Engr 5A
F.Brewer
Homework #3
Due Wed at beginning of class.
Reading: Handout (especially more techniques)
Ref: Ma 5a Text
1. Find general solutions for the following linear differential equations: Hint: if you cant make
the equation into a known form, try
Engr 5A
F.Brewer
Homework #2
Due Wed at beginning of class.
Reading: Handout
Ref: Ma 5a Text, ECE 2a text
1. Consider an endless network of resistors, each 1, as shown below. Find an exact expression
for the resistance of the entire network from point a t
1.(a)
e
(b)
3
i 2 n + -
2
29 e
(c)
e
(d)
2. (a)
n: interger
5
i 2 n + atan -
2
i 2 n + -
2
=e
i n + -
4
1
i 2 n -
2
1
1
cos - i sin - = e
2
2
3 ( cos ( 2 ) + i sin ( 2 ) )
(b)
2 ( cos ( ) + i sin ( ) ) = 2
(c)
e
(d)
1
i
i(a + i)
- = - = - ( 1 + i
MA 94
F.Brewer
Homework #1
Reading: Handout
Ref: Churchill, R. V. Complex Variables and Applications McGraw Hill
1. Find polar representations for the following complex numbers:
a) i
b) 2 + 5 i
c) i
d)
1
1
cos - i sin -
2
2
2. Find rectangular represent
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #9
(last assignment)
Homework due: Wednesday, 5 December 2001
1. In class and in Demo 12 we analyzed solutions to the nonlinear ODE
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #8
Homework due: Wednesday, 28 November 2001
1. Consider the system of coupled dierential equations described by the matrix equatio
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #7
Homework due: Wednesday, 13 November 2001
1. Consider the matrix
A=
1
3
2
2
21
40
1 2
31
4
1
3
1
.
(1)
(a) Use Mathematica to nd
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #6
Homework due: Wednesday, 6 November 2001
1. Consider the following matrix:
abc
M= 0 d e
00f
(a) Form the partitioned matrix [M|
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #5
Homework due: Wednesday, 31 October 2001
1. Consider the following set of linear algebraic equations:
3x1 + 4x2 + x3 = 3
x1 + x2
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #4
Homework due: Wednesday, 24 October 2001
Note: Every student should work on the homework by himself or herself. It is ok to to g
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #3
Homework due: Wednesday, 17 October 2001
Reading: Mathematica Primer Chapter 4
1. (a) Use the DSolve function of Mathematica to
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #2
Homework due: Wednesday, 10 October 2001
Reading: Mathematica Primer Chapters 3
1. (a) Use Mathematica to plot the slope (direct
Department of Chemical Engineering
University of California, Santa Barbara
Eng 5A
Instructor: David Pine
Fall 2001
Homework #1
Homework due: Wednesday, 3 October 2001
Reading: Mathematica Primer Chapters 1-2
Note: You are strongly encouraged to do items 1
Quiz 1
1. y1(x) and y2(x) are both solutions to a linear differential equation L1, what does that imply
about
ay 1 ( x ) + by 2 ( x )
This is also a solution of L1. (Superposition of solutions for linear differential equations).
2. Find the general soluti
Differential Equations and Linear
Superposition
Basic Idea: Provide solution in closed form
Like Integration, no general solutions in closed form
Order of equation: highest derivative in equation
e.g.
d 3y
d x3
+x
dy
+ x2 y = 0
dx
is a 3rd order, non-l
Engr 5a
F.Brewer
Homework #7
Due next Wed
1. Express A-1, A2 and all powers of A as a linear combination of A and I, nd etA:
10 = A
12
2. Express A-1, A2 and all powers of A as a linear combination of A and I, nd etA:
1 0 = A
01
3. Express all powers of A
Engr 5A
F.Brewer
Homework #4
Due:Wed. at beginning of class.
Reading: Handout
Ref: Ma 5a Text, ECE 2a text
1. The following differential equation has one solution that is a polynomial in x, - nd the poly3
nomial solution: ( 2 x 3 x ) y + 4 y + 6 xy = 0
2.