MATH 241 -- Vecor (Multivariable) Calculus (Calculus III)
Professor Matt Miller (miller@math.sc.edu)
Section 501, MWF 11:15-12:05, LC 310

Note: If this page looks out of date, please Reload or Refresh it.

Text: Calculus--Early Transcendentals by Anton, Bivens and Davis, Wiley, 2005, 8th ed. You will also need a graphing calculator (TI-83, 83-Plus preferred).

  • Class topics and problems
    You will observe that I assign homework BEFORE we talk about a topic. That is because I really want you to READ the material, and struggle a bit with the problems; then the class and my lecture, or the group work, will make more sense to you, and you will be in a better position to ask good questions. Attempting problems and seeing where you get stuck is much more useful (albeit painful) than churning through problems that you basically already know how to do! In all sections you should first do the Quick Check Exercises. If a problem has multiple parts you should attempt them all, unless otherwise indicated.
  • January 11-15. Introduction to vector algebra and geometry. Read the text sections 12.1-12.4. In 12.1, do problems QCE (see above), 1, 2, 3, 4 (optional for now, this is easier to do with parametric equations), 5, 6a, 8, 10, 11, 17, 18, 23, 25, 27ac, 31, 34, 47. In 12.2, do problems 3, 5, 8, 10b, 12adf, 13d, 14b, 15abef, 17, 20, 22, 25, 34, 35, 41, 42, 46, 47, 51. Also if u and v are vectors with their tails at a common point, sketch them and the vecor v-u on a single diagram. In 12.3, do problems 1acde, 2, 3, 8, 9, 10, 14, 24, 25, 26b, 27c, 28, 29, 43, 44. In 12.4, do problems 1, 3, 4, 5, 7ab, 10. There will be a quiz on 12.1-12.3 on Wednesday, 20 January (postponed to Friday as a take-home).
  • January 20-22. Cross products (cont.), parametric and explicit equations of lines. Read sections 12.5-12.6. Do problems 12.4 #11, 13, 17, 18, 21, 22*, 24, 27 (use projection and NOT the formula); do problems 12.5 #3b, 5b, 7b, 9b, 10b, 15, 17, 23, 24*, 25, 26*, 27, 31, 43 (use projection and NOT a formula), 45* (same comment), 48-50. Here is Quiz 1 and its solutions. The starred problems are due on Wednesday, 27 January.
  • January 25-29. Planes, quadric surfaces, vector valued functions. Read sections 12.6, 12.7, 13.1-13.2. Remember: it is always a good idea to do the Quick Check Exercises. In section 12.6, do problems #3, 4, 8, 9, 11, 12* (give the standard and also parametric equations), 13, 15, 17b, 18a*, 18b*, 22*, 23, 24, 31, 32, 39, 41, 45. The starred problems are due on Friday, 29 January. In section 12.7, do problems 1, 5, 7, 8, 11, 13, 15, 19, 43*. In section 3.1 do problems #1, 2, 4, 7, 11, 13, 14, 17, 31, 41, 45*; in 13.2 do problems #7, 8, 9, 10, 12*, 13, 14, 16, 19, 22*, 23, 29, 31, 32, 36, 49, 53*. The starred problems of 12.7-13.2 are due on Wednesday, 3 February.
  • February 1-5. Smooth curves, arclength, curvature, motion. Read sections 13.3-13.6. In section 13.3, do problems #1, 2, 5, 6*, 7*, 10, 17, 19, 23, 24*, 25. The starred problems of 13.3 are due on Friday, 5 February. Review Quiz 2 and its solutions. Here is a Challenge Problem that you may turn in on Monday, 8 February for some bonus points. In 13.4, do problems #1, 2, 5, 7, 11; in 13.5, do #1, 2*, 3, 5, 6*, 9, 13, 14*, 48 (you can avoid using problem 19 by taking the parameterization x = t and y = e^t), 49; in 13.6, do #1, 2, 3, 5, 6, 7, 9, 11*, 17, 19, 25, 26*, 27, 31, 32, 43, 53, 54. For these last three sections, turn in the starred problems on Wednesday, 10 February.
  • February 8-12. Review, Exam 1, graphical representations of functions of 2 or 3 variables Review Quiz 2 and its solutions. Read sections 14.1-14.2. In section 14.1, do problems #1, 7, 13, 19-22, 23, 25, 26, 29, 30*, 35-38, 39, 40*, 41, 43, 45, 46*, 47, 48, 49, 50*, 51, 53, 55, 57. The starred problems of 14.1 are due on Wednesday, 17 February.
  • February 15-19. Limits, continuity and partial derivatives Read sections 14.2-14.3. In section 14.2, do problems #1, 3, 5, 6, 7, 8, 9, 11, 13, 16*, 25, 26*, 28*. In section 14.3 do problems #1abgh, 2abgh, 3, 5, 8, 12*, 13, 14, 16*, 19, 21, 31, 47, 53, 67, 68, 70*, 71, 85b, 86a, 87. The starred problems of 14.2 and 14.3 are due on Wednesday, 24 February. read section 14.4. In 14.4 do problems #1, 2, 3, 9, 10, 11, 13, 17, 22*, 28*, 50, 53, 54*. The starred problems will be due on Friday, 26 February.
