University of Rhode Island    Department of Mathematics

# Fall 2019

TuTh 11-12:15 Swan Hall 309

 Instructor: Dr. M. Kulenovic, Lippitt Hall 202D, 874-4436, mkulenovic@uri.edu Text:  McCallum, Hughes-Hallet, et. al., Multivariable Calculus, 7-th Edition Prerequisites: MTH 142 or equivalent Calculators: A graphing calculator is required Office Hours: TuTh 12:30-2 and by appointment

Introduction
MTH 243 is a third calculus course, with the focus on functions of two, three or more variables and the extensions of the ideas of single variable calculus to higher dimension. We will continue to use Mathematica in this course. The Mathematica software is available in the campus computer labs and can be downloaded for free. Our work with Mathematica will be organized into Mathematica projects  that you can download from SAKAI.

Objectives.  At the conclusion of this course 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 functions in  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 extremal and saddle points (for functions of two variables only), use these concepts to solve unconstrained optimization problems.

5.      Calculate double and triple integrals algebraically, change variables in integrals  from rectangular coordinates to polar, cylindrical, spherical coordinates (and vice versa).

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 to problems in physics and geometry,

9.      Calculate flux integrals geometrically and algebraically over surface graphs, portions of cylinders, and portions of spheres.

10.  Use and interpret the Green’s theorem.

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

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

Key: E1 and E2 correspond to Exams 1 and 2, FE = Final Exam, CW = Class Work(Quizzes), Mp=Mathematica projects..
.

How to get help
I may help you with questions, just stop by my office. There will be tutors available as well. See AEC (Academic Enhancement Center) tutoring schedule.

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

Multivariable Calculus Mathlets

Mathematica Worksheets

The practice problems, exams and Mathematica Notebooks are part of Sakai .

## MTH 243/2  Calculus III Fall 2019

 Day Event Text Suggested Problems 09/04/19 12.1 7,11,12,19,21, 29 12.2 1-7,9,11,16,18,19 09/09/19 12.3 1-7,11,20,28,31 12.4 1-5,8,10,11,23,24,31 09/16/19 12.5 1-7,8,25 13.1 1-7,8,14,29,31 09/23/19 13.2 1-7,14,19,28,31 09/30/19 13.3 1-4,8,14,16,19, 37,41 13.4 1-5,11,19,22,29 10/07/19 14.1 1-7,14,17,23 14.2 1-5,14,22-28,35,41 10/14/19 14.3 1-7,14,15,22,23 14.4 1-7,19, 29,35,49,53 10/21/19 14.5 1-7,14,19,23,28,31 14.6 1-7,11,14,20,23 10/21/19 14.7 1-11,14,22,31 15.1 1-7,19-22,25 10/28/19 15.2 2,5,7,14-16,19-21,23 16.1 3,5,7,11 11/04/19 EXAM 1 16.2 1-7,11-14,18,28-37 16.3 1-5,7-11,28-31,41 11/11/19 16.4 1-11,14,16,17,20-23 16.5 1-7,14-16,20-31,35 11/18/19 16.7 1-7,10,11 17.1 1-11, 28,32,35,41,49 11/25/19 17.2 1-7,14-16,22-28,31 17.4 1-11,14 12/02/19 EXAM 2 18.1 1-10,14-16,19 18.2 1-11,15 18.3 1-7,11,14,19,22,28 12/09/19 18.4 1-7,16,19,22 19.1 1-4,10,11,14,19 FINAL EXAM