Dierential Equations.
Math 361 Fall 2013
Instructor
Dr. Mark Lammers
250 Bear Hall
Oce Hours
[email protected]
962-3958
http:/people.uncw.edu/lammersm/
MWF 2-3
Text A First Course In Dierential Equations, with Modeling Applications, Tenth Edition,
Dennis
UNCW MAT 361 Differential Equations
6.1: Definition of the Laplace Transform
Practice Propblems P315: 1, 3, 5, 7, 11, 15, 16, 21, 25
Home Work P315: 6, 15, 28
Many practical engineering problems involve mechanical or electrical
systems acted on by discont
UNCW MAT 361 Differential Equations
6.2: Solution of Initial Value Problems
Practice Problems P324: #1, 3, 5, 7, 11, 13, 15, 17, 21, 22, 25
Home Work P324: #9, 12, 16, 19
Lcfw_f (t) = F (s) =
st
e f (t)dt
0
Z
Theorem6.2.1: Suppose that f is continuous an
UNCW MAT361: Differential Equations
5.2 Series Solutions Near an Ordinary Point, Part I
Practice Problems: #1, 3, 9, 11.
HW: P259 #2, 4, 7.
Consider a second order linear equation
P (x)
X
d2 y
dy
+
R(x)y
=
0
y
=
a
+
a
(x
x
)
+
=
an (x x0 )n
+
Q(x)
0
1
0
d
Review 2 Math 361
Any term in bold face know the denition well enough to state it on the test. The denition you give should be
very similar to the one in the book or one with similar detail.
Section 4.2 Reduction of order. y2 = y1 (x)
e P dx
dx .
2
y1 (x)
MATH 361 Quiz 6
Name:
Show all work. 10 points.
1. After a mass weighing 10 pounds is attached to a 5-foot spring, the spring measures 7
feet. The system is placed in a medium that oers a damping force numerically equal to the
instantaneous velocity. Find
Review 1 Math 361
Any term in bold face know the denition well enough to state it on the
test. The denition you give should be very similar to the one in the book or one with similar
detail.
Section 1.1
order of a dierential equation,linear dierential equ
MATH 361 Quiz 5
Name:
Show all work. 5 points each.
1. Solve the Cauchy-Euler equation x2 y + 5xy + 4y = 0
2. Reduce the system of dierential equations to one involving just x(t) by elimination and
solve. YOu do not have to solve for y(t) or the constants
MATH 361 Quiz 4
Name:
Show all work. 5 points each.
1. Solve by undetermined coecients y + y = 3
2. Use variation of parameters to solve y + y = sin(x)
MATH 361 Quiz 1
Name:
Show all work. 5 points each.
1. Solve the separable equation
x2
dy
= y xy
dx
2. Solve the linear dierential equation
dy
x y = x2 sin(x)
dx
MATH 361 Quiz 2
Name:
Show all work. 5 points each.
1. Show that the equation (x y 3 + y 2 sin x)dx = (3xy 2 + 2y cos x)dy is exact and solve it
implicitly.
2. Solve the Bernoulli equation
x
dy
1
+y = 2
dx
y
MATH 361 Quiz 3
Name:
Show all work. 5 points each.
1. Given that y = ex is a solution to the de y y = 0 use reduction of order to nd the
other solution.
2. Find the general solution of y + 8y + 16y = 0
UNCW MAT 361 Differential Equations
4.1: General Theory of nth Order Linear Equations
Chapter 4: Higher Order Linear Equations
(1) L[y] =
dn y
dn1 y
dy
+
p
(t)
+ + pn1 (t) + pn (t)y = g(t)
1
n
n1
dt
dt
dt
nonhomogeneous equation
(2) L[y] =
dn y
dn1 y
dy
+
UNCW MAT 361 Differential Equations
3.2: Fundamental Solutions of Linear Homogeneous Equations
Practice Problems: P155 odd 1-25, except 19.
HW: P155: #4, 23, 25, 30, 34.
Theorem 3.2.1 Consider the initial value problem
y 00 + p(t)y 0 + q(t)y = g(t),
y(t0
MATH 361 Quiz 1
Name:
Show all work. 5 points each.
1. Solve the separable equation
dx
= 4(x2 + 1)
dt
2. Solve the linear dierential equation
dy
+ y = e3x
dx
MATH 361 Quiz 4
Name:
Show all work. 5 points each.
1. Solve the homogeneous equation y y 12y = 0 .
2. Solve the non-homogeneous equation y y 12y = e4x by undetermined coecients.