MAT 322 Analysis in several dimensions

Spring 2009


It is the student's responsability to check this page frequently for changes and updates. Changes will be announced in class and, if appropriate, on the web page. Students are responsible for announcements made in class and/or on the web-page.

Academic Calendars. Campus map.


This is a rigorous introduction to calculus in several variables. Topics to be covered include: continuity, integration and differentiation in Euclidean n-space, differential maps, implicit and inverse function theorem, Stokes' theorem.


Calculus on manifolds, a modern approach to classical theorems of advanced calculus, by M. Spivak, 5th edition, Westview Press, 1971.


Tu+Th 2:20pm-3:40pm, Library N3063, Instructor: Mark De Cataldo.


Punctuality: no late arrivals, no early departures: they are disruptive. If, occasionally, you need to arrive late and/or leave early, let the instructor know beforehand.

Silence: it is always a good rule and even more important for us since it is a big class; do show respect to other fellow students by not disturbing the class.

No cells (including text messaging, etc.).

No food.


The prerequisites for this course are:

  • C or higher in MAT 203, 205 , or AMS 261;
  • C or higher in MAT 211 or AMS 210;
  • or higher in MAT 320;
  • or permission of the instructor.
  • Advisory Pre- or Corequisite MAT 310.

  • GRADE: Midterm I = 25%, Midterm II =25%, Final = 35%, Homework = 15%.

    Maximum scores: Midterms I and II: 250pts each; homework: 150pts, each homework: 15pts (the best ten are used to grade); Final 350pts. Total maximum: 1000pts.

    The numerical grade will be converted to a final letter grade only after the final test has been graded. However, after each midterm an approximate letter grade will be given to you.

    To do well in this class we strongly encourage you to: read the section to be covered before class, do the homework, plan to work on reading and homework for 6-8hours a week, start preparing for tests well in advance.


    The sections to be covered will be announced well in advance.

    Bring your Stony Brook ID. No books, no notes, no calculators, no phones etc.

    Be sure to be available on these days and times:

    Midterm I: TH FEB 26, in class.

    Covers: p.1 to p.30 (up to ex. 2.27). (We did not cover ``oscillation" and it will not be on the test). The relevant hmk assignements are #1, #2 and #3. You should know the statements and the proofs of all theorems, and be comfortable with all the exercises on the book, even the ones which were not assigned (except the ones about oscillation). I will announce the number of problems on the test the week before. Of course the length will be compatible with the fact that it is a 80-minute-test.

    Midterm I with solutions.

    Midterm II: TH APR 2, in class.

    Covers sections: p.30 (Derivatives) to p.56 (up to ex. 3.22). The relevant hmk assignements are #4, #6, #7 and #8. You should know the statements and the proofs of all theorems (not the proof of the inverse and implicit function thms) and be comfortable with all the exercises on the book, even the ones which were not assigned (except the ones about oscillation). Test format similar to the one of midterm I

    Midterm II with solutions.

    Final:TU MAY 19, 2:00-4:30pm; Location: MAT TOWER P-131.

    Covers all sections up to page 108. Relevant hmk assignements: all. You should know the statements of all theorems. You should know the proofs of the following theorems/facts: 1.3, 1.9, 2.6; 2.9, 2.12, 3.6; 4.1, 4.6, 4.10(3), Exercise 4.19, and be comfortable with all the exercises on the book, even the ones which were not assigned (except the ones about oscillation). Test format similar to the one of midterms, except that it will have 10 problems.

    Please note that the final's time is assigned by Registrar's. If you have a conflict with another class it probably means that the other class has placed the final in conflict with this class (please resolve this issue with the instructor in charge of the other class).

    de Cataldo's office hours for the final: WED May 13, 9:30-11:30am, and MO May 18, 1:30-3pm.

    Appoximate curve for the final: A>=300; C>= 210

    Final with solutions. (the solutions posted refer to an earleir version of the final (which had a bit more problems, arranged in a different order).

    Important. You must bring your SUNY ID to the exams. There will be no make-ups for missed exams and homework. However, if you miss a midterm exam for an acceptable and documented reason, then the relevant mid-term will be `dropped' (ignored) in computing your course grade. A letter stating that you were seen by a doctor or other medical personnel is NOT an acceptable document, unless it states that it was reasonable/proper for you to seek medical attention and medically necessary for you to miss the exam (for privacy reasons this note/letter need not state anything beyond this). If you miss more than one midterm etc., we shall evaluate the circumstances. Incompletes will be granted only if documented circumstances beyond your control prevent you from taking the final exam.


    A range: 850 and up; B range 700 and up; C range 600 and up. D range 450 and up. F is below 450.


    We shall (tentatively) cover ????

    Week of Jan 27 (TU) :???

