Syllabus for Math 3020, Differential Equations
Term: Fall 2013
Instructor: Pasha Zusmanovich
Office: 3211 Science Building
Office hours: TBA
Phone: 530-6546
Email: pzusmanovich@nccu.edu
Course title: Differential Equations
Prerequisite: C or better in Math 2020
Required Text: Differential Equations, Blanchard, Devaney and Hall, Third or Fourth Edition,
Brooks/Cole Publishing Co.
Technology:
1. DETools: A set of software programs designed to allow students to become familiar
with qualitative and numerical approaches to differential equations. Using DETools,
students are expected to explore and experiment with various differential equations and
the behavior of their solutions.
2. MATLAB or other software: A crash course will be provided. Students are expected to
write simple programs.
Reference Books:
1. Elementary Differential Equations and Boundary Value Problems, Boyce, William,
th
and DiPrima, and Richard, 4 edition, John Wiley & Sons
nd
2. Intro to Differential Equations and Dynamical Systems, R. Williamson, 2 edition,
McGraw Hill.
3. Modern Differential Equations, Abell, Braselton, Second Edition, Harcourt
4. Differential Equations, Simmons, Krantz, The Walter Rudin Student Series in
Advanced Mathematics, McGraw Hill. 2007
Objectives: Introductory course in ordinary differential equations. Qualitative, analytic, and
numerical approaches are stressed throughout the course in our approach to understanding
solutions of differential equations. In particular, the qualitative approach adopts a modern
dynamical system point of view and investigates the long-term behavior of solutions and the role
of parameters. The core of the course consists of chapters 1, 2, and 3. In addition, we will also
discuss some selected topics from chapter 4 such as forcing and resonance. The course will
conclude with a discussion of Laplace transforms (Chapter 6). MATLAB (or other software) will
be used for numerical computation and visualization of differential equations.
Learning Outcome: After a successful completion of this course, a student should be able to:
• develop mathematical models based on ordinary differential equation
• determine the existence and uniqueness of a solution
• determine appropriate methods for finding analytic solutions if attainable
• discuss the long term behaviors of solutions qualitatively
• apply numerical methods for the problems whose analytic solutions are difficult or
impossible to find
• write simple programs using MATLAB
• use eigenvalues and eigenvectors to find solutions in linear systems of ode
• use Laplace transforms to handle problems that have discontinuous forcing terms
Course outline:
1. First-order differential equations
• Modeling via differential equations
• Analytic, qualitative, numerical techniques
• Existence, Uniqueness of solutions
• Dynamical systems techniques
2. First-order systems
• Modeling and the geometry of systems
• Euler’s method for systems
3. Linear systems
• Linearity principle
• Straight-line solutions
• Phase plane analysis
• Complex eigenvalues, repeated and zero eigenvalues
• Second-order linear equations
4. Forcing and Resonance
• Forced harmonic oscillators
• Sinusoidal forcing, resonance
5. Laplace transformation
• Laplace and inverse Laplace transformations
• Discontinuous functions
• Delta functions and impulse forcing
6. Numerical methods and other selected methods (if time permits)
• Improved Euler’s method
• Runge-Kutta method
• Introduction to Fourier series
Tests and Evaluation: We will have three unit tests (55%) and a comprehensive final
examination (25%). Remaining 20% of your grade will come from homework, quizzes, and
projects.
Grading Scale: A(90 – 100), B(80 – 89), C(70 – 79), D( 60 – 69), F( below 60).
Attendance and makeup polices: Attendance will be taken every class period. If you miss four
classes (for a class meeting twice a week) or six classes (for a class meeting three times a week),
you may be assigned a grade of NW or NF for nonattendance in accordance with university
policy. No makeup tests will be given unless appropriate documentation is provided to justify
your absence on the day of a test, e.g., absence form from a university organization, NCCU
Health Center/doctor’s note on official stationery, accident/police report, a copy of an obituary.
Student Support Services for Students with Disabilities: Students with disabilities (physical,
psychological, learning disability, etc.) who would like to request accommodations need to
register with the Office of Student Support Services in Suite G20 in the Student Services
Building or by contacting Kesha Lee, Director at (919)530-6325 or klee@nccu.edu. If you are
already registered in the office, you will need to return to the office each semester to review
your information and receive updated accommodations.