Math 0290: Differential Equations

Instructor: Catalin Trenchea
Lectures: MWF 1:00-1:50pm, 105 Lawrence Hall



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

Overview

The discovery of Infinitesimal Calculus by Newton and Leibniz at the end of the XVII century provided scientists and engineers with two very powerful tools: the derivative and the integral. The derivative measures change and the integral measures accumulation. When modeling engineering systems we often have to incorporate a quantity and its rate of change (and perhaps the rate of change of the rate of change) into an equation. These are called differential equations. Sometimes the equation also involves how a certain quantity accumulates. We then work with integral equations. In this course we will concentrate almost exclusively on differential equations.

Until relatively recently, books on differential equations contained long list of recipes on how to compute solutions that can be expressed with explicit formulas. Today we are fortunate to have access to fast inexpensive computers so that we can concentrate on understanding the models and their implications in different engineering disciplines rather than be burdened with rather boring calculations.

The computational tool that we will use is MatLab, a professional scientific computing environment favored in Engineering and Mathematics.

Textbooks

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 http://math.rice.edu~dfield/ at Rice University.

Grades

Your course grade will be determined as follows: Some sections may deviate slightly from this recipe. Any deviations will be announced by your instructor at the beginning of the term.

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

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.

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 the Office of Disability Resources and Services, 216 William Pitt Union (412) 624-7890 as early as possible in the term.

Schedule and practice problems

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
M1 Number 1
Solutions

Week 2:
Separation of variables
First order linear equations
Plotting with MatLab
 2.2 Number 1-18, 33-35 Homework: 3,5,9,33
2.3 Number 8-10 Homework: 9
2.4 Number 1-21 Homework: 5,15,19
2.5 Number 1-10 Homework: 1,5
M2 Number 15-20
Solutions

Week 3:
Modeling
DFIELD
 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
Solutions

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
Solutions

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
Solutions

Week 6:
Review and Exam
Laplace Transform
 5.1 Number 1-29 Homework: 7,13,15,29

Week 7:
Laplace Transform (cont.)
 5.2 Number 1-41 Homework: 5,11,19,29
Solutions
5.3 Number 1-36 Homework: 3,7,11,19
5.4 Number 1-26 Homework: 7,11,21
Solutions

Week 8:
Laplace Transform (cont.)
Numerical methods
 5.5 Number 1-25 Homework: 1,3,11,17
5.6 Number 1-9 Homework: 2,3,5,7
6.1 Number 1-5 Homework: 3,5
M5 Number 1-6
Solutions

Week 9:
Introduction to systems
 8.1 Number 1-16 Homework: 5,7,13,15
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: 3,13,15,59
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
 9.9 Number 1-6, 12-15 Homework: 1,3,5,13,15
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
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
Review
13.1 Number 1-9
13.2 Number 1-18