Math 0290 *** Differential Equations *** Spring 2012       

Instructor: David Swigon, Thackeray 511, 412-624-4689, swigon@pitt.edu

Lectures:  MWF 12:00-12:50pm, LAWRN 205

Office Hours: MW 1:30-3pm, Thackeray 511, or by appointment.

Grader: Hang Nguyen, nguyentienhang@gmail.com , Office hours: TBA

Course Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math0290.html

Prerequisites

Single-variable calculus (Math 0420, 0450, or equivalent) including Taylor series, linear algebra (Math 1180, 1185 or equivalent) including eigenvalues and eigenvectors.

Textbook

* Polking, Boggess and Arnold, Differential Equations with Boundary Value Problems, second edition, Pearson Prentice-Hall 2006, ISBN 0131862367

* Polking and Arnold,Ordinary Differential Equations using MatLab, Third Edition, Pearson Prentice-Hall , ISBN 0131456792

(Both available at The Book Center on Fifth Ave.)

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.

Java applets for pplane and dfield programs can be found at http://math.rice.edu/~dfield/dfpp.html . They run in your browser without the need for Matlab software.

Grading Scheme

Homework Assignments: 20%

Two Midterm Exams: 40% (20% each)

Cumulative Final Exam: 40%

HW and Exam grades

Exam Policies

Exam dates will be announced ahead of time. Any student with a serious conflict should alert the instructor ahead of time, before the exam date, to discuss arrangements and should be prepared to show documentation establishing validity of the conflict. The time and place of the departmental final exam has been scheduled by the registrar. According to the policies of the Department of Mathematics, your final grade may not exceed your final exam grade by more than one letter grade.

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. The schedule and a list of homework problems will be posted below.  Homework is due at the beginning of a class one week after it was assigned.

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.

 

 

 

 

 

WEEK

READING & PRACTICE

(M# = MatLab book)

TOPICS

HOMEWORK

Collected on Friday 1wk after assigned

Jan 4 Jan 6

2.1 Number 1-6, 12-15

2.2 Number 1-18, 33-35

M1

First order initial value problems

Separation of variables

1.1 Number 1, 5, 11

2.1 Number 1, 3, 5, 13, 15

Solutions

Jan 9 Jan 13

2.3 Number 8-10

2.4 Number 1-21

M2 Number 15-20

Models of motion

First order linear equations

2.2 Number 3, 5, 9, 33

2.3 Number 9

2.4 Number 5, 15, 19

Solutions

Jan 16

M.L.K. Day (no school)

Jan 18 Jan 20

3.1 Number 10-13

3.3 Number 3, 5

M3 Number 1-12

Modeling

DFIELD

3.1 Number 10, 13

3.3 Number 3, 5

M3 Number 1

Solutions

Jan 23 Jan 27

3.4 Number 1-10

4.1 Number 1-20

4.3 Number 1-36

M4 Number 1-8, 17, 18

Second order homogeneous equations

Function m-files

3.4 Number 1, 3, 7, 11

4.1 Number 1, 3, 9, 17

4.3 Number 1, 9, 17, 35

Solutions

Jan 30 - Feb 3

4.4 Number 1-12

4.5 Number 1-29

4.6 Number 1-10

4.7 Number 3-6, 12-15

M5 Number 1-6

Nonhomogeneous second order equations

4.4 Number 11, 12

4.5 Number 1, 5, 11, 15, 19

4.6 Number 1, 3, 5

Solutions

Feb 6 Feb 10

6.1 Number 1-5

5.1 Number 1-29

5.2 Number 1-41

5.3 Number 1-36

Numerical Methods

Laplace Transform

4.5 Number 27, 29

4.7 Number 3, 13, 15 (No need to use the transfer function, find the steady state solution using any method)

6.1 Number 3, 5

Solutions

Feb 13

5.4 Number 1-26

Laplace Transform

 

Feb 15

Review

Exam review sheet

Sample exam

Sample exam results

5.1 Number 7, 13, 15, 29

5.2 Number 5, 11, 19, 29

5.3 Number 3, 7, 11, 19

Solutions

Feb 17

 

Midterm Exam I

Covers 1.1, 2.1-2.5, 3.1, 3.3, 4.1-4.7, 6.1

 

Feb 20 Feb 24

5.5 Number 1-25

5.6 Number 1-9

5.7 Number 4-24, 26-31

Laplace Transform methods

Convolutions

5.4 Number 7, 11, 21

5.5 Number 1, 3, 11, 17

5.6 Number 2, 3, 5, 7

Solutions

Feb 27 Mar 2

8.1 Number 1-16

8.2 Number 13-16

Introduction to systems

Geometrical interpretation of solutions

5.7 Number 6, 8, 10

8.1 Number 5, 7, 13, 15

8.2 Number 11, 13, 15

Solutions

Mar 5 Mar 9

 

Spring Break

 

Mar 12 - Mar 16

8.3 Number 1-6

9.1 Number 1-8, 16-23

9.2 Number 1-27, 58, 59

Qualitative analysis

Constant coefficient homogeneous 2x2 systems

8.3 Number 1, 3, 5

9.1 Number 3, 5, 17, 19

9.2 Number 3, 17, 23, 59

Solutions

Mar 19 Mar 23

9.3 Number 1-23

9.4 Number 1-12

10.1 Number 1-18

Nonlinear systems; equilibria, linearization, stability

Trace-determinant plane

9.3 Number 11, 13, 15, 17, 21, 23

9.9 Number 1, 3, 13, 15

Solutions

Mar 26 Mar 30

10.2 Number 1-4

10.3 Number 1-16

10.5 Number 1-10

Long term behavior,

Nullclines

Conserved quantities

10.1 Number 3, 5, 7

10.2 Number 1, 3

10.3 Number 3, 7, 11

Solutions

Apr 2 Apr 6

12.1 Number 1-17

12.3 Number 1-32

Fourier series

12.1 Number 5, 7, 13, 17

12.3 Number 9, 17, 21, 29

Solutions

Apr 9 Apr 13

13.1 Number 1-9

13.2 Number 1-18

Heat equation

Separation of variables

 

Apr 16

Review

Exam II review sheet

Exam II sample

Exam II sample results

 

Apr 18

Midterm Exam II

Covers 5.1-5.7, 8.1-8.3, 9.1-9.3, 10.1-10.2, 12.1,12.3

Solutions

 

Apr 20

Review for final exam

Sample final exam 1

Sample final exam 2

(Since the old finals followed different syllabus, our final may have different format and cover different material.)

 

Wednesday

Apr 25

 

FINAL EXAM

10:00 - 11:50 am

Room: 121 Lawrence Hall