  • February 22-26. Differentiability, chain rule, directional derivatives, gradients, tangent planes Reread 14.4, then read 14.5-14.7. Section 14.5 is very straightforward once you make the upside down tree diagram of which variables depend on which, so I won't say much about it. Do problems #1, 2, 7, 9, 11, 12, 17-19, 23, 35, 36, 39, 40, 41, 46, 51, 55a*, 56a*, 56c*. Treat #63 as a Challenge problem. In 14.6, do problems #1, 2, 3, 5, 8, 9,13, 15, 16*, 26, 27, 30, 31, 38, 40*, 41, 42*, 47, 49, 51, 64, 73a, 75. Starred problems of 14.5 and 14.6 will be collected on Wed., March 3. In section 14.7 do problems #1, 2, 7, 8*, 9, 10, 13, 16a*, 18, 19, 23, 31, 32; the starred problems will be collected on Friday, March 5.
  • March 1-5. Tangent planes (cont.), max/min theory and practice Read sections 14.8 and 14.9. Do problems #5, 6, 7, 8, 9, 11, 12*, 15, 23, 24, 27, 29, 30, 32*, 35 from 14.8 and #1, 2, 5, 6*, 9, 11, 13, 15, 22, 30 from 14.9. The starred problems are due on Wednesday, 17 March.
  • March 8-15. Spring Break
  • March 15-19 Max/min (cont.), double integrals, Exam 2 Read sections 15.1 and 15.2. Don't forget about the Quick Check Exercises. Do #3-7, 9, 10, 14, 15, 17, 21, 22 from 15.1 and #1, 3, 5, 8*, 9, 12*, 13, 14, 17, 18*, 20, 24, 25, 29, 33, 34*, 47, 49, 51, 52*. Starred problems will be collected on Wed., 24 March.
  • March 22-26. Double integrals in polar coord's, triple integrals Read sections 15.3 and 15.5. Do #1-4, 7, 9, 10, 11, 13, 14, 15, 17, 18*, 19, 23, 24*, 25, 26*, 27, 30, 32, 34 in 15.3. Treat #41 as a Challenge problem. Starred problems will be collected on Mon., 29 March. Do problems #2-5, 11, 12, 15, 16*, 17, 18, 19, 20a*, 32* in 15.5; do problems #1-4, 5, 7-9, 10*, 12-15, 16* in 15.7. Starred problems will be collected on Wed., 31 March.
  • March 29-April 2. Vector fields, line integrals, potential functions for conservative fields Read sections 16.1-16.3. Do #1-4, 6*, 7, 11, 37b, 38b*, 43 from 16.1; #1, 3, 4, 9, 10a, 10b*, 10c*, 15, 16, 17, 19, 29, 30, 37, 41 from 16.2; and #1, 2, 4*, 6, 7, 8b* (do the integration of the line integral), 8ac* (here's where the potential function comes in), 10, 11, 16, 17, 23-25, 27 from 16.3. Starred problems will be collected on Wed., 7 April.
  • April 5-9. Computation of line integrals, Green's Theorem Read section 16.4. Do problems #1, 2, 4, 6, 8*, 10*, 12, 17, 35. Starred problems will be collected on Monday, 12 April.
  • April 12-16. Computation of line integrals, Green's Theorem (cont.), Exam 3
  • April 19-26. Change of variables, review of course Read section 15.8. Do problems #1-3, 5-8 (also do 5-8 using the reciprocal trick), 17, 18, 19, 20, 21, 22, 24, 31, 32, 35, 43, 47.
  • Exams
  • Here is the Departmental day by day syllabus. You can see that the pace is very fast.
  • FIRST EXAM: Wednesday 10 February (postponed by one class day!) and the solution key. It is not a bad idea to look at the old exams and final for sample questions, but the order of the topics has changed over the years, so you won't find a perfect correspondence. With the present syllabus and text, so far we have covered 12.1-12.7 and 13.1-13.3 pretty thoroughly, and pieces of 13.4, 13.5, 13.6. Compare your class notes with the text to see specific topics. The quizzes hit the real basics, but not everything.
  • SECOND EXAM: Friday, 19 March and the solution key and a correction. We have covered 14.1-14.9 pretty thoroughly. You definitely need to know about contour lines (level curves), level surfaces, first and second derivatives, the multivariable chain rule, gradients and their properties, linear approximation, tangent planes, finding and classifying relative max and min, using Lagrange multipliers to find absolute max and min values on a region with a nince boundary. Compare your class notes with the text to see specific topics. The quizzes #4-6 hit the real basics, but not everything.
  • THIRD EXAM: Friday, 16 April and the solution key . The exam covers 15.1-15.3, 15.5, 15.7, 16.1 (except for divergence and curl), 16.2-16.4. As usual the quizzes #7-9 illustrate the basics, but not absolutely everything. You will need to know Green's Theorem, how to test for conservative vector fields, what dV looks like in cylindrical and spherical coordinates.
  • FINAL EXAM: Tuesday, 4 May, 9 am.

    • Last modified: April 5, 2010