MAP 2302 (Introduction to Differential Equations)
Course Syllabus Ref# 889005
MIAMI-DADE COLLEGE, North Campus
Department of Mathematics
MDC North Campus 11380 NW 27 AV Miami, FL 33167-3418
Course ID
Instructions
Reference Number&
Ref# 889005 Introduction to Differential Equations
Course Name
Semester
2015-2 (Fall 2016) T Jan 5, F Apr 22. 16 weeks 3 credit hours
Instructor Name
Dr. Manuel Caramés, Ph.D. Mathematics and Physics Associate Professor Sr.
Prereq.
MAC 2312 with a grade of “C" or better.
Textbook
Title,MyMath
Ed.
Includes
A Fir A First Course in Differential Equations, 10th edition
&Author
by Dennis G. Zill, Cengage Learning.
Calculator Policy
Students can use claculators.
Class Times/Room
M, W , F 08:00 AM to 08:50AM / 7210
Office Hours
M, W, F 09:00 AM – 09:50 AM; T, R 08:00 AM – 09:40 AM
Office Phone #
305-237-1013
Email Address
mcarames@mdc.edu
Attendance Policy
Students with 2 or more unexcused absences may be withdrawn by the instructor. Students are still responsible for withdrawing
themselves if they want to receive a “W”. Tardiness is not accepted at all. ONE SECOND
Academic Dishonesty
Students may be penalized on an assignment grade or on the overall grade in the course if they cheat. Please refer to the Student Rights
Policy
and Responsibilities Handbook for the official Academic Dishonesty
Policy.http://www.mdc.edu/policy/student_rights_and_responsibilities.pdf
ADA
In compliance with the Americans with Disabilities Act (ADA), all qualified students enrolled in this course are entitled to reasonable
accommodations. Please notify the instructor during the first week of class of any accommodations needed for this course.
Math Center
For assistance, please contact your instructor during advisement hours and/or visit the Math Center in Room 2222. For Math Center hours
of operation, call 305-237-1421.
Make-Up Policy
There is NOT Make-up tests
Grading Policy
Tentative Course
“Subject to Change with Written Notice”.
Schedule
Week # 1
1)
1.1, (1.2–reading only)
2)
2.1, 2.2
Week # 2
3)
2.3
4)
2.4
Week # 3
5)
2.5
6)
2.6 (Bernoulli eqns. only), 2.7
Week # 4
7)
Review
8)
Test #1
Week # 5
9)
3.1, 3.2
10)
3.3
Week # 6
11)
4.1.1, 4.1.2
12)
4.1.3
Week # 7
13)
4.2, 4.3
14)
4.5, 4.6
Week # 8
15)
4.7
16)
Review
Week # 9
17)
Test #2
18)
5.1, 5.2
Week # 10
19)
5.3 (5.4–reading only)
20)
6.1
Week # 11
21)
6.2
22)
6.3
Week # 12
23)
6.4.1
24)
Review
Week # 13
25)
Test #3
26)
7.1, 7.2
Week # 14
27)
7.3
28)
7.4
Week # 15
29)
7.5
30)
8.1
Week # 16
31)
Review
32)
Test #4
Course Competencies
Classify an ordinary differential equation (ODE) by order, and tell whether it is linear or nonlinear.
2)
Write a simple ODE to model a physical situation.
3)
Find the differential equation of a family of curves.
4)
Define what it means for a function to be a solution of an ODE; distinguish between explicit and implicit solutions.
5)
Understand the difference between the general solution of an ODE and a particular solution; know the relationship between
the order of an ODE and the number of essential parameters involved in the general solution; know how to use initial conditions or
boundary conditions to find a particular solution if the general solution is known.
y   f (x).
6)
Solve simple ODE's of the form
7)
State and apply the Existence/Uniqueness Theorem for first-order initial value problems.
8)
Classify and solve first-order ODE's of the following types: separable, homogeneous, exact, and linear; as well as identify and
solve ODE's that can be reduced to one of those types by means of a change of variables (particularly, ODE's that are linear in the two
variables, and Bernoulli equations.)