    Week of Apr 6-11 (TU 7, TH 9): Spring break, no class.

    Week of May 5 (last day of class TH May 7): ???


    Posted here every mid-week and due the following week in class on the first day of class the following week (usually a Tuesday). Graded homework will be returned the following week (usually on a Tuesday).

    Questions about the grading of the homework should be directed to the grader.

    There will be NO EXCEPTIONS to the following two rules: late homework will not be accepted and the homework must be stapled with a metallic staple.

    Hmk 1, due TU Feb 3: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6. Solutions HMK # 1.

    Hmk 2, due TU Feb 10: 1.14, 1.16, 1.19, 1.20, 1.22, 1.24, 1.25, 1.28, 1.29, 2.5, 2.6, 2.7, 2.8. Solutions HMK # 2.

    Hmk 3, due TU Feb 17: 2.11, 2.12, 2.13, 2.15 (do this for n=2), 2.20, 2.21, 2.24, 2.25, 2.27. Solutions HMK # 3.

    Hmk 4, due TU Feb 24: 2.29, 2.32, 2,33, 2,35, 2.36, 2.37, 2.39. DO NOT HAND-IN THIS HMK assignement. Focus on the test. These problems can be tackled after the test and we will post solutions. Solutions HMK # 4.

    Hmk 5, due TU Mar 3: Since we did not cover any material beyond what in Hmk 4, hand in Hmk 4.

    Hmk 6, due TU Mar 10: 1. Differentiate implicitly to find dy/dx: a: x^2 -3xy +y^2 -2x +y -5; b: cos x + tan xy +5 =0; c: ln squareroot(x^2+y^2) + xy =4; d: x/(x^2+y^2) - y^2 =6. 2. Differentiate implicitly to find the first partial derivatives of z: a: x^2 + y^2 +z^2 =25; b: tan (x+y) + tan (y+z) =1; c: e^{xz} + xy=0; d: xlny + y^2z+z^2 =8; 3. Differentiate implicitly to find the first partial derivatives of w: a. xyz + xzw -yzw +w^2 =5; b: cos xy + sin yz +wz =20. Solutions HMK # 6.

    Hmk 7, due TU Mar 17: Complete the proof of Lemma 3-1 for upper sums, 3.1, 3.2. 3.3, 3.5, 3.8, 3.13. Solutions HMK # 7.

    Hmk 8, due TU Mar 24: 3:14, 3.18, 3.20, 3.22. Solutions HMK # 8.

    Hmk 9, due TU Apr 14 (note two hmks due this week): 3.25, 3.28, 3.29, 3.31. Solutions HMK # 9.

    Hmk 10, due TU Apr 14 (note two hmks due this week): 3.32, 3.33, 3.34, 3.37. Solutions HMK # 10.

    Hmk 11, due TU Apr 21: 3.35, 3.40, 3.41. Solutions HMK # 11.

    Hmk 12, due TU Apr 28: 4.1, 4.2, 4.3, 4.9, 4.11. Solutions HMK # 12.

    Hmk 13, due TU May 5: 4.14, 4.15, 4.16, 4.17, 4.18, 4.19. Solutions HMK # 13.

    Hmk 14: not to be handed-in: 4.22, 4.23, 4.25, 4.26, 4.29, 4.31, 4.32. We will post solutions. Solutions HMK # 14.


    Please use email only for emergencies.

    The best way is to approach us after the lectures/recitations or to see us during office hours. If you put forward a request by email that is not an emergency, I will assume that you will approach me in person before/after class or during office hours. If you need to fix an appointment, please do so in person. E-mail is not a good way to ask math questions, as our typing abilities are very limited. After the course is over, if you have a question about your final grade, send a letter (not an e-mail) to your instructor, c/o Dept. Math, SUNY Stony Brook, Stony Brook N.Y. 11794-3651. If appropriate, you will receive a written reply. These matters will be dealt with in writing only; that way, we have a written record of what the student says, and what we reply.


    Instructor: Mark de Cataldo; mde at math dot sunysb dot edu ; Office Hours: TU+TH 11:15-12:45, MAT TOWER 5-108

    Grader: Sayed Ali Aleyasin; sali at math dot sunysb dot edu ; Office Hours: Mon & Fri: 13-14 in room S-240Z (door opens in the MLC), and Th 15-16 in the MLC.


    (*) The MATH LEARNING CENTER (MLC), located in MATHEMATICS BUILDING, FLOOR S, ROOM S-240A, (631) 632-9845, is a place where students can go for help and/or to form study groups. Check the link for more info, including hours. (**) The instructors have regular office hours.


    Read the paragraph ``GRADE" above about how scores are added up etc. Please also read about grades.


    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website:

  • Mark Andrea de Cataldo's homepage.
  • Quod non est in web non est in mundo