Multivariable Calculus: 18.02 (`Spring' 1999)

• Syllabus

  Here is the main hand-out including the syllabus.
  

• Lectures

  Tuesdays and Thursdays at 1PM, Fridays at 2PM in 54-100, by R. Melrose.

• In class examinations

  All four of these will be in Walker during the usual Friday lecture time, 2-3PM, on February 19, March 12, April 9 and April 30.

• Make-up exams

  There will be make-up exams on the 4 consecutive days starting the Monday after the Friday of an exam. Without a convincing (e.g. medical) excuse you will recieve at most `a good B' (around 75% credit) for taking the make-up, versus the standard, exam. You may take the make-up whatever your grade on the original test, that is even if you passed the test. This is a liberlization of the original policy.

• Recitations and Instructors

  • MW 10 in 2-135 by R. Stanley (2-375, 3-7930) rstan@math.mit.edu
  • MW 12 in 2-151 by M. Grinberg (2-181, 3-3665) grinberg@math.mit.edu
  • MW 1 in 2-151 by G. Toth (2-334, 3-7775) toth@math.mit.edu
  • MW 2 in 2-147 by G. Toth (2-334, 3-7775) toth@math.mit.edu
  • MW 2 in 2-142 by G. Bozin (2-088, 2-1194) bozin@math.mit.edu
  • MW 2 in 2-143 by A. Henderson (2-251, 3-7566) anthonyh@math.mit.edu
  • TR 10 in 2-146 by J. Grodal (2-087, 2-1193) jg@math.mit.edu
  • TR 11 in 2-146 by R. Kleinberg (2-230, 3-7557) rdk@math.mit.edu
  • TR 11 in 2-135 by A.-M. Castravet (2-229, 3-1589) noni@math.mit.edu
  • TR 12 in 8-302 by C.-O. Chow (2-333, 3-7826) cchow@math.mit.edu

• Homework

  • Problems1
    Problems1.ps (As postscript)
    Problems1.pdf (As acrobat)
    This is not due at all. It is intended to be done by Feb 5 but will not be graded. Do not hand it in.

  • Problems2
    Problems2.ps (As postscript)
    Problems2.pdf (As acrobat)
    Due Feb 12, 1999.
    Problems2-Sol
    Problems2-Sol.ps (As postscript)
    Problems2-Sol.pdf (As acrobat)
    

  • Problems3 (After Feb 18, 2PM with solutions)
    Problems3.ps (As postscript)
    Problems3.pdf (As acrobat)
    Due Feb 18, 1999.

  • Problems4 (Due Feb 26, 1:45 PM, after 2PM with solutions)
    Problems4.ps (As postscript)
    Problems4.pdf (As acrobat)
    

  • Problems5 (Due Mar 11, 12:45 PM, after 2PM with solutions)
    Problems5.ps (As postscript)
    Problems5.pdf (As acrobat)
    

  • Problems6 (In principle due Mar 19, 12:45, in practice March 29, 12:00 -- with solutions)
    Problems6.ps (As postscript)
    Problems6.pdf(As acrobat)
    

  • Problems7(Now with solutions. Was due Apr 2, 1:45)
    Problems7.ps (As postscript)
    Problems7.pdf(As acrobat)
    

  • Problems8(Due Apr 8, 12:45).
    Problems8.ps (As postscript)
    Problems8.pdf(As acrobat)
    Solutions will be available in lecture on April 8 and here at 12:45.