1
MAP 2302 (Introduction to Differential Equations)
Course Syllabus Ref# 889005
9)
Apply first-order ODE's to the solution of simple problems in physics and chemistry.
10)
State and apply the Existence/Uniqueness Theorem for linear initial value problems of order .
11)
Know the definition of linear dependence/independence of a set of functions over a given interval; use the superposition
principle to construct the complete solution of an order linear homogeneous ODE from a set of independent solutions.
12)
Use the Wronskian to test a set of solutions of a linear homogeneous ODE for linear independence.
13)
Use Reduction of Order to find a second solution of a linear homogeneous ODE if a nontrivial solution is known.
14)
Use the roots of the auxiliary equation to produce the complete solution of a linear homogeneous ODE with constant
coefficients.
15)
Use linear homogeneous ODE's to model both undamped and damped harmonic oscillation.
16)
Produce the complete solution of a non-homogeneous linear ODE with constant coefficients from a particular solution and a
complementary solution.
17)
Express a linear ODE with constant coefficients in terms of differential operators.
x k e ax cosbx or x k e ax sin bx
18)
Find a differential annihilator for any function of the form:
.
19)
Use the method of Undetermined Coefficients to solve selected non-homogeneous linear ODE's with constant coefficients.
20)
Use the method of Variation of Parameters to solve non-homogeneous linear ODE's.
21)
Apply non-homogeneous linear ODE's to the study of mechanical systems, in particular to the study of un-damped, forced
vibration.
22)
Define the Laplace transform of a function f(t), and use that definition to compute the transform of a function.
23)
Use a table of Laplace transforms to find the transform of a function f(t).
24)
Use a table of Laplace transforms to find the inverse transform of a function F(s).
25)
Apply the first shifting theorem for Laplace transforms.
26)
Use appropriate theorems to compute Laplace transforms of derivatives and integrals.
27)
Apply the above skills involving Laplace transforms to the solution of linear initial value problems with constant coefficients.
28)
Apply theorems involving the derivatives of a Laplace transform.
29)
Find the Laplace transform of a periodic function.
30)
Define and compute the convolution of two functions; apply the convolution theorem.
31)
Use the unit step function to describe a piecewise-continuous function, and use the second shifting theorem to find the
Laplace transform of that function.
32)
Apply the above skills involving Laplace transforms to the solution of linear initial value problems with constant coefficients
and periodic or piecewise-continuous driving functions.
33)
Use the method of Taylor series to write an approximating polynomial solution of an initial value problem.
34)
Use a recursion formula to find the general term of a power series solution of an ODE.
35)
Identify the singular points in the complex plane of an ODE with polynomial coefficients, and know the significance of those
singular points with regard to the validity of a power series solution of the corresponding initial value problem.
36)
Find a recursion formula for the power series solution of an ODE with analytic coefficients, and use that recursion formula to
either write an approximating polynomial solution or find the general term of the power series solution.
37)
Use the method of elimination to solve a system of linear ODE's with constant coefficients.
MyMathLab Access
Instructions for Accessing this required website are attached. If you have taken this course before with the same textbook, you do not
need to purchase a new Access Code. Otherwise, you must purchase an Access Code in order to use MyMathLab. If you cannot afford to
purchase the access code right away, the website will give you the option of a free trial for the first two weeks. When the free trial
expires, you must upgrade. If you can document that your financial aid has been delayed, the mathematics department can loan you an
access code. Call 305-237-1358 for more information.
Technical Support (if
MML required)
If you have any difficulty accessing this website Contact Product Support at http://www.mymathlab.com/student-supportfor
live CHAT, FAQ’s or email,
or phone support at 1-800-677-6337.

If you experience long wait times, please document your wait time and report it to the Math Department via email.

If you experience technical problems and you have been assigned an incident number, but you have not received assistance,
email the Chairperson.
Math tutoring services are provided through http://www.pearsontutorservices.com/
The toll-free student number is 1.800.877.3016.
The department does NOT provide Course ID’s for the college level courses; however, there are some sample MML courses available for
you to copy. Generic course IDs are available from the Math Dep’t. for students interested in accessing MML on their own.
