Math 1270: Ordinary Differential Equations 1 Spring 2013
Instructor: David Swigon
Office: Thackeray 511, 4126244689, swigon@pitt.edu
Lectures: MWF 12:0012:50pm, Thackeray 524
Office Hours: MW 1:303:00pm, Thackeray 511, or by appointment.
Course Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math1270.html
Course Description
This course is covers the theory of ordinary differential equations (ODEs) at the undergraduate level. The topics include classical methods of solving first order ODEs, linear higherorder ODEs and systems of first order linear and nonlinear ODEs. Geometric qualitative methods for autonomous systems of first order ODEs and solution of boundary value problems will be briefly discussed.
Prerequisites
Singlevariable calculus (Math 0420, 0450, or equivalent) including Taylor series, linear algebra (Math 1180, 1185 or equivalent) including eigenvalues and eigenvectors.
Textbook
W.E. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9^{th} edition, John Wiley & Sons, 2009. ISBN 9780470383346 (Available at The Book Center on Fifth Ave.)
Alternative/supplementary
texts:
M. Tenenbaum & H. Pollard, Ordinary Differential Equations, Dover 1985, ISBN 0486649407
E. A. Coddington, An Introduction to Ordinary Differential Equations, Dover 1989, ISBN 0486659429
Grading Scheme
Homework Assignments: 25%
Midterm Exams: 20% each
Final Exam: 35%
Schedule
Homework is due at the beginning of a class one week after it was assigned. You may work with other students on homework but do not submit solutions that are identical copies of each other, as such will be discarded.
Some homework assignments will require the use of a computer software to perform numerical computation or symbolic manipulation. You may use any computer program (e.g., XPP, ODE Architect, MATLAB, Maple, Mathematica) in solving the homework. Each such use should be explicitly documented (e.g., “eigenvalues computed with MATLAB”). A list of appropriate computer programs is given below.
Program 
Utility 
Availability 
Numerical solution of ODEs with GUI 
Free for download, Windows and Unix versions 

ODE Architect 
Numerical solution of ODEs with GUI 
Free with the Textbook 
Numerical solution of ODEs, Symbolic manipulation, Matrix algebra 
Benedum and GSCC computer labs, Windows/OSX/Linux/Unix version for $10 from Pitt SLS 

Numerical solution of ODEs, Symbolic manipulation, Matrix algebra 
Benedum and GSCC computer labs 

Numerical solution of ODEs, Symbolic manipulation, Matrix algebra 
Benedum and GSCC computer labs, Windows/OSX/Linux/Unix version for $10 from Pitt SLS 
Disability Resource Services
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 4126487890 or 4123837355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.
Academic
Integrity
Cheating/plagiarism will not be tolerated. Students suspected of
violating the University of Pittsburgh Policy on Academic Integrity will incur
a minimum sanction of a zero score for the quiz, exam or paper in question.
Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students
or use library resources, but each student must write up his or her solutions
independently. Copying solutions from other students will be considered cheating,
and handled accordingly.
Syllabus
Week 
Reading 
Topics 
Homework 
Notes 
Jan 7 – Jan 11 
1.14 2.1, 2.4 
Introduction, Classification, First order ODEs – linear equations, Existence and uniqueness of solutions of linear equations 


Jan 14 – Jan 18 
2.2, 2.4, 2.3 
Separable equations, Existence and uniqueness of solutions of nonlinear equations, Models using 1^{st} order ODEs, 


Jan 23 – Jan 25 
2.5, 2.6 2.8 
Autonomous equations and population dynamics, Exact equations and integrating factors 


Jan 28 – Feb 1 
2.7, 8.13 
Numerical solution of ODEs – Euler method, Improved Euler method, Error & Stabillity 


Feb 4 – Feb 8 
3.1, 3.45 
Higher order ODEs – Homogeneous equations with constant coefficients, Complex roots, Repeated roots, Fundamental solutions of linear homogeneous equations, Linear Independence and the Wronskian, 


Feb 11 – Feb 15 
3.23, 3.67 
Nonhomogeneous equations – undetermined coefficients, Variation of parameters 


Feb 18 – Feb 22 
3.8 
Vibrations 


Feb 25 

Review 


Feb 27 

Midterm Exam I 


Mar 1 
7.13 
Review of matrix theory 


Mar 4 – Mar 8 
7.48 
Systems of first order linear ODEs, Homogeneous systems with constant coefficients Repeated eigenvalues, Complex eigenvalues, Fundamental matrices 


Mar 11 – Mar 15 
SPRING BREAK 


Mar 18 – Mar 22 
7.7, 7.1, 7.9 
Matrix exponential, Nonhomogeneous linear systems, RLC circuits 


Mar 25 – Mar 29 
9.12 
Nonlinear differential equations, phase plane analysis 


Apr 1 – Apr 5 
9.34 
Stability, Cooperative systems 


Apr 8 Apr 10 
Review Midterm Exam II 


Apr 12 
9.5 
Predatorprey equations 


Apr 15 – Apr 19 
9.6 
Lyapunov’s method Review 


Saturday, Apr 27 2:00  3:50pm 

Final Exam 

