
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
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 55
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" - 2