University of Rhode Island    Department of Mathematics

# MTH 243  Calculus III  Fall 2000

## Section 4 - Shepard 432 - Providence

 Instructor: Orlando Merino, Tyler Hall 220, Phone No. 874-4442, merino@math.uri.edu Text:  McCallum, Hughes-Hallet, et. al., Multivariable Calculus Prerequisites: MTH 142 or equivalent Calculators: A graphing calculator is required

Introduction
MTH 243 is a third calculus course, with the focus on functions of 2,3, or more variables and the extensions of the ideas of elementary calculus to higher dimension. We will continue to use Maple V  in this course. The Maple software is available in the campus computer labs. Our work with Maple will be organized into Maple projects  that you can download from this web site, or will be handed to you in class.

Objectives.  At the conclusion of this semester you will be able to:

1. Read and interpret 3d plots and 2d/3d contour diagrams,  read and interpret tables of functions of several variables, and  plot by hand the graph of simple functions of 2 variables, and simple contour plots of 2 or 3 variables.
2. do calculations with vectors that involve the concepts of addition, scalar multiplication, dot product, cross product, magnitude, projection, and use these concepts in geometry and physics applications.
3. calculate partial and directional derivatives, gradients and differentials of function of several variables, use local linearization to approximate functions,
4. Calculate critical points, use the second derivative test to determine local extrema and saddle points (for functions of two variables only),  use these concepts to solve unconstrained optimization problems, and use Lagrange multipliers to solve constrained optimization problems.
5. Calculate double and triple integrals algebraically, change variables in integrals  from rectangular coordinates to polar, cylindrical, spherical coordinates (and viceversa).
6. use the concept of parametrization to represent curves and surfaces
7. represent and interpret plots of vector fields (including flow lines)
8. use vector valued functions to do calculations of line integrals, flux integrals, divergence, and curl, apply these concepts and Green's theorem to problems in physics and geometry,
9. Calculate flux integrals geometrically and algebraically over surface graphs, portions of cylinders, and portions of spheres.

Evaluation
There will be three exams and a comprehensive final.  The course grade will be computed as follows:

Course grade =  ( 100 E1 + 100 E2 + 100 E3  + 200 FE + 200 CW ) / 700

Key: E1, E2, and E3 correspond to Exams, FE = Final Exam, CW = Class Work.
Class Work may include collected homework, quizzes, Maple assignments or special projects.

How to get help
I may help you with questions whenever you can find me in my office.  If you want to make sure that I will be there just set up an appointment.  Also, I can answer questions by electronic mail.

### MTH 243 Calculus III Section 4 (Providence) Fall 2000

The following calendar gives a timetable for the course. Your class may be slightly behind or ahead at any given time. Below the calendar is a list of sections in the textbook, with suggested problems. Some of these may be done in class, others as homework. Your instructor will be more specific. You should attempt them all. (Note: In the problem lists, a notation like 3-9 means that all the problems 3,4,5,6,7,8,9 are assigned.)
 Week Events Section Problems Sep 4 Classes  begin sep 6 11.1 11.2 11.3 11,12,17-20  1,3,9,11,13,18,19 2,3,4,5,10 Sep 11 11.4 11.5 12.1 1,2,3,8,9,11,22,23 1,2,5,7,13,14,15  1,3-8,21,22,27,28 Sep 18 12.2 12.3 12.4 1-4,6,8,9,13,15  1,3,5,7,8,10,13,14,17,20,28 1,3,5,8,13-15 Sep 25 13.1 13.2 1,3,5,9,14,15 1-5,7,11,15,17,22,23,33,35 Oct 2 EXAM 1 13.3 13.4 1,4,5,11,12,15,21  3,5,8,9,13-15,23,31,37,38 Oct 9 no class M 13.5 13.6 13.7 1,7,9,10,13  1,3,5,9,13,15,17,18,25* 1,3,5,9,11,15,17 Oct 16 14.1 14.3 1,2,5,7,12,14,17,18 5,7,13,22 Oct 23 15.1 15.2 15.3 2,4,13 1,2,5-10,12,15,19,22  2-5,9,10,1314 Oct 30 15.5 15.6 16.1 13,5,7,9,11-13,15,19,21  1-11,15,17,21 5,7,11,14,16,17,21, 22, 33 Nov 6 16.2 16.3 1,3,4,6,7,11,12,15,17,23,31,32 1,3,7,9,17,22,23 Nov 13 no class M  EXAM 2 App G 17.1 odd 1-15,16 1,3,6,8-11 Nov 20 No class Th,F  Thanksgiving 17.2 18.1 5,6,9 1,4,5,7,10,13,15,19 Nov 27 18.2 18.3 18.4 1,3,4,6,9,11,15  1,3,4,7,9,12,19 1,3,5,6,11-13 Dec 4 19.1 19.2 1,2,4,5,11,13,14,17  1,3,4,11,13,14 Dec 11 Last class M