Math 0290: Differential Equations

Instructor: Catalin Trenchea
Lectures: MWF 10:00-10:50pm, G36 Benedum Hall

Office Hours: Tue. 2:00pm-3:30pm, Th. 9:00am-10:30am and by appointment
Office: Thackeray 606
Phone: (412) 624-5681


Differential equations are an important branch of mathematics. They have a rich mathematical formalization, as well as a very successful history of being applied to important problems in physics, chemistry, engineering, and biology. This course will introduce primarily linear, first and second order differential equations. Solution techniques for separable equations, homogeneous and inhomogeneous equations, as well as an intuition for modeling-based applications will be presented. The application of Laplace transforms to differential equations, systems of linear differential equations, linearization of nonlinear systems, and phase plane methods will be introduced. Fourier series and their application to simple partial differential equations will be treated. MATLAB based numerical solution and visualization will be briefly covered.


These two items will be packaged together in the Pitt Bookstore.

Other Materials

You will need some MatLab add-on software for differential equations. It can be downloaded from at Rice University.


Your course grade will be determined as follows: Grading:
Assignments: Ten assignments will be given throughout the term. The best eight assignments will be used to compute the final assignment grade. The assignment grade will be 20% of the course grade.

Midterm Exams: There will be two in class midterm examinations given. The second midterm will not be cumulative to the first. In other words, the second midterm will only cover course material not covered by first midterm exam. Each midterm exam grade will be 20%(x2) of the course grade.

Final Exam: The final exam grade will be 40% of the course grade and will take place during exams week. Your course grade will not exceed your final exam grade by more than one letter grade.

A/A-:90-100%, B/B±: 80-89%, C/C±: 70-79%, D/D+: 60-69%, F: < 60%

Some sections may deviate slightly from this recipe. Any deviations will be announced by your instructor at the beginning of the term.

MATLAB component: The study of differential equations often uses computer algorithms to gain solutions to relevant problems in physics, biology, chemistry, and engineering. Several assignment problems will taken from the problem sets in the MATLAB supplemental textbook. These problems will be of use to the student in both acquiring a visual sense of differential equations and their solutions, as well as give an introduction into standard-practice techniques currently used in many disciplines.

Homework policies

Students are required to complete the homework problems; very few students can learn this material without constant practice. Students are welcome to work together on homework. However, each student must turn in his or her own assignments, and no copying from another student's work is permitted. Deadline extensions for homework will not be given. Students are encouraged to discuss with your professor about homework problems if you'd like additional feedback.

Final Exam Policy

All day sections will take a departmental final exam at a time and place to be scheduled by the registrar. Evening sections will meet through final exam week, and the final exam will be given during the last one or two scheduled class periods.

Final Grade Policy

Your final grade should not exceed your final exam grade by more than one letter grade.

Office Hours

Your instructor will announce his office hours.

Academic Integrity

The University of Pittsburgh Academic Integrity Code is available at The code states that "A student has an obligation to exhibit honesty and to respect the ethical standards of the academy in carrying out his or her academic assignments." The website lists examples of actions that violate this code. Students are expected to adhere to the Academic Integrity Code, and violations of the code will be dealt with seriously.

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.

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, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

Schedule and practice problems

Approximate schedule for lectures. References of the form a.b refer to sections in the main textbook. References of the form Ma refer to Chapter a of the MatLab supplement.

Week 1:
Modeling with differential equations
First order initial value problems
1.1 Number 1-11. Homework: 1,2,5,7,11
2.1 Number 1-6, 12-15. Homework: 1,3,5,12,13,15
2.2 Number 1-18, 33-35 Homework: 3,5,9,33
M1 Number 1

Week 2:
Separation of variables
First order linear equations
Plotting with MatLab
2.3 Number 8-10 Homework: 9
2.4 Number 1-21 Homework: 5,15,19
M2 Number 15-20

Week 3:
3.1 Number 10, 12, 13 Homework: 10,13
3.3 Number 3, 5 Homework: 3,5
3.4 Number 1-10 Homework: 1,3,5,7,11
M3 Number 1-12 Homework: 1

Week 4:
Second order equations
Function m-files
4.1 Number 1-20 Homework: 1,3,9,17
4.3 Number 1-36 Homework: 1,9,17,35
4.4 Number 1-12 Homework: 1,7
M4 Number 1-8, 17, 18

Week 5:
Second order equations (cont)
4.5 Number 1-29 Homework: 1,5,11,15,19
4.6 Number 1-10 Homework: 1,3,5
4.7 Number 3-6, 12-15 Homework: 3,13

Week 6:
Review and Exam
Laplace Transform
5.1 Number 1-29 Homework: 7,13,15,29
5.2 Number 1-41 Homework: 5,11,19,29
5.3 Number 1-36 Homework: 3,7,11,19

Week 7:
Laplace Transform (cont.)
5.4 Number 1-26 Homework: 7,11,21
5.5 Number 1-25 Homework: 1,3,11,17
5.6 Number 1-9 Homework: 2,3,5,7
5.7 Number 4-10

Week 8:
Numerical methods
Introduction to systems
6.1 Number 1-5 Homework: 3,5
8.1 Number 1-16 Homework: 5,7,13,15
M5 Number 1-6 Homework: 2,3

Week 9:
Systems (cont.)
8.2 Number 13-16 (use PPLANE7) Homework: 11,13,15
8.3 Number 1-6 Homework: 1,3,5

Week 10:
Constant coefficient homogeneous 2x2 systems
9.1 Number 1-8, 16-23 Homework: 3,5,17,19
9.2 Number 1-27, 58, 59 Homework: 3,13,15,41,49
9.3 Number 1-23 Homework: 1,11,21

Week 11:
Inhomogeneous systemes: Undetermined coefficients and variation of parameters
Nonlinear systems; equilibria, linearization, stability, nullclines
10.1 Number 1-18 Homework: 3,7,15
10.2 Number 1-4 Homework: 1,3

Week 12:
Nonlinear systems; equilibria, linearization, stability, nullclines
10.3 Number 1-16 Homework: 3,7,11
10.4 Number 1-4 Homework: 1,2
10.5 Number 1-24 Homework: 1,11,21
Review and Exam

Week 13:
Fourier series
12.1 Number 1-17 Homework: 5,7,13,17
12.3 Number 1-32 Homework: 3,7,19,31

Week 14:
Heat equation
Separation of variables
13.1 Number 1-9
13.2 Number 1-18