University of Rhode Island Department of Mathematics

MTH 243/1 Calculus III

Spring 2012

Instructor: Dr. M. Kulenovic, Lippitt Hall 202D, 874-4436, mkulenovic@mail.uri.edu

Text: McCallum, Hughes-Hallet, et. al., Multivariable Calculus, 5-th Edition

Prerequisites: MTH 142 or equivalent

Calculators: A graphing calculator is required

Office Hours: M, W 1-2 p.m.; F: 10-11 and by appointment

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. The Mathematica software is available in the campus computer labs. Our work with will be organized into Mathematica 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:

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.
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.
calculate partial and directional derivatives, gradients and differentials of function of several variables, use local linearization to approximate functions,
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.
Calculate double and triple integrals algebraically, change variables in integrals from rectangular coordinates to polar, cylindrical, spherical coordinates (and viceversa).
use the concept of parametrization to represent curves and surfaces
represent and interpret plots of vector fields (including flow lines)
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,
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 = ( 20 E1 + 20 E2 + 30 FE + 20 CW +10Math) / 100

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

How to get help
I may help you with questions, just stop by my office. Tutors will be available as well.

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.

Tutoring

Multivariable Calculus Mathlets

WileyPlus codes:

Section 1: MWF 12-1: http://edugen.wileyplus.com/edugen/class/cls263963/

Mathematica Notebooks

Inside Sakai

MTH 243-01 Calculus III Spring 2012

Day	Event	Text	Problems
Jan. 23		12.1	11,12,19,22, 29, 34
		12.2	1,5,7,9,11,16,18,19
Jan 30		12.3	1,4,5,7,10,20,28,30
		12.4	1,2,8,10,11,23,2430
		12.5	1,2,7,8,29
Feb 6		13.1	1-6,8,14,29,30
		13.2	11,14,19,28,30
		13.3	1,4,8,14,16,19,27,37,42
Feb 13		13.4	1,4,5,10,19,22,27
		14.1	1,3,7,14,17,20
		14.2	1,4,5,14,22-28,35,41
Feb 27		14.3	1-7,14,15,22,
		14.4	1-11,19,22,29,35,49,58,64
		14.5	1-11,14,19,23,28,35
Mar 5		14.6	1,4,7,11,14,20,23
	TEST 1	14.7	1-10,14,22,31,35
Mar 12-18			Spring Break

Mar 19		15.1	1-11,19-22
		15.2	2,5,7,14-16,19-21,23
Mar 26		16.1	1-7,11-14,19,28-30,34-40
		16.2	1-5,7-11,28-31,41,42
April 2		16.3	1,4,5-11,14,16,17,20-23
		16.4	1-7,14-16,20-23,31,32,35
April 9		16.5	1,4,5,7,10,11, 30, 31
		17.1	1,4,8,11,19,20,28,32,35,41,47
April 16		17.2	1-7,14-16,22-28,
		17.4	1-10, 20
April 23	TEST 2	18.1	1,3,5-10,14-16
		18.2	1-11,16, 21, 23, 25, 31
April 30			Classes end

May 1-2			Reading days