University of Rhode Island Department of Mathematics
TuTh 1112:15 Swan Hall 309
Instructor: Dr. M. Kulenovic, Lippitt Hall 202D, 8744436, mkulenovic@uri.edu 
Text: McCallum, HughesHallet, et. al., Multