Chapter 1
Basic Concepts
What is a Differential Equation?
O Definition: An equation
involving an unknown
function and its
derivatives.
O ODE vs PDE
O The order of a differential
equation is the order of
the highest derivative
appearing in the
equation.
O
Test 4 Review
Spring 2017
1.
Find Laplace Transforms and inverse Laplace Transforms.
These will include all of the common ones we talk about in
class, including those involving the Unit Step Function and
Convolutions.
2.
Write piecewise functions in terms
Spring Mass Problems
1.
A spring with natural length 0.5 m has length 50.5 cm with a
mass of 2 gm suspended from it. The mass is initially displaced
1.5 cm above equilibrium and released with zero
velocity. Find its displacement for t > 0.
2.
A 10 kg mass
Using Laplace Transforms to Evaluate Improper Integrals
Example:
Consider the integral
t 23e2t dt . We all know how to evaluate this
0
integral using integration by parts 23 times, but probably none of us are willing
Using Convolution to Evaluate Integrals
t
Example:
Consider the integral
10 (t )7 d . We all know how to
0
evaluate this integral by multiplying the integrand out, but probably none of us are
willing to do so. Ano
Review Sheet for the Final Exam.
No Calculator
1.
Find Laplace Transforms and inverse Laplace Transforms.
These will include all of the common ones we talk about in
class, including those involving the Unit Step Function and
Convolutions.
2.
Write piecewi
DIFFERENTIAL EQUATIONS TEST 3 TOPICS SPRING 2017
HERE IS A LIST OF TOPICS TO BE ADDRESSED ON TEST 3. TO STUDY FOR
THE TEST, MAKE SURE YOU HAVE LEARNED HOW TO DO ALL OF THE
PROBLEMS IN YOUR ASSIGNED HOMEWORK, ALL OF THE EXAMPLES
DONE IN CLASS, AND MAKE SUR
DIFFERENTIAL EQUATIONS TEST 1 REVIEW SPRING 2017
HERE IS A LIST OF TOPICS TO BE ADDRESSED ON TEST 1. TO STUDY FOR
THE TEST, MAKE SURE YOU HAVE LEARNED HOW TO DO ALL OF THE
PROBLEMS IN YOUR ASSIGNED HOMEWORK , ALL OF THE EXAMPLES
DONE IN CLASS, AND MAKE SU
Cramers Rule to Solve a 2x2 Linear System for x and y :
System:
a1 x + b1 y = c1
a2 x + b2 y = c2
Solution:
Let D =
a1 b1
,
a2 b2
Dx =
c1 b1
,
c2 b2
Dy =
a1 c1
a2 c 2
If D 0 , then x =
Dx
,
D
y=
Dy
D
.
Theorem: Suppose y1, y2 ,
MAP2302 Differential Equations
Summer 2017
CRN 30368 TR 6:30-8:05 PM Room 8-248
Professor: Joseph Geil
E-mail: [email protected]
Office:
Office Phone:
Course Type:
Bld 1-330
407 582-8913
Campus
This syllabus is a contract between the student and t
Understanding the Governing Differential Equations of Spring Mass
Systems:
Preliminary Notes and Notation:
1. In this discussion, the position of the mass at time t 0 will be
given by the function x = x(t), with down being the positive
direction in the ph
Differential Equations Daily Assignments Spring 2017
Text: Schaums Outlines Differential Equations, Fourth Edition,
Bronson and Costa
Notes: The problems assigned on this page are from the Schaums Outline. Before
attempting any particular group of problem
Name:
Test 2
Do your work neatly on the test itself. Remember that you are graded on the work that is shown on the
paper, so make sure it is readable and complete.
1) Solve the DE 6 + 13 = 0.
2) Solve the DE 12 + 36 = 0; y(0)=0,y(0)=1,y(0)=-7.
1
3) Solve
Convolution and Series Circuits
Recall from earlier in the semester that an RLC series circuit is governed by the
differential equation
di
q
+ Ri + = E(t) , where L, R, and C are the inductance, resistance, and
dt
C
capacitance, i(t) is current
Spring Mass Problems 2
1.
An object is in simple harmonic motion with circular frequency
, with x(0) = x0 > 0 and x(0) = v0 > 0 . Find its displacement for
t > 0. Also, find the amplitude of the oscillation and give
formulas for the sine and cosine of th
'
MAP 2302
DE
1.
*r,"-D'b
Quiz 3
DeVoe
Given the differential equatio
", # -
(w+3)21w -27
A) Draw a phase line diagram.
[t*])/cfw_-a\=o
:
\;t u,'r xu) ; -':1 c' #
fu')
*'
?
5ou'l'c."*
#"
Y\o?t"A-
B) Label the equilibrium solutions as either a sink(stable)
MAP 2302
DE
Quiz 9
Name
DeVoe
You should be using OUR Laplace table - not the one in Appendix A. Make sure you
show all your work and reference the number of the property you are using from the
Laplace table given online.
1.
Find the Laplace of the functi
*^
Quiz 5
")al)&*
DeVoe
particular spring has a spring constant of 18 N/m. Suppose a2kgmass is hung on the
spring and is initially sent in motion with an upward velocity of L/2 meters per second, 2
meter below the equilibrium position.
L. A
A) Write down
MAP 2302
Nu-",
Quiz8
DE
I
DeVoe
You should be using OUR Laplace table - not the one in Appendix A. Make sure you show all your
work and reference.the number of the property you are using from the Laplace table given onlini.
L Find f.cfw_e2'cos(3r) using t
Differential Equations
Spring Term 2011
Course:
Text:
MAP 2302 Differential Equations (3 credit hours)
A First Course in Differential Equations (9th edition) by Zill
Instructor:
James Lang
Office: 4-235
Phone: 407-582-2490
Email: [email protected]
DE Review Exam 2 (Sections 4.1-4.4 plus 5.1)
I.
Solving linear differential equations
A)
Homogeneous equations with constant coefficients
Use y = emx and get the auxiliary eqn.
B)
Nonhomogenous equations
y = yc + yp
To get yp use the method of undetermine
DE Review Exam 3
I.
Definition and properties of Laplace transforms
A)
B)
Use the integral definition of the Laplace transform.
Apply properties in the "short" table to find transforms.
II.
Given a "new" Laplace transform formula, apply the formula to fin