Dr. Vincent Bates, vbates@mdc.edu 305-237-1358
As graduates of Miami Dade College, students will have achieved the 10 College Learning Outcomes:
MyMathLab Tutors
(if MML required)
Course ID (if MML
required)
Chairperson
College-wide Learning
Outcomes

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Communicate effectively using listening, speaking, reading, and writing skills.
Use quantitative analytical skills to evaluate and process numerical data. In this course students will need to read and identify data
from graphs and charts. Students will also learn to develop quantitative skills to interpret data from graphs. Also, students will
solve algebraic equations and inequalities and manipulate data through unit analysis.
Solve problems using critical and creative thinking and scientific reasoning. In the process of solving mathematical problems,
students will need to use critical thinking skills to interpret solutions. Creativity in solving problems is constantly encouraged in
this course and viewed as an important skill in mathematics. Critical skills are heavily emphasized in this course.
Formulate strategies to locate, evaluate, and apply information.
In this course students will often need to solve real-life word problems, which apply the mathematical concepts presented.
Students will work to solve these problems and identify relevant information in the problems in order to be able to solve them.
Demonstrate knowledge of diverse cultures, including global and historical perspectives.
In this course, whenever possible, students will be introduced to the use of mathematics through diverse cultures as well as
historical notes on the mathematical concepts you learn.
Create strategies that can be used to fulfill personal, civic, and social responsibilities. This outcome is heavily reinforced in this
course.
Demonstrate knowledge of ethical thinking and its application to issues in society. This outcome is not reinforced in this course.
Use computer and emerging technologies effectively. In this course students will use the computers to do home works and exams.
Demonstrate an appreciation for aesthetics and creative activities.
This outcome is not reinforced in this course.
Describe how natural systems function and recognize the impact of humans on the environment. This outcome is reinforced in this
course.
NOTES:
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MAP 2302 (Introduction to Differential Equations)
Course Syllabus Ref# 889005
1)
The registration to webAssign begins Wednesday January the 13th and finishes Wednesday January the 27st.
You need to be registered in this period of time. NO EXCUSES!! YOU WILL BE DROPPED IF YOU DON’T
COMPLAY WITH THIS REQUISITE.
2) Cell phones and any sounding devices are TOTALLY PROHIBITED. They need TO BE OFF BEFORE YOU ENTER
THE CLASS. The instructor may ask the student to leave the class for the first time. If the indiscipline is
repeated the instructor may withdraw the student from the course.
3) COMING TO THE BOARD when student is asked for, IS MANDATORY. YOU WILL BE DROPPE FROM THE CLASSA
IF YOU DON’T COMPLY WITH THIS REGULATION!! NO EXCEPTIONS!!.
4) Home works could be taken as many times as you want and the system will record your best grade. Exams
could be taken once and they are timed. Make sure you do your home works and exams in the school in order
for you to avoid problems with the internet. These are examples of not good excuses: “Professor at home the
internet was gone”; “Professor, please, reopen the exam for me, I submit it before I finish”; “Please, reopen
the exam, I hit the wrong key” etc, etc, etc.
NO REOPENNINGS AT ALL .
5) Punctuality. You will not be allow to enter the class is you are late. ONE SECOND IS LATE!! IT WILL BE COUNT
AS AN ABSENCE. If you have 3 Absences you will be DROPPED!!
6) My voice is laud, please, DO NOT BE AFRAID!!
7) ANY ABSENCE IS INEXCUSABLE. I believe you; the problem is that you missed the class!!
8) I understand that in our University we do not have a dressing code policy but to come to my class you must
dress professionally and appropriately. What does it mean? Male students CAN NOT wear neither pants nor
shorts showing their underwear or sleeve less T-shirts. Female students CAN NOT wear camisoles or shorty
shorts.
9) RIGHT ANSWERS MEAN NOTHING!!
10) I AM YOUR PROFESSOR NOT YOUR SECRETARY. DON’T EMAIL ME ASKING THINGS THAT ARE ON THE
SYLLABUS.
11) I want to discuss with each of you your schedule, at the school as well as at work. Maybe I have some advices
for you!!
12) Do not drop the class: “DON’T POSTPONE THE DISGRACE TO LATER TIME” “DON’T BE A QUITTER”
3