Math 135: Ordinary Dierential Equations
Homework 1: Second Order Dierential Equations
Due on: Fri.,Jan. 15, 2016 - 9:00 AMi
Chapter 31 : Second order linear equations
Section 15, p. 91/92 : # 3 & # 11
Math 135 Ordinary Differential Equations
Summer Session A 2013
Homework #1 Solutions
Instructions: Solve the following problems and be sure to show all of your work.
1. Finding Antiderivatives. Find t
Math 135: Ordinary Dierential Equations
Homework 4: Fourier Series
Due on: Fri. Feb. 5th, 9:00-9:50AM
Problem 1 Chapter 6: p. 256 # 2
Problem 2 Chapter 6: p. 256 # 4
Problem 3 Chapter 6: p.269 # 1
Pro
Math 135: Ordinary Dierential Equations
Homework 5: Fourier Series & Boundary value problems
Due on: Friday, Februray 12, 2016, 9:00-9:50AM
Problem 1 The function f (x) has period 2 and it is dened by
Fourier Series
Problem 1
Given the Fourier series expansion of a 2-periodic function, f (x) dened in [, ]
f (x) =
a0
+
an cos(nx) + bn sin(nx),
2
n=1
show, using trigonometric identities (or otherwise
The Dirac Delta Function
and Impulse Response
In applications, we are often encountered with linear systems, originally at
rest, excited by a sudden large force (such as a large applied voltage to an
Math 135: Ordinary Differential Equations
Homework 2: Laplace Transforms I
Due on: Fri., Jan 22, 2016, 9:00- 9:50 AM
Problem 1 Evaluate those of the following improper integrals that converge:
Z
1
(i
Math 135: Ordinary Dierential Equations
Homework 3: Laplace Transforms II
Due on: Fri. Jan. 29, 9:00- 9:50 AM
i
Problem 1
Use the Laplace transform technique to solve the following IVP:
y 6y + 9y = 0,
MAT 146
University of California
Spring 2014
Homework 1
due Friday April 11, 2014 in class
1. Stanley, Chapter 1.2
Suppose that the graph G has 15 vertices and that the number of closed
walks of lengt
135 Homework 1- Due Tuesday, October 10, in discussion section.
Homework should be written neatly and clearly explained. If it requires more than one sheet, the
sheets must be stapled. Include your na
135 Homework 2- Due Tuesday, October 17, in discussion section.
Homework should be written neatly and clearly explained. If it requires more than one sheet,
the sheets must be stapled. Include your na
135 Homework 3- Due Tuesday, October 24, in discussion section.
Homework should be written neatly and clearly explained. If it requires more than one sheet,
the sheets must be stapled. Include your na
Math 135A, Fall 2015.
Homework 3, due Th., Oct. 22
1. There are three bags: A (contains 2 white and 4 red balls), B (8 white, 4 red) and C (1 white 3
red). You select one ball at random from each bag,
Math 135A, Fall 2015.
Homework 1, due Th., Oct. 8
1. Fifteen married couples are at a dance lesson. Assume that (male-female) dance pairs are assigned
at random. (a) What is the number of possible ass
Math 135A, Fall 2015.
Homework 2, due Th., Oct. 15
1. Three tours, A, B, and C, are oered to a group of 100 tourists. It turns out that 28 tourists sign
for A, 26 for B, 16 for C, 12 for both A and B,
Math 135A, Fall 2015.
Homework 5, due Th., Nov. 12
1. Assume that weekly sales of diesel fuel at a gas station are X tons, where X is a random variable
with distribution function
c(1 x)4 0 < x < 1,
f
Math 135A, Fall 2015.
Homework 6, due Th., Nov. 26
1. A fair die is rolled twice. Compute the joint p.m.f. of X and Y , where X is the rst number rolled
and Y is the largest of the two numbers rolled.
Math 135A, Fall 2015.
Homework 4, due Th., Nov. 5
1. Roll a pair of fair dice successively, and each time observe the sum rolled. What is the probability
of getting two 7s before getting six even numb
Math 135A, Winter 2014.
Homework 7, due Tue., Dec. 3
1. Joint density of (X, Y ) is given by
f (x, y) = xex(y+1) ,
x, y > 0.
(a) Find the conditional density of Y given X = x. (b) Compute the density
NOTES ON THE EXISTENCE AND UNIQUENESS THEOREM
FOR FIRST ORDER DIFFERENTIAL EQUATIONS
I. Statement of the theorem.
We consider the initial value problem
(1.1)
y (x) = F (x, y(x)
y(x0 ) = y0 .
Here we a
Math 135-2, Midterm 1
Solutions
Note: a Laplace transform table is provided on the final page.
Problem 1
Let f (x) = x and g(x) = x2 . Compute the function h = f g.
h(x) = (f g)(x)
Z x
f (x t)g(t) dt
Math 135-2, Homework 3
Solutions
Problem 53.4
Use the methods of both Examples 1 and 2 to solve each of the following differential equations:
(a) y + 5y + 6y = 5e3t , y(0) = y (0) = 0.
(a) First, lets