MATH 321-03, 06 Differential Equations
Section 03: MWF 1:00pm-1:50pm
McLaury 306
Section 06: MWF 3:00pm-3:50pm
EEP 208
Instructor: Brent Deschamp
Office: McLaury 316B
Email: [email protected]
Phone: 605-394-2476
Website: http://webpages.sdsmt.edu/∼bdescham
Office Hours:
Monday 10-11am
Tuesday 9-10am, 3-4pm
Wednesday 2-3pm
Thursday
Friday 10-11am
And by appointment
Text: A First Course in Differential Equations by Dennis G. Zill, Tenth Edition.
Course Description: Selected topics from ordinary differential equations including development
and applications of first order, higher order linear, and systems of linear equations, general
solutions and solutions to initial-value problems using matrices. Additional topics may include
Laplace transforms and power series solutions. MATH 225 and MATH 321 may be taken
concurrently or in either order. In addition to analytical methods this course will also provide
an introduction to numerical solution techniques. Prerequisites: MATH 125 with a minimum
grade of C. 3 credits.
Course Outcomes: A student who successfully completes this course should be able to:
1. Identify an appropriate method and use it to solve first order ordinary differential equation.
2. Solve homogeneous and non-homogeneous higher-order ordinary differential equations.
3. Implement the use of Laplace Transforms to solve an ordinary differential equation.
4. Analyze and solve applications involving ordinary differential equations. Some examples
of applications include: circuits, vibrating systems, chemical mixing, and population
modeling.
5. Apply the techniques for solving linear systems of ordinary differential equations.
6. Implement the use of a software package to aid in solving differential equations numerically and analytically.
Grading: Grading will be different between the two sections. Be sure to read the correct column
in the following table.
1
Homework
Quizzes
Exam 1
Exam 2
Exam 3
Exam 4
Section 03
17%
15%
17%
17%
17%
17%
Section 06
0%
15%
21%
21%
21%
22%
Exams will be held during the common exam hour 7-8am on Thursdays, dates to be determined.
The final exam is scheduled for Wednesday, May 6, from 3-4:50pm.
For the purposes of this class no grade of D will be given.
Help: I am here to make sure you learn and understand the material. It is your job to let me
know when you are having difficulties. I will be glad to work around your schedule to help
you.
Students with special needs or requiring special accommodation should contact the instructor
and the campus ADA coordinator at 394-1924 at the earliest opportunity.
Technology: Maple 13 will be required. While computers are not banned from the classroom, the
only reason you should have your computer out is to take notes. If you are taking notes, your
computer screen should be down. This is a consequence of past problems, and this decision
has been made in order to improve student performance.
Homework: Homework will be handled differently between the two sections. Be careful to read
the correct section.
Section 03: Homework will be assigned and collected via WebAssign. You will need to log
in to the WebAssign website and enroll in this course. Homework will be due one week
after the material for that section is completed in class.
Section 06: Homework will be assigned regularly, but will not be collected. Assignments
will be short, but will cover the material presented. Homework is a learning tool. If quiz
and exam scores are low it is an indication that more homework should be done beyond
what is assigned.
Quizzes: Quizzes will be given regularly. They will mirror homework problems, and may be given
one week after homework for that section has been assigned. The extra time provides an
opportunity for questions. No warning of quizzes will be given. Quizzes are there to give
you an indication of how well you understand the material. If quiz scores are low it is an
indication that more homework should be done beyond what is assigned. Makeup quizzes
will only be given for those who give advance notice of a legitimate absence.
2
Freedom in Learning: Under Board of Regents and University policy student academic performance may be evaluated solely on an academic basis, not on opinions or conduct in matters
unrelated to academic standards. Students should be free to take reasoned exception to the
data or views offered in any course of study and to reserve judgment about matters of opinion,
but they are responsible for learning the content of any course of study for which they are
enrolled. Students who believe that an academic evaluation reflects prejudiced or capricious
consideration of student opinions or conduct unrelated to academic standards should contact
the dean of the college which offers the class to initiate a review of the evaluation.
All of this is subject to change.
3
The Deadly Sins of Mathematics
(Adapted from Dr. Kowalski)
If any of the following mistakes are made on a quiz or exam problem, zero points will be assigned
as a grade for that problem.
