# 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 prepa ration 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 as signments 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
(1-2 hours daily) is excellent preparation for quizzes and exams.

Students with Disabilities: If you are a student with a documented disability
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, ph one numbers : 219-989-2455, 219-989-2454(voice/TTY) or 219-989-
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, non-verbal 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: 1-12, 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: 1-8, 10, 22, 29 Sec. 2.5: 7, 11, 14 Tue 09/22 2.6 Substitutions and Transformations Sec. 2.6: 1-8, 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 Mass-Spring 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 Unde termined 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 Higher-order 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

EMERGENCY PROCEDURE GUIDES: In the event of…
Fire…

• Know the location of the fire alarms, fire extinguishers and evacuation routes and exits.
• Evacuate when the alarm sounds.
• Help ensure everyone evacuates.
• Assist others during the evacuation.
• Call University Police (2911 if you are using a campus phone or 899.2911) if you or
others need assistance or if someone is trapped in an elevator.
Severe Weather…
• Know the location of your Storm Safe Area.
• Listen for announcements via the campus public address system .
• Help ensure everyone is aware and follows instructions.
Medical Emergency…
• Immediately call University Police (989.2911)
• Immediately call 9-911 (if you are using a campus phone or 911 if you are using a
cell phone) if an ambulance is needed.
Power Failure
• If it lasts more than a few seconds…secure your space and go to the first floor.
• Listen for announcements via the campus public address system.
• Help ensure everyone follows instructions.
• REMEMBER…emergency lighting is limited in duration…it is intended to help you

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