MATH 241 -- Vector Calculus

Professor Matt Miller
miller@math.sc.edu

Section 5 Tu Th 2:00 -- 3:15 in LeConte 112
Text: Calculus, 8th ed. by Varberg, Purcell, Rigdon


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  • Class topics and problems
  • Aug. 21. Parametric equations
    Do problems 1, 4, 6, 7, 9, 11, 13, 14, 17, 21, 25, 31, 34, 37, 38, 40 from 13.1. Find a parameterization for the curve y^2 = x^3, for the curve 4x^2 + 4y^2 = 16, and for the curve x^2 + y^2 = 1 NOT using trig functions. Read section 13.2 of the text.
  • Aug. 25-28. Operations on vectors, motion
    Do problems CR 1-4, PS 1, 3-5, 7, 9, 10 from 13.2 and CR 1-3, PS 1, 3, 4, 5, 6 from 13.3. Continue with 13.3, problems 7, 10, 11, 13-15, 19-20, 23, 25, 33, and turn in 32 for up to 4 bonus points; then do 13.4, problems 5, 6, 10, 13, 14, 21, 23-25, 27-28, and turn in 36 for up to 4 bonus points.
  • Sept. 2-4. Vectors and 3D space
    Do problems CR 1-4 and PS 1, 3, 10, 11b, 13, 17, 18, 21, 22 from 14.1 and CR 1-4, PS 1a, 2a, 5, 7, 9, 11, 21, 25, 27, 28, 30, 32, 33 (use vector or scalar projection instead of the formula for point to plane distance) from 14.2. Do CR 1-4 and PS 3-7, 11-12, 17-18, 21 from 14.3. Read 14.4 and do CR 1-4.
  • Sept. 9-11. Lines, planes, parametric equations, surfaces
    Continue with 14.4 PS 1, 3, 5, 6, 9, 10, 13, 14, 17, 18, 23, 24, and 21 for bonus points if turned in by 9/11. Do 14.5 CR 1-2, PS 1, 3, 7, 8, 12, 15, 16, 22. Do 14.6 CR 1-4, PS 1-3, 6-8, 10, 13, 14, 17, 33.
  • Sept. 16-18. Functions of two variables
    Do 15.1 PS 3, 5-7, 9-11, 13, 15, 20, 23, 26, 41 and 15.2 PS 1, 3, 4, 7, 8, 10, 11, 14, 17, 21, 23 between Tuesday and Thursday. Then do 15.1 CR 1-4, 15.2 CR 2-4, PS 25, 26, 29. What do you notice about the contour lines for the plane 3x - 2y - z = 18? Read section 15.4. and problems CR 1-4, PS 1, 3, 4, 6, 19.
  • Sept. 23-25. Gradients and Exam 1
    Complete the homeworks from 15.1, 15.2, and 15.4 listed above. For review be sure you can work all the quiz problems perfectly. Then work on these supplemental probelms. You won't have time to do all of them, but in many cases you should be able to say, "I can do that with confidence," so just move on. Do page 570 problem 10, section 13.6 CT 1, 2, 4, 7, 8, 13 23 and STP 1, 3, 6 (TL only), 7, 8, 10b, 11, 14, and 20. In section 14.8 do CT 2-7, 29, and STP 3acd, 4a, 6, 7d, 8bc, 11, 20 (v and a only), 22, 25, 28, 29, 36; in section 15.10 do CT 1 and STP 3-6, 13. BEFORE the exam read the handout pp. 577-579 and 587-588. Do problems 10, 12-15, 17, and 6, 7, and 9 on p. 588. ****** AFTER the exam read pp. 591-594 in the handout. Do problems 33-35 from 15.1, problems 40, 43, and 50ac from 15.2, problems 7 and 9 from 15.4, read 15.5 and do CR 1-4.
  • Sept. 30-Oct. 2. Gradients, tangent planes, directional derivatives, and linear approximations
    Be sure you have done all the stuff listed above from 15.1 to 15.5; then go on to do section 15.4 PS 11-15, 21; section 15.5 PS 1-7, 9, 11; and section 15.7 CR 1-4, PS 1, 3, 5, 6, 15, 17, 26.
  • Oct. 7-9. Gradients, tangent planes, linear approximations, chain rule, local max/min
    Do all the problems on the handout ("Worksheet"). Do PS 15-17, 19, 31 from 15.5; do CR 1-4, PS 1-3, 5, 8, 10, 13, 28, 29 from 15.6; do PS 13, 23-25 from 15.7; do CR 1-4, PS 1, 3, 6, 11, 12, 24, 25 from 15.8. Take a look at the Maple worksheets to get a better feel for the geometric interpretation of partial derivatives, gradient, tangent planes, and so forth. More on different types of sets can be found at the end of section 15.3.
