University of Rhode Island    Department of Mathematics

# Summer 2009

MTWTh 8-9:45 a.m. Lippitt Hall 204

 Instructor: Dr. M. Kulenovic, Lippitt Hall 200A, 874-4436, mkulenovic@mail.uri.edu Text:  McCallum, Hughes-Hallet, et. al., Multivariable Calculus, 4-th Edition Prerequisites: MTH 142 or equivalent Calculators: A graphing calculator is required Office Hours: MTWTh 1-2

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 12  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 and Stoke's theorems 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 two exams and a comprehensive final.  The course grade will be computed as follows:

Course grade =  ( 25 E1 + 25 E2 +  30 FE + 10 CW +10Mp) / 100

Key: E1, E2, and E3 correspond to Exams, FE = Final Exam, CW = Class Work(Quizzes), Mp=Maple.
Class Work consists of quizzes.

How to get help

Special Accomodations
Students who need special accomodations and who have documentation from Disability Services (874-2098) should make arrangements with Dr. Kulenovic as soon as possible.

Summer Tutoring

Multivariable Calculus Mathlets

Maple Worksheets

Below are instructions that you may find helpful when getting started with your Maple assignments:

Maple worksheets

## MTH 243-1000  Calculus III Summer 2009

 Text   Problems Day Event Monday, May 18 12.1 11,12,19-22, 29, 34 12.2 1,5,7,9,11,16,18,19 May 19 12.3 1,4,5,7,10,20,28,30 12.4 1,2,8,10,11,23,2430 May 20 12.5 1,2,7,8,28 13.1 1-6,8,14,29,30 May 21 13.2 11,14,19,28,30 13.3 1,4,8,14,16,19,2736,37,42 May 25 May 26 13.4 1,4,5,10,19,22,27 14.1 1,3,7,14,17,20 May 27 14.2 1,4,5,14,22-28,35,41 May 28 14.3 1-7,14,15,22, 14.4 1-11,19,22,29,35,49,58,64 June 1 14.5 1-11,14,19,23,28,35 14.6 1,4,7,11,14,20,23 June 2 14.7 1-10,14,22,31,35 15.1 1-11,19-22 June 3 15.2 2,5,7,14-16,19-21,23 June 4 TEST 1 16.2 1-7,11-14,18,28-30,34-40 16.3 1-5,7-11,28-31,41,42 June 8 16.4 1,4,5-11,14,16,17,20-23 June 9 16.5 1-7,14-16,20-23,31,32,35 16.7 1-4,10,11 June 10 17.1 1-11,19,20,28,32,35,41,47 17.2 1-7,14-16,22-28, June 11 17.4 1-10 18.1 1,3,5-10,14-16 June 15 18.2 1-11,16 18.3 1-6,11,14,19,22,28 June 16 TEST 2 18.4 1-7,16,19,22 19.1 1-4,10,11,14,19 June 17 19.2 1-10 20.1 1-11,14,19 June 18 FINAL EXAM 20.2 20.3 2-7