Course Syllabus
Ordinary Differential Equations
MATHEMATICS DEPARTMENT
Houston Community College-Southeast
Chuen Huang, Ph.D.
Phone 713.718.7150
E-mail: chuen.huang@hccs.edu
Math 2320 Ordinary Differential Equations
CRN 68918
Course Syllabus and Outline
SYLLABUS FOR MATH 2320
(Revised May 2006)
Catalog Description: MATH 2320 Ordinary Differential Equations. Topics include initial value problems
for first order and linear second order equations, Picard iterations, series solutions, and boundary value
problems. Laplace transforms and numerical methods. Prerequisite: MATH 2414.
3 credit (3 lecture).
Prerequisites: MATH 2414 with a grade of “C” or better.
Course Intent: This course provides the background in sciences for further study in mathematics and its
applications.
Audience: This is a sophomore level mathematics course, which requires a background consisting of
Calculus I and II.
Course Objectives: Upon completion of this course, a student should be able to:
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Verify that a function is a solution for a given differential equation.
Derive a differential equation from a given physical situation.
Determine by inspection at least two solutions of a given initial-value problem.
Solve a given differential equation by separation of variables or by using an appropriate substitution.
Solve given exact differential equations subject in indicated initial conditions.
Solve the given Ricatti equation.
Use Picard’s method to find y1, y2, y3 for a given differential equation.
Find the orthogonal trajectories of a given family of curves.
Determine whether a set of functions are linearly dependent or independent on (-,).
Determine whether an nth-order differential equation is homogeneous, or nonhomogeneous.
Apply the superposition principle for homogeneous and nonhomogeneous equations.
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Given a differential equation and one solution, find the second solution.
Solve a given differential equation by undetermined coefficients.
Find a linearly independent function that is annihilated by a given differential operator.
Solve given differential equation by variation of parameters or by involving Cauchy-Euler equations.
Find the interval of convergence of a given power series.
For a given differential equation, find two linearly independent power series solutions about a point.
Use the method of Frobenius to obtain two linearly independent series solutions about the point x 0=0.
Find the Laplace Transform of a given function.
Find the inverse Laplace Transform of a given function.
Given a Laplace Transform of an integral, evaluate the transform without evaluating the integral.
Use the Laplace transform to solve the given differential equation subject to the given boundaries.
Solve the given system of differential equations by either systemic elimination or determinants.
Use the Laplace transform to solve a given system of differential equations.
Rewrite a given system in normal form.
Solve a given system of equations by either Gaussian elimination or Gauss-Jordan elimination.
Solve a given system of linear first-order equations using matrices.
Solve a given system of homogeneous linear systems.
Use the method of undetermined coefficients to solve a given system on (-,).
Use variation of parameters to solve a given system of equations.
Use matrix exponentials.
Sketch the direction field for a given differential equation.
Given an initial-value problem, use Euler formula to obtain a four-decimal approximation.
Given an initial-value problem, use Runge-Kutta methods to obtain a four decimal approximation.
Use the finite difference method to approximate a solution for a second-order differential equation.
Textbook: Zill, Dennis, A First Course in Differential Equations with Modeling Applications, Brooks Cole
Publishing Company, 8th ed., 2005.
Class Attendance: Class is very important. If some unavoidable situation arises which causes you to miss
class, then please keep me advised. Otherwise, if you absences exceed four classes during this course, you
can expect to be administratively withdrawn. Attendance count will begin with the first class of the second
week of class.
Supplemental Materials: A videotape series is available in the library.
Advising Times: MW 8:30-9am, 1:00-1:30 PM, TR 8:00-9:00 AM, ESID 1026
Calculators: Calculators may be used for homework. However, calculators are never to be used on
quizzes or examinations.
Course Outline: Instructors may find it preferable to cover the course topics in the order listed below.
However, the instructor may choose to organize topics in any order, but all material must be covered.
APPROXIMATE TIME
TEXT REFERENCE
UNIT I - Introduction to Differential Equations
(4 hours)
Sections: 1.1, 1.2, 1.3
This unit begins with some definitions and introduces certain terminology. Included are Initial-Value
problems and some mathematical modeling.
UNIT II - First-order Differential Equations
Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6
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(6 hours)
This unit includes the solution of first-order differential equations using the following techniques/methods:
separation of variables, exact equations, linear equations, solutions by substitution, and a numerical
solution.
UNIT III - Modeling with First-Order Differential Equations
(4 hours)
Sections: 3.1, 3.2, 3.3
This unit solves some of the problems that commonly arise in modeling applications.
UNIT IV - Differential Equations of Higher Order
(8 hours)
Sections: 4.1, 4.2, 4.3, 4.4, 4.5,
4.6, 4.7, 4.8, 4.9
This unit begins with some preliminary theorems including reduction of order. Also included are the
techniques to solve homogeneous linear equations (with constant coefficients). Cauchy-Euler equations and
some nonlinear equations. The chapter includes the study of Undetermined Coefficients (Superposition
approach). Undetermined Coefficients (Annihilator approach ) and Variation of parameters.
UNIT V - Modeling with Higher Order Differential Equations
(3 hours)
Sections: 5.1, 5.2, 5.3
This unit begins with Linear Equations and initial-value problems. Also, included are Linear Equations Boundary-Value problems and nonlinear equations.
