Math 2171 (Differential Equations) Graded Homework 1
DUE 09/02/09
1. (Direction Field.) (a)=5 points, (b)=3 points, (c)=2 points.
(a) Let p(t) represent the population (in thousands) of a certain species. Over the square
0 t 4, 0 y 4, neatly sketch the di
Final Examination - Math 374, Frank Thorne ([email protected])
Monday, May 4, 2015
Please work without books, notes. calculators, or any assistance from others. Unless otherwise
stated, justication is required for full credit.
(1) (6 points, justication
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Midterm Examination 1 - Math 374, Frank Thorne ([email protected])
Wednesday, February 18, 2015
Please work without books, notes, calculators, or any assistance from others. You dont need
to justify your answers except where noted; however, wrong answers
Midterm Examination 2 - Math 374, Frank Thorne ([email protected])
Wednesday, March 27, 2015
Please work without books, notes, calculators, or any assistance from others.
There are five questions. In each case give a proof by mathematical induction regul
Quiz 6 - Math 374, Frank Thorne ([email protected])
Monday, March 2, 2015
Prove, using mathematical induction, that
n+1
X
i 2i = n 2n+2 + 2,
i=1
for all integers n 0.
Solution. For n = 0, the statement says that
1
X
i 2i = 0 20+2 + 2,
i=1
i.e., that 2 =
Math 2171 (McGoff ): Practice Exam 2
Name:
I have adhered to the UNC Charlotte Code of Student Academic Integrity in completing
this exam. Sign below.
Write clear answers that have good grammar and consist of complete sentences. Show all
of your work. The
Math 2171 (McGoff ): Practice Exam 3
Name:
I have adhered to the UNC Charlotte Code of Student Academic Integrity in completing
this exam. Sign below.
Write clear answers that have good grammar and consist of complete sentences. Show all
of your work. The
Math 2171 (McGoff ): Practice Exam 1
Name:
I have adhered to the UNC Charlotte Code of Student Academic Integrity in completing
this exam. Sign below.
Write clear answers that have good grammar and consist of complete sentences. Show all
of your work. The
Quiz 11 - Math 374, Frank Thorne ([email protected])
Monday, April 20, 2015
1. (a) How many 9-bit strings contain exactly seven 1s?
Solution. Out of nine places, you must pick 7 of them to contain 1s, and the other two
will contain 0s. The answer is
9
Quiz 4 - Math 374, Frank Thorne ([email protected])
Monday, February 9, 2015
(1) Let D be the set of all USC students, let M (s) be s is a math major, let C(s) be s is a
computer science student, and let E(s) be s is an engineering student. Express each
Math 2171 (Differential Equations) Graded Homework 2
DUE 09/23/09
1. (Linear and Separable First Order IVPs.) (5 points each). Solve the following initial value
problems. Problems (a)-(c) can be solved explicitly, but leave your solution to part (d) in
im
DIFFERENTIAL EQUATIONS. MATH 2171-090
O. SAFRONOV
This course consists of the three parts:
1. First order equations
2. Second order equations
3. Laplace transforms
We are going to use the textbook Fundamentals of Differential Equations
by Nagle, Saff, and
DIFFERENTIAL EQUATIONS
(Due: the 19th of October)
Find a particular solution of the given equation
1.
y 00 + 3y = 7e2x .
2.
y 00 y 0 + y = x2 2x + 5.
3.
y 00 + 2y 0 + 2y = 4(x + 1)ex .
Solve the initial value problems
4.
y 00 + y = x, y(0) = 0, y 0 (0) =
Homework assignment 1
1. Find the values of the parameter r for which the function y = erx is a
solution of the equation
y 00 11y 0 + 30y = 0.
2. Find the values of the parameter r for which the function y = ex sin(rx)
is a solution of the equation
y 00 2
For most springs this force is directly proportional to the displacement y and is thus given by
where the positive constant k is known as the stiffness and the negative sign reflects the opposing nature
of the force. Hookes law, as equation (1) is commonl
This case arises when we consider massspring oscillators vibrating freelythat is,
without external forces applied. Equation (2) is called the homogeneous form of equation
(1);() is thenonhomogeneity in (1).
Example 4
Find the general solution of (4) 3 + 2