Hill College
112 Lamar Drive
Hillsboro, Texas 76645
COURSE SYLLABUS
Course Prefix and Number
Course Title
MATH 2320
Differential Equations
Prepared by: Amanda Whisenant
Instructor
Date: August 2013
Approved by:
Date:
Dean of Instruction
Approved by:
Date:
Vice President of Instruction
D i s a b i l i t i e s / AD A
In accordance with the requirements of the Americans with Disabilities Act (ADA) and
the regulations published by the United States Department of Justice 28 C.F.R.
35.107(a), Hill College’s designated ADA coordinator, Melanie Betz, Director of
Academic Advising & Student Success, shall be responsible for coordinating the
College’s efforts to comply with and carry out its responsibilities under ADA. Students
with disabilities requiring physical, classroom, or testing accommodations should
contact the Director of Academic Advising & Student Success, at (254)659-7651.
Course Description: MATH 2320 Differential Equations
Ordinary differential equations, including linear equations, systems of equations,
equations with variable coefficients, existence and uniqueness of solutions, series
solutions, singular points, transform methods, and boundary value problems;
application of differential equations to real-world problems.
Lecture Hours:
3
Lab. Hours:
3
Semester Credit Hours:
3
Prerequisites:
MATH 2414 or equivalent, or approval of instructor.
Introduction and Purpose:
This course is meant both as a terminal math course and to prepare students
for more advanced topics in mathematics and engineering.
Instructional Materials:
Textbooks: Differential Equations, 4th ed. By Blanchard, Devaney, and Hall
Supplies: Pencils, paper, and graphing calculator.
Objectives/Learning Outcomes:
At the completion of this course the student should be able to:
1. Identify homogeneous equations, homogeneous equations with constant
coefficients, and exact and linear differential equations.
2. Solve ordinary differential equations and systems of equations using:
a) Direct integration
b) Separation of variables
c) Reduction of order
d) Methods of undetermined coefficients and variation of parameters
e) Series solutions
f) Operator methods for finding particular solutions
g) Laplace transform methods
3. Determine particular solutions to differential equations with given boundary
conditions or initial conditions.
4. Analyze real-world problems in fields such as Biology, Chemistry, Economics,
Engineering, and Physics, including problems related to population dynamics,
mixtures, growth and decay, heating and cooling, electronic circuits, and
Newtonian mechanics.
The students' success in completing these objectives will be measured using a
set of examinations and assignments described, in detail under the section of
this syllabus headed “Method of Evaluation”.
Methods of Instruction:
This course will be taught face-to-face and by various distance learning
delivery methods.
Audio-visual materials and computer-based technology will be used when
appropriate. Students will be shown how to use a calculator where appropriate.
Methods of Evaluation:
A series of three or more major exams and homework will be given during the
semester; this will make up 75% of the student's final grade. The
comprehensive final will count as 25%.
Letter grades for the course will be based on the following percentages:
90 - 100%
80 - 89%
70 - 79%
60 - 69%
Below 60%
A
B
C
D
F
Class policies:
Regular attendance at all class meetings is expected. Disruptions in class will
not be tolerated.
Topic Outline:
First Order Differential Equations
Separation of variables, linear equations
Qualitative techniques
Euler’s Method
Existence and Uniqueness
Equilibria and the phase line
Bifurcations
First Order systems
Qualitative Methods
Analytic Methods for Special Cases
Euler’s Method
Linear Systems
Properties and the Linearity Principle
Eigenvalues, Eigenvectors, Straight Line Solutions
Phase Plane
Complex Eigenvalues
2nd and Higher Order D.E.’s
Forcing and Resonance
Forcing
Sinusoidal Forcing
Amplitude and Phase of Steady State
Nonlinear Systems
Equilibrium Point Analysis and Linearization
Qualitative Analysis
Hamiltonian Systems
Discrete Dynamical Systems
Discrete Logistic Function
Fixed Points and Periodic Points
Bifurcations
Chaos
Bibliography
Differential Equations, By Blanchard, Devaney, and Hall