The main topics of this course are (ordinary) differential equations (ODE's), especially linear ones, and linear algebra. Just like linear algebra is needed to obtain a full understanding of the calculus of functions of many variables, so its also an essential ingredient in understanding how to solve linear ODE's. These ODE's are equations involving functions of one variable - in contrast to the multivariable calculus in MAT 307. We will also delve a little bit into the world of nonlinear ODE's.

MAT 307 and MAT 308 together cover the same material at MAT 203, MAT 211 and MAT 303 at a somewhat more theoretical level. This means that this course is going to movequicklyand will be a significant amount of work. Since about half of the linear algebra material was covered already in MAT 307, you should have taken either MAT 307 or MAT 211 before taking MAT 308.

There is a lot of material in the text that cannot be covered in class, and you will need to read the relevant sections on your own. The text is rather densely written, so you may not understand it on the first or even second reading. Keep trying - it will eventually pay off handsomely. Ask questions to your instructor and TA.

ANNOUNCEMENTS:

FINAL EXAM: Monday, May 13, 8:30 - 11:00pm, in the usual lecture room: Library W4530

The exam will be cumulative, covering the full semester: roughly 1/3 linear algebra and 2/3 differential equations.

Here is a Practice Final Exam:

Practice Final

Ignore the first few pages of the Practice exam and start only with Problem 2 on. No sheet of notes allowed on this exam.

Midterm II: Take Home Exam, Wed. Apr 17. Due in class on Mon, Apr 22.

Pick up exam at end of lecture class on Wed, Apr 17.

Email me if you have any questions during the exam.

Exam Topics: Chapters 11, 12, 13.1-13.2

Midterm I: Wednesday, March 6, 4-5:20pm, in Lecture Class.

Exam Topics: All of Chapter 3 + what we did in Chapter 10.

Here are two practice midterms. They are from the previous 2 years of MAT 308.

Practice I

This exam covers material that will be on the exam, but it rather easy. Our exam will probably be harder.

Practice II

This exam is quite hard. Its a take home exam, allowing notes, text, etc, but is more difficult than our exam. Problem 7(c) won't come up, nor will anything like Problem 10.

Topics in text to skip:

Ch.10.1B

Ch.11.3D

Ch.11.7 - but read phase portait discussion in Ch.11.7C

Ch.11.8

Ch.12.3

Ch.12.4

Topics in text to read:

Ch.10.2-10.3; some of the applications. You choose whatever interests you.

Ch.3.3.B

Ch.3.5.C

MAT 308

Lecture and RecitationFinal Exam: Monday May 13, 8:30-11:00pm, Place: TBA

LEC 1

MW

4:00pm- 5:20pm

Library

W4530

Michael Anderson

Recitation

Th

4:00pm-4:53pm

Earth & Space

183

Seyed Ali Aleyasin

Instructor:Michael Anderson

Office Location:4-110 Math Tower

Email:anderson at math.sunysb.edu

Web site:http://www.math.sunysb.edu/~anderson

Office hours:Tu/Th/F 2-3pm & by appointment in 4-110 Math Tower

Recitation Instructor (TA):

R01:Seyed Ali Aleyasin

Email:aleyasin at math dot sunysb dot edu

Office: 2-121 Math Tower

Office hours:Th, 1-3pm in MLC, Th, 3-4pm in 2-121

## Course Text:

Multivariable Mathematics, 4th Edition, by Williamson and Trotter (Pearson/Prentice-Hall, Inc.).## Homework and Quizzes:

As last semester in MAT 307, there will be both Homework assignments and quizzes, alternating roughly weekly; one week HW, the next week quiz, etc. There will be HW problems given roughly every week - see the assignments below - and each quiz may contain problems taken from the HW assignments. HW will be collected during the recitations, as determined by your TA; they should always be turned in at the beginning of the recitation class.

Please, remember that your solutions of the homework problems and quizzes are important documents. You should keep them to the end of the semester.Although only a random selection of problems on each homework will be graded by your TA, it is important that you do all the HW problems (or at least as many as possible). You should not expect to do well on the exams without the work and experience that goes into solving the HW and quiz problems.