UNIT VI -Series Solutions of Linear Equations
(4 hours)
Sections: 6.1, 6.2, 6.3,
This unit begins with a review of Power Series and then proceeds to Power Series solutions. Also included
are solutions about ordinary and singular points. The two special functions - Bessel’s equation and
Legendre’s equation.
UNIT VII -Laplace Transform
(7 hours)
Sections: 7.1, 7.2, 7.3,
7.4, 7.5, 7.6,
This unit begins with the definition of the Laplace transform with some introductory examples. Included
are the theorems of first and second translation, derivatives of a transform. Also, transforms of derivatives,
integrals and periodic functions and the Dirac Delta Function. The chapter concludes with systems of
Linear Equations.
UNIT VIII -Systems of First-Order Linear Differential Equations
(7 hours)
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Sections: 8.1, 8.2, 8.3,
8.4(Optional)
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This unit begins with the preliminary theory to solve Homogeneous Linear Systems with Constant
Coefficients (including distinct real eignenvalues, repeated eigenvalues and complex eigenvalues). Also,
included are variation of parameters and matrix exponential.
UNIT IX -Numerical Methods for Ordinary Differential Equations
(5 hours)
Sections: 9.1, 9.2, 9.3
9.4(Optional)
Week
Topics
1-2
UNIT I - Introduction to Differential Equations
3-4
UNIT II - First-order Differential Equations
2.4, 2.5, 2.6
(6 hours)
5-6
UNIT III - Modeling with First-Order Differential Equations
3.1, 3.2, 3.3
(4 hours)
7-8
UNIT IV - Differential Equations of Higher Order
(8 hours)
4.9
Sections: 2.1, 2.2, 2.3,
Sections:
Sections: 4.1, 4.2, 4.3, 4.4, 4.5,
4.6, 4 .7, 4.8,
9-10
UNIT V - Modeling with Higher Order Differential Equations
5.1, 5.2, 5.3
(3 hours)
Sections:
UNIT VI Series Solutions of Linear Equations
6.1, 6.2, 6.3,
(4 hours)
Sections:
UNIT VII Laplace Transform
7.1, 7.2, 7.3,
(7 hours)
7.4, 7.5, 7.6,
Sections:
UNIT VIII Systems of First-Order Linear Differential Equations
8.1, 8.2, 8.3,
(7 hours) 8.4(Optional)
Sections:
11-12
13-14
15-16
UNIT IX, Numerical Methods for Ordinary Differential Equations
Sections: 9.1, 9.2, 9.3
(5 hours)
(9.4 optional)
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Math 2320
Final Exam May 9, 2011, Monday, 1:30 PM.
Departmental Policies:
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Each instructor must cover all course topics by the end of the semester. The final exam is
comprehensive and questions on it can deal with any of the course objectives.
Each student should receive a copy of the instructor’s student syllabus for the course during the first
week of class.
A minimum of three in class tests and a comprehensive final examination must be given. The final
examination must be taken by all students.
All major tests should be announced at least one week or the equivalent in advance.
The final exam must count for at least 25 to 40 percent of the final grade.
The final course average will be used in the usual manner (90-100 ”A”; 80-89 “B”; 70-79 “C”;
60-69 “D”; Below 60 “F”).
Either an open book or a take home major test may be given at the discretion of the instructor.
Any review sheet should be comprehensive and the student should not feel that classroom notes,
homework, and tests may be ignored in favor of the review sheet for any examination.
Resource Materials: Any student enrolled in Math 2320 at HCCS has access to the Academic Support
Center where they may get additional help in understanding the theory or in improving their skills. The
Center is staffed with mathematics faculty and student assistants, and offers tutorial help, video tapes and
computer-assisted drills. Also available is a student’s Solutions manual which may be obtained from the
Bookstore.
Suggested Methods: It is helpful to begin each class with questions concerning the material discussed and
the assigned homework problems. In presenting new material, it is suggested that an explanation be
followed by students working examples in class. Students should be encouraged to work the review
exercises at the end of each chapter. Also, they should be encouraged to visit the Academic Support Center
at their respective colleges.
Americans With Disabilities Act (ADA): Students with Disabilities: Any student with a documented
disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Disability Services Office at the respective college at the beginning of
each semester
NOTICE: Students who take a course for the third time or more may soon face significant tuition/fee
increases at HCC and other Texas public colleges and universities. If you are considering course
withdrawal because you are not earning passing grades, confer with your professor/counselor as early as
possible about your study habits, reading and writing homework, test-taking skills, attendance, course
participation, and opportunities for tutoring or other assistance that might be available.
No student may disrupt or otherwise interfere with any educational activity being performed by a
member of the College System.
Core Curriculum: The basic intellectual competencies for core courses include reading, writing, speaking,
listening, critical thinking, and computer literacy.
Academic Honesty: All Houston Community College System students are required to exercise academic
honesty in completion of all tests and assignments. Penalties for academic dishonesty (cheating on a test,
plagiarism, collusion on an assignment, etc.) may include, but are not limited to a reduced grade or a "0" on
that test or assignment, a "W" in the course, or an "F" in that course.
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