  • Problems9(Due Apr 23 1:45PM, with solutions).
    Problems9.ps (As postscript)
    Problems9.pdf(As acrobat)
    

  • Problems10(Due Apr 29, 12:45, now with solution).
    Problems10.ps (As postscript)
    Problems10.pdf(As acrobat)
    

  • Problems11(Due May 7, 1:45, now with solutions).
    Problems11.ps (As postscript)
    Problems11.pdf(As acrobat)
    

  • Practice Problems for Final
    prac-prob
    prac-prob.ps (As postscript)
    prac-prob.pdf(As acrobat)
    

• Practice Exams

  • Practice Exam 1 (now with solutions)
    Exam1-Prac
    Exam1-Prac.ps (As postscript)
    Exam1-Prac.pdf (As acrobat)

  • Exam 1 (with solutions)
    Exam1
    Exam1.ps (As postscript)
    Exam1.pdf (As acrobat)

  • Practice Exam 2 (now with partial solutions)
    Practice-Exam2
    Practice-Exam2.ps (As postscript)
    Practice-Exam2.pdf (As acrobat)

  • Exam 2 (with solutions)
    Exam2
    Exam2.ps (As postscript)
    Exam2.pdf (As acrobat)

  • Practice Exam 3 (with solutions)
    Practice-Exam3
    Practice-Exam3.ps (As postscript)
    Practice-Exam3.pdf (As acrobat)

  • Exam 3 (with solutions)
    Exam3
    Exam3.ps (As postscript)
    Exam3.pdf (As acrobat)

  • Practice Exam 4 (A couple of these questions a very similar to recent problems -- don't expect this on the actual exam!)
    Now with solutions
    Practice-Exam4
    Practice-Exam4.ps (As postscript)
    Practice-Exam4.pdf (As acrobat)
    
  • Exam 4 (with solutions)
    Exam4
    Exam4.ps (As postscript)
    Exam4.pdf (As acrobat)

  • Practice Final (The pictures may be a bit messed up, I will try to fix them later. Solutions at the end.)
    Now with solutions
    Practice-Final
    Practice-Final.ps (As postscript)
    Practice-Final.pdf (As acrobat)
    

• Brief Lecture notes

  • First part, Lectures 1-6
    
  • Second part, Lectures 7-14
    
  • Third part, Lectures 15-26
    
  • Lecture 27: April 13 Triple integrals: Read: EP, sect. 12.8 to p. 787. Read: SN I, pp. I.2, I.3; Read EP 14.6, pp. 926-929 ; Read EN 14.7, pp.~934-6.
    1. Reduction to iterated integrals
    2. Reduction to double integrals -- shadow region in the plane
    3. Cylindrical polar coordinates
  • Lecture 28: April 15 Spherical polar coordinates: Read: Notes I, p. I.4; EP 14.7, pp.~936-940.
    1. Volume differential
    2. Examples with spheres
    3. Gravitation attraction
  • Lecture 29: April 16 Gravitational problems: Read: SN sect. G and SN, Vector Calculus, section 8.
    1. Newton's theorem
    2. Vector fields in 3-space.
  • Lecture 30: April 22 Surface integrals and flux: Read: SN, Vector Calculus, section 9.
    1. Vector fields in 3 space
    2. Surface differential, dS
    3. Flux integrals
  • Lecture 31: April 23 Applications of flux, Divergence theorem
    1. Physical examples of flux
    2. Two-sided surfaces
    3. Closed surfaces
    4. Divergence theorem
  • Lecture 32: April 27 Divergence theorem in more general regions. Read EP p 1000-1003.
    1. Del notation.
    2. Examples of flux integrals
    3. Gauss theorem.
  • Lecture 33: April 28 More examples of Divergence Theorem and Review.
  • Lecture 34: April 29 Fourth in-class exam (Walker) covering material in lectures 27 - 33.
  • Lecture 35: May 4 Line integrals in 3 space. Read SN: Sections 11, 12 and p. 15.
    1. Evaluation by parameterization
    2. Gradient fields
    3. Integrability condition
    4. Definition of curl
  • Lecture 36: May 6 Stokes' theorem: Read: SN Section 13, EP Section 15.7.
    1. Finding potentials
    2. Differential notation
    3. Stokes' theorem
  • Lecture 37: May 7 Stokes' theorem and applications
  • Lecture 38: May 11 Review i: Proof of Stokes' theorem
  • Lecture 39: May 13 General review.