1. False Distribution
Thou shalt no distribute (or factor) anything across a sum (or difference), except multiplication.
ˆ
a
b+c
a+b
c
ˆ (a
a
a
b + c
= ac + cb
+ b)c 6= ac
6=
+ bc
– Ex1: (x + 2)2 6= x2 + 22
(x + 2)2 = x2 + 4x + 4
√
√
√
– Ex2: t + 5 6= t + 5
ˆ sin (a + b) 6= sin a + sin b
ˆ ea+b 6= ea + eb
ˆ log (a + b) 6= log a + log b
log (ab) = log a + log b
2. False Cancellation
Thou shalt not cancel any expression from a fraction, except common factors found after thou
hast factored first.
ˆ
ˆ
ˆ
ax+b
a 6= x
sin a
a
sin b 6= b
ln a
a
ln b 6= b
+b
3. False Products
Thou shalt not differentiate any product (or quotient, or composition) factor-by-factor.
ˆ
ˆ
d
dx
(f (x)g(x)) 6=
df
dx
Z
f (x) · g(x) dx 6=
dg
· dx
Z
Z
g(x) dx
f (x) dx ·
ˆ (f ◦ g)(x) 6= f (x)g(x)
(f ◦ g)(x) = f (g(x))
df
dg
d
dx ((f ◦ g)(x)) 6= dx · dx
4
4. Trignorance
Thou shalt not plead ignorance of trigonometric (or inverse trigonometric) functions at standard values. Thou shalt also know the standard trigonometric and inverse trigonometric
derivatives and integrals.
ˆ cos (2x)·2 6= cos (4x)
ˆ tan−1 (x) 6= cot x
(tan x)−1 = cot x
ˆ
d
dx (sec (2x))
d
dx (sec (2x))
6= sec · tan (2x)
= 2 sec (2x)· tan (2x)
5. Other common sins
ˆ ln 0 6= 0
ln 1 = 0
ˆ ea ln b 6= ab
a
ea ln b = eln b = ba
√
ˆ −9 6= 3
√
−9 = 3i
Z
1
ˆ
ln (x) dx 6=
x
5
MATH 321 Differential Equations
Homework Assignments (Zill, Tenth Edition)
Section
Page
Problems
1.1
Definitions
10
1–8, 13, 14
2.2
Separable Equations
51
1–7, 23
2.3
Linear Equations
61
1–10
3.1
Linear Models
90
3, 5, 9, 17
2.5
Bernoulli ODE
74
15–22
-
Reducing Second Order Equations
see below
Exam 1
4.3
Homogeneous Equations
137
1–19 (odd)
4.2
Reduction of Order
131
1–4, 9–11
4.4
Method of Undetermined Coefficients
147
2–11, 21–24
4.6
Variation of Parameters
161
2, 3, 5, 6, 10, 12
5.1
Linear Models
205
21, 25, 29
7.1
Laplace Transform
280
11–18, 25, 28, 30–32 (use table)
7.2
Inverse Transforms
288
[1–9 (odd), 11–13, 16, 17, 20, 23–29 (odd), 30]
[31, 32, 35, 37, 39]
7.3
Operational Properties I
297
[27–30], [37–39, 41–43, 45, 47, 49–54, 63–68]
7.5
Dirac Delta Function
315
4, 5, 8, 10, 11
8.1
Linear Systems
332
1, 7, 11
8.2
Homogeneous Linear Systems
346
[1–3, 11], [33–35, 41], [22–25]
8.3
Nonhomogeneous Linear Systems
354
12, 15, 21–24
2.6
Euler’s Method
79
1–4
9.2
Runge-Kutta Methods
371
3–6
9.4
Higher-Order Methods
379
1–4
Exam 2
Exam 3
Exam 4
Additional problems for 2.5. Solve the following ODE’s by reducing the ODE to first order.
1.
3.
5.
t2 y 00 + 2ty 0 − 1 = 0,
y 00 + t(y 0 )2 = 0
y 00 + y 0 = e−t
t>0
2.
4.
6.
6
ty 00 + y 0 = 1,
t>0
y 00 − 2y 0 = 2e2t
t2 y 00 = (y 0 )2 ,
t>0