  • Oct. 16. Max/min on closed and bounded sets, Lagrange multipliers
    Do 15.8 CR 1-4, PS 1, 3, 6, 11-13, 24-25, read 15.9, and then do 15.9 CR 1-4, PS 1-3. Be able to explain the method of Lagrange multipliers.
  • Oct. 21-23. Max/min (conclusion), double integrals
    Do 15.9, PS 9, 10; do 16.1 CR 1-4, PS 1, 4-9, 11, 15, 22, 23; do 16.2 CR 1-4, PS 1, 3, 5 7, 9, 10-12. That's just warm up; the real stuff is in 16.3, where you should do CR 1-4, PS 5-14 (yes, do 'em all!), 19, 23-25, 31, 32, 36, 39.
  • Oct. 28-30. Double integrals in polar coordinates, line integrals
    Do section 16.4, problems CR 1-4, PS 1, 3-6, 11-14, 16, 18, 25, 29. Read 17.1 and 17.2 very thoroughly; this is a whole new idea, and takes time to settle in. You may omit the material on divergence and curl. Then work on 17.1, problems CR 1-2, PS 1, 2, 5, 6, 8-10, and 17.2 CR 1-4, PS 1 3-9, 12.
  • Nov. 4-6. Line integrals and conservative vector fields
    Continue with 17.2, problems 19, 21, 22, 24, 26*(note that pounds are a measure of force in totally obsolete English units--mass, as understood by physicists, is measured in slugs, I think--anyways, in this case the force is directed entirely downwards, being nothing more than the force on the squirrel due to gravity). Then do 17.3, problems 1, 2, 5-7, 11, 12, 25*, 26*. Do problems p. 727 #7, p. 832 #1-4, p.833 #12, 20, 21, 22, 24, 25
    HAVE YOU DECIDED ON A PROJECT AND FOUND A (SOME) PARTNER(S) YET?
  • Nov. 11-13. Green's Theorem
    Finish up the assigned problems from 17.1-17.3 and the supplement. Go to 17.4 and do problems 1-3, 5, 7, 8, 17-19, and conclude with problems 6, 7, 10, 11-14 on p. 857 of the supplement. Friday, 14 November is the last day to get assistance on projects.
  • Nov. 18-20. Triple integrals
    Projects are due in class on Nov. 18. From 16.7 do PS 1, 3, 4, 6, 8-10, 13-17, 19, 20, 22, 27, 29. Review problems for the exam will be announced on Thursday.
  • Nov. 25. Exam 2
  • Dec. 2-4. Triple integrals in cylindrical and sperical coordinates
    In 14.7 do CR 1-4, PS 2-5, 7-9, 11, 13-15; in 16.7 do CR 1 and PS 21; in 16.8 do CR 1-4, PS 1-4, 12, 14, 16.

  • Exams and Projects
  • Thursday, Sept. 25: FIRST EXAM: covers text sections 13.1-13.4, 14.1-14.6, 15.1-15.2, and the gradient vecor (15.4). Be sure you can work all the quiz problems to this point, and study each end of chapter review. The exam will not include problems on the geometric meaning of the partial derivatives and gradient vector.
  • PROJECT : Topics will be distributed from October 23-28. Keep checking to see if more options come up; meanwhile think about with whom you will work (you are to work in groups of 2 or 3, or 4 at the most). The final reports are due in class Tuesday, November 18.
  • Tuesday, Nov. 25: SECOND EXAM: covers text sections 15.4-15.9, 16.1-16.4, 17.1-17.4, all supplements, and 16.7.
  • FINAL EXAM: Wednesday, Dec. 10 (2-5 pm) in regular classroom. All sections listed above will be covered, including any material that is discussed in class the week after the second exam and Thanksgiving (14.7 and 16.8). Formulas as agreed upon in class will be provided, but I remind you that you MUST know Green's Theorem; I will not give it to you; you must also know what a potential function is in the case of a conservative vector field.

    • Last modified: December 2, 2003