Linear algebra and multivariable calculus are closely related subjects. Even though algebra and analysis (calculus) seem very different, they come together in very naturally in this arena. Differential calculus deals with understanding complicated nonlinear behavior (functions) by linearization (the derivative). When working with more than one variable, the linear objects are more complicated and are organized or understood in terms of linear algebra.

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 MAT 307 only covers about half of the material in MAT 211, students who complete only MAT 307 and not MAT 308 may need to take MAT 211.

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: Tuesday, Dec 11, 8:30 - 11:00pm in Melville Library E4310

The final exam is cumulative, covering the full semester of topics. However, there will be a heavy emphasis (about 2/3) on the later chapters, Ch. 7, 8, 9, with only about 1/3 on Chapters 1, 2, 4-6. Most all the problems will be computational, of the same character as HW problems. There may be one or two which are more conceptual, testing your understanding of the theory. None of the problems will be intense or hard computationally, where you have to do complicated Calc I type integrals.Here is the Final Exam

Due to the cancelation of classes last week,Midterm II will be cancelled. Exam and HW/Quiz percentages will be adjusted accordingly. We need the time in class for lectures to cover lots of remaining material and can't spare a full class for an exam. We plan to start on Monday, November 5 with Chapter 7: Integration.

Hand in HW due Oct 29 to your TA on Monday, Nov 5.

MIDTERM I: Wednesday, Oct 3, 4:00-5:20 in Lecture Class

The exam will have 5-6 problems covering topics in: Chapters 1, 2 and Chapter 4. Difficulty of the problems will vary (some easy, some harder) but overall similar to level of HW problems. No proofs.Here is the Midterm Exam

Topics in text you can skip.- Ch.1.5.B

- Ch.2.1.B

- Ch.2.2.D: Checking for independence discussion, p.71-73.

- Ch.2.5.C,D: Its good to know this material - its part of standard linear algebra course. But you won't need it in MAT 307.

- Ch. 3. All of it.

- Ch.4.1.E

- Ch.4.2.C
- Ch.5.5

- Ch. 5.3B

- Ch. 5.5

- Ch. 6.1D

- Ch. 6.4F
- Ch. 7.5

- Ch. 7.6 (great if you read it anyway though).

- Ch. 7.7

- Ch. 8.2 + 8.3.
- Ch. 9: All discussion of physical interpretation, equation of continuity, circulation, etc.
- Ch. 9.3C: orientation
- CH. 9.4B: interpretation of divergence (but good to know anyway).
- Ch. 9.5B: interpretation of curl (but good to know also).
- Ch. 9.6 on.

Topics in text you need to read, not covered in class.- Ch.2.2.C. Discussion of linear independence and dependence,

- Ch.2.5.E. Theorems 5.8 and 5.9 Cramer's rule (quite useful).
- Ch.4.2.C. First page, but ignore computer work (unless you're interested).
- Ch.4.2.D.
- Ch.4.3C - Clairaut's theorem
- Ch.4.4.B.
- Ch.5.1
- Ch.5.3B - Mean value theorem
- Ch.6.4D,E - Saddle points, 2nd derivative test
- Ch.6.5 Curvilinear Coordinates

MAT 307

Lecture and RecitationFinal Exam: Tuesday Dec 11, 8:30-11:00pm, Place: Library E4310

LEC 1

MW

4:00pm- 5:20pm

Chemistry

128

Michael Anderson

Recitation

M

5:30pm-6:23pm

Physics

P118

Cheng Hao

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 in 4-110 Math Tower

Recitation Instructor (TA):

R01:Cheng Hao

Email:hao at math dot sunysb dot edu

Office: 3-101 Math Tower

Office hours:TBA

## Course Text:

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

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

30%

Midterm I: Wed, Oct 5, In Lecture Class

25%

Midterm II (Wiped out by Sandy)

0%

Final Exam, Tuesday, Dec 11, 8:30-11:00pm, Place: Library E4310,

45% (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 at .

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

Aug 27

1.1: Coordinate Vectors

1.2: Geometric Vectors

1.3: Lines and Planes

1.4: Dot Products

1.1: 2, 10, 12

1.2: 2, 3, 6, 8

1.3: 2, 6, 8, 18, 22

1.4: 2, 4, 6, 8, 14, 16, 18.Sept 10, HW

Sept 10

2.1: Systems of Equations

2.2: Matrix Methods

2.3: Matrix Algebra

2.4: Inverse Matrices

2.1A: 2, 4, 8, 16, 18

2.2ABC: (p.69) 2, 7, 12, 28

2.3: 2, 10, 12, 16, 48Sept 17, Q

Sept 17

2.4Inverse Matrices

2.5Determinants

4.1Functions of 1 variable

4.2Several Variables

2.4: 5, 8, 13

2.5: 2, 3, 7, 12

4.1ABCD: 4, 12, 14, 15, 17

4.1F: (p.187) 5, 7Sept 24, HW

Sept 24

4.2Several Variables

4.3Partial Derivatives

4.4Parametrized Surfaces

4.2AB:3, 4, 10, 16

4.2C:2, 6

4.3:3, 8, 10,, 29, 30

4.4AB:2, 7, 11Oct 1, Q

Oct 1

Ch.4/Midterm Review

MidtermI, Wed.No HW/Quiz this week

---

Oct 8

5.1Limits and Continuity

5.2Real Valued Functions

5.3Directional Derivatives

5.4Vector Valued Functions

5.2: 2, 7, 9, 10

5.3: 4, 8, 9, 20

5.4: 2, 9, 18, 21, 27Oct 15, HW

Oct 15

6.1Gradient Vector Fields

6.2The Chain Rule

6.1ABC: 2, 5, 8, 15, 25, 28, 38

6.2A: 2, 6, 8

6.2B: 9Oct 22, Q

Oct 22

6.3Implicit Differentiation

6.4Extreme Values

6.3: 4, 12

6.4ABCD: 4, 8, 14, 16

6.4E: 4, 8, 12Oct 29, HW

Oct 29

Classes Canceled

--

--

Nov 5

7.1-7.3Multiple Integrals

7.1: 4, 8, 12, 21

7.2: 4, 8, 9, 20

7.3: 2, 4Nov 12, Q

Nov 12

7.4Change of Variables

8.1Line Integrals

8.4Flows, Div and Curl

7.4: 7, 8, 10, 17, 22

8.1: 2, 3, 6, 14, 15, 25

8.4: 1, 2, (div problems only), 7, 11Nov 19, HW

Nov 19

8.4Flows, Div and Curl

9.2Conservative FieldsNo HW/Quiz due after Thanksgiving

--

Nov 26

9.1Green's Theorem

9.3Surface Integrals

9.1: 1, 2, 10, 11

9.2: 3, 4, 5, 6, 10, 12, 13

9.3: 2(b), 9Dec 3, Q

Dec 3

9.4Gauss' Theorem

9.5Stokes' Theorem

9.4: 5, 6, 7, 8, 11

9.5: 3, 7, 9, 10, 19(answer in back of book is wrong)Dec 10:Do Not hand in