Late homeworks will not be accepted except under very exceptional circumstances. Likewise, no late quizzes will be given. All policies regarding HW, quizzes and your grades for this part of the course are fully decided by your TA.

## Grading Policy:

Grades will be computed according to the following percentages:

Homework and Quizzes

25%

Midterm I, Wed. March 6, in class

20%

Midterm II

20%

Final Exam, Monday, May 13, 8:30-11:00pm, Place: Library W4530

35% (cumulative)

No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.

Resources:If you have questions regarding the course material at any time during the semester, you are encouraged to visit your instructor or TA during office hours, or make a separate appointment if necessary. Your instructors will also reply to email, within reason. Another excellent source of help is the Mathematics Learning Center (S240A in the Math Building - basement level), which is staffed by advanced math majors, graduate students and faculty daily. For a schedule of their hours, check their website.

Students with Disabilities:If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, please Disability Support Services at (631) 632-6748 DSS . DSS office: Room 133 in the Humanities Building. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information go to the DSS website above.

Academic Integrity:Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another persons work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website here.

Critical Incident Management:Stony Brook University expects students to respect the rights,privleges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits the students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Handbook and the Faculty-Employee Handbook.

## Schedule of Topics

In the table below, HW means homework is due to hand in, Q means quiz.

Week of

Topics

Problems Due

Due Date

Jan 28

10.1: 1st order DE, direction fields

10.2: Separation of variables

10.3: linear equations, integrating factors

10.1A: 2, 3, 7, 8, 11, 20, 25

10.2: 4, 9, 18, 19, 21

10.3: 6, 7, 11Feb 7, HW

Feb 4

3.1: Linear Maps/Euclidean spaces

3.2: Vector Spaces

3.3: Linear Maps/Vector spaces

3.1: 2, 4, 6, 8, 12, 19

3.2: 6, 7, 8, 10, 11, 12, 16, 20, 23, 24

3.3: 8, 9, 13, 17Feb 14, Q

Feb 11

3.4Image and Null Space

3.5Coordinates and Dimension

3.6Eigenvalues and Eigenvectors

3.4: 8 - 12, 16, 18, 19, 21

3.5AB: 4, 8, 15-17, 24, 27

3.5C: 3, 4, 7, 8Feb 21, HW

Feb 25

3.6Eigenvalues and Eigenvectors

3.7Inner Products

3.6A:2, 4, 6, 9, 13, 14

3.6BC:4, 7, 8, 9, 10

3.7A:1, 2, 8Feb 28, Q

March 4

Ch.3/Ch.10/Midterm Review

MidtermI, Wed. March 6No HW/Quiz this week

---

March 11

11.1Differential Operators

11.2Complex Solutions, Higher Order Eqns

11.3Nonhomogeneous Eqns

11.1: 8, 9, 14, 16, 38

11.2A: 15, 18, 20, 31, 32

11.2BC: 1, 4, 8March 14, HW

March 25

11.4Oscillations

11.5Laplace Transform

11.6Convolution

11.3AB: 2, 5, 6, 10

11.3CD: 2, 9

11.4: 12

11.5:19, 20, 21March 28 Q

Apr 1

12.1Vector Fields

12.2Linear Systems

12.1ABC: 1, 4, 7, 8, 24, 34,

12.1D: 7

12.2: 5, 18Apr 4, HW

Apr 8

13.1Eigenvalues/vectors

13.2Matrix exponentials

12.1ABC: 2, 3

13.1: 7, 10, 11, 15Apr 11, Q

Apr 15

13.3Non-homogeneous equations

Review

Midterm II:Take-Home Exam, Wed Apr 17No HW/Q

Apr 22

--Midterm Discussion

13.4Equilibrium and StabilityNo HW/Q this week

--

Apr 29

13.4Equilibrium and Stability

13.4Nonlinear Systems

14.6Differential Equations

13.4A2, 4, 6, 13, 21

13.4B2, 5, 9May 2, HW

May 6

14.6/14.7Power Series Solutions

Review

14.6: 5, 8

14.7: 3, 4May 9, Q