Math 215, Winter 2014
Midterm 2, February 27
Name:
SID:
Instructor:
Section:
Instructions
The total time allowed is 60 minutes.
The total score is 50 points.
Use the reverse side of each page if you need extra space.
Show all your work. A correct answ
Math 215, Winter 2014
Midterm 1, January 30
Name:
SID:
Instructor:
Section:
Instructions
The total time allowed is 60 minutes.
The total score is 50 points.
Use the reverse side of each page if you need extra space.
Show all your work. A correct answe
Math 215, Winter 2014
Midterm 3, March 27
Name:
SID:
Instructor:
Section:
Instructions
The total time allowed is 60 minutes.
The total score is 50 points.
Use the reverse side of each page if you need extra space.
Show all your work. A correct answer
HOMEWORK 1 SOLUTIONS: MATH 215
Problem 1: In each case, solve for y (t):
a. y + 2y = 0 with y (0) = 1.
b. y + 2y = 3et with y (0) = 2.
1
c. y 2y = te2t with y ( 4 ) = 0.
d. ty 2y = t3 sin t with y ( ) = 0.
3
e. t3 y + 8t2 y = e(t
)
with y (1) = 1.
Solutio
HOMEWORK 4: MATH 215 Winter 2014
1. Find the solution to the initial value problems:
(i) y + 4y + 5y = 0 with y(0) = 1, y (0) = 0.
(ii) y + 2y + 2y = 0 with y(/4) = 2, y (/4) = 2.
2. Find the solution to the initial value problems:
(i) y 2y 3y = 3e2t w
HOMEWORK 2: Math 215 January 2014
1. Find the solution y(t) to
y =
3 2
1 2
y,
with y(0) =
3
3
.
Also, describe the behavior of the solution for large t.
2. Solve the following system of dierential equations with initial conditions and sketch the solution.
HOMEWORK 2: Math 215 January 2014
1. Find the solution y (t) to
3 2
1 2
y=
y,
3
3
with y (0) =
.
Also, describe the behavior of the solution for large t.
Solution:
The characteristic polynomial is
2 + 5 + 4 = 0
with roots 1, 4. The eigenvector equation fo
HOMEWORK 6: MATH 215
Problem 1: An LRC circuit has inductance 0.5H, resistance 1, and capacitance 1F .
(a) What is the transfer function H(s)?
(b) What is the impulse response h(t)?
(c) If the input voltage is f (t) = 3 (t), what is the output y(t)? Give
HOMEWORK SHEET 5: MATH 215
1.
(a) The functions sinh(t) and cosh(t) are dened by
sinh(t) =
1 t
e et ,
2
cosh(t) =
1 t
e + et .
2
Prove that sinh(0) = 0, cosh(0) = 1, cosh(t) = cosh(t), sinh(t) = sinh(t) and
d
sinh(t) = cosh(t) ,
dt
d
cosh(t) = sinh(t) .
Math 215 - Homework #3 Due Friday, February 14, 2014.
1. A competing species model. A stylized model of competing species with population densities
x(t) and y(t) is given by
dx
= x(1 x y),
dt
1 y 3x
dy
=y
dt
2 4
4
.
First, nd all four critical points. T
HOMEWORK 1: MATH 215
Due in class on Monday, Jan 20th
Show all relevant work for credit. You will be marked for your work and your answer as appropriate.
Working with others is encouraged but you must submit your own work and identify who you worked with