Differential Equations
Overview: MA 264 is a three credit first course in
differential equations for
students majoring in mathematics, engineering, chemistry, and physics. Topics
include first and second order differential equations , mathematical models ,
numerical methods involving differential equations, systems and phase plane
analysis, theory of higher order linear differential equations, and the Laplace
transform and applications to solving differential equations.
Prerequisites: MA 261 or equivalent preparation with a grade of C or
higher.
Textbook: Fundamentals of Differential Equations (Seventh Edition) by R. K.
Nagle, E. B. Saff, and A. D. Snider, published by Pearson Education, Inc., 2008.
Course Goals:
• classify differential equations by order , linearity, and homogeneity;
• solve certain classes of first order ODEs (separable, linear, exact,
homogeneous, Bernoulli, and equations with linear coefficients );
• solve second and higher order ODEs with constant coefficients;
• solve differential equations numerically using Euler ‟s method;
• use direction fields/phase plane for qualitative analysis of the integral
curves
(it may include equilibrium solutions and their classifications).
Homework: Homework problems will be taken from the Exercise Set following
each
section of the textbook. Doing daily assignments is essential to being
successful
in this course. Class time will be devoted to questions concerning
difficulties with
homework problems. Keep in mind that sufficient time spent on
these assignments
(12 hours daily) is excellent preparation for quizzes and
exams.
Students with Disabilities: If you are a student with a
documented disability
who will require academic/classroom accommodations in this
course, please register
with the Coordinator of Services for Students with
Disabilities in the Student
Support Services Office located in the Student Union
and Library Building (SUL),
Room 341, phone numbers : 2199892455,
2199892454(voice/TTY) or 219989
2920.
Extra Help: See me in my office and work with other students.
Academic Honesty: The following is an Honor Code and an Honor Pledge to
which
all Purdue University Calumet Students must adhere: “I understand that
academic
dishonesty will not be tolerated at Purdue University Calumet. I am here
to
learn. Through learning, I will strive to become a better person and a more
valuable contributor to society. I understand that dishonesty in the classroom,
through cheating, plagiarism or other dishonest acts defeats this purpose and
disgraces the mission and quality of a Purdue University Calumet education.
Therefore, I make the following pledge: „In accordance with the honor code, I
will
not engage in dishonesty in my academic activities, and I will not tolerate
such
dishonesty by other students.'”
Civility: Purdue University Calumet places a priority on student learning. We
value
the inherent worth and dignity of every person, thereby fostering a
community of
mutual respect. We believe that in order to achieve these ideals,
all Purdue
University Calumet students are expected, while in the role as
student or
representative of the university, to exhibit and practice civil
behaviors, defined as
behaviors that:
1. Respect faculty, staff, fellow students, guests, and all university property,
policies, rules and regulations
2. Take responsibility for one‟s choices and actions
3. Accept consequences of one‟s inappropriate choices and actions
4. Communicate in a professional and courteous manner in all forms, and at all
times , whether verbal, nonverbal or written
Lecture Schedule
(subject to small changes without prior notice)
Date 
Section 
Homework 
Tue 09/01

1.1 Background
1.2 Solutions and Initial Value Problems 
Section 1.1: 112, 13
Sec. 1.2: 1, 2, 7, 10, 21 
Thu 09/03 
1.3 Direction Fields 
Section 1.3: 1, 5, 8, 11 
Tue 09/08

Homework 1 due & Quiz
1.4 The Approximation Method of Euler 
Section 1.4: 4, 6, 11, 15

Thu 09/10

2.1 Motion of a Falling Body
2.2 Separable Equations 
Sec. 2.2: 3, 6, 10, 17, 24

Tue 09/15 
2.3 Linear Equations 
Sec. 2.3: 2, 4, 8, 14,20 
Thu 09/17 
Homework 2 due & Quiz
2.4 Exact Equations
2.5 Special Integrating Factors 
Sec. 2.4: 18, 10, 22, 29
Sec. 2.5: 7, 11, 14 
Tue 09/22 
2.6 Substitutions and Transformations 
Sec. 2.6: 18, 10, 18, 22, 30, 42 
Thu 09/24 
EXAM I (from Chapters 1 and 2) & Homework 3 due 

Tue 09/29

3.1 Mathematical Modeling
3.2 Compartmental Analysis 
Sec. 3.2: 2, 5, 6, 8, 14

Thu 10/01

3.3 Heating and Cooling of Buildings
3.4 Newtonian Mechanics 
Sec. 3.3: 2, 4, 8
Sec. 3.4: 1, 2, 4, 6, 9 
Tue 10/06

Homework 4 due & Quiz
4.1 The MassSpring Oscillator 
Sec. 4.1: 3, 5, 8

Thu 10/08

4.2 Homogeneous Linear Equations: The General
Solution
4.3 Auxiliary Equations with Complex Roots 
Sec. 4.2: 2, 4, 7, 14, 20
Sec. 4.3: 3, 6, 10, 21, 26 
Tue 10/13

Homework 5 due & Quiz
4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients 
Sec. 4.4: 2, 11, 14, 17, 20 
Thu 10/15 
4.5 The Superposition Principle and Undetermined
Coefficients Revisited 
Sec. 4.5: 1, 4, 7, 10, 18, 26 
Tue 10/20 
4.6 Variation of Parameters 
Sec. 4.6: 2, 4, 6, 12, 16 
Thu 10/22 
EXAM II (from Chapters 3 and 4) & Homework 6 due 

Tue 10/27

5.1 Interconnected Fluid Tanks
5.2 Elimination Method for Systems with Constant Coefficients 
Sec. 5.2: 3, 6, 14, 20, 21

Thu 10/29

Homework 7 due & Quiz
5.3 Solving Systems and Higherorder Equations Numerically 
Sec. 5.3: 2, 3, 10

Tue 11/03 
5.4 Introduction to the Phase Plane 
Sec. 5.4: 2, 4, 6, 7, 12 
Thu 11/05

Homework 8 due & Quiz
6.1 Basic Theory of Linear Differential Equations 
Sec. 6.1: 1, 3, 8, 15, 20

Tue 11/10 
6.2 Homogeneous Linear Equations with Constant
Coefficients 
Sec. 6.2: 3, 6, 12, 20, 22 
Thu 11/12

Homework 9 due & Quiz
6.3 Undetermined Coefficients and the Annihilator Method 
Sec. 6.3: 2, 4, 8, 12, 21, 32

Tue 11/17 
6.4 Method of Variation of Parameters 
Sec. 6.4: 1, 4, 7, 10 
Thu 11/19 
Exam III (from Chapters 5 and 6) & Homework 10
due 

Tue 11/24

7.2 Definition of the Laplace Transform
7.3 Properties of the Laplace Transform 
Sec. 7.2: 2, 4, 10, 14
Sec. 7.3: 3, 7, 10 
Thu 11/26 
No Class (Thanksgiving Day) 

Tue 12/01 
7.4 Inverse Laplace Transform 
Sec. 7.4: 1, 3, 5, 8 
Thu 12/03 
7.5 Solving Initial Value Problems 
Sec. 7.5: 2, 4, 7, 10 
Tue 12/08 
Project Discussions & REVIEW 

Thu 12/10

Project Discussions & REVIEW
Project deadline 

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