University of Rhode Island    Department of Mathematics   Fall 2006

# MTH 243  Multivariable Calculus III

Section 200 (Providence Campus)- Th. 7-9:45 p.m.

 Instructor: Dr. Orlando Merino, Tyler Hall 220, 874-4442, merino@math.uri.edu Text:  James Stewart, Multivariable Calculus Concepts & Context, 3rd edition, Brooks/Cole, Chapters 9--13. Prerequisites: MTH 142 or equivalent Calculators: A graphing calculator is required

Exam Dates and Suggested Homework Problems can be found HERE

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. In this course we will use the Maple software, which is available in the computer lab located in the third floor of the Shepard Building (also available in Kingston's Campus). Our work with Maple will be organized into Maple projects  that 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 =  ( 15 E1 + 15 E2 +  35 FE + 35 CW ) / 100

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.
At least 50% of the Final Exam will consist of questions on the material discussed after the second exam.

How to get help
I will be available in the Shepard Building for questions from 6:30 to 7:00 pm on Thursdays, at a location to be announced in class. Also, I may help you with questions during office hours in Kingston. Other times are possible with an appointment. Also, I will answer all questions sent by electronic mail.

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

URI Civility Policy
Teachers at the University of Rhode Island are committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are cosidered unacceptable. The course instructor will have disruptive persons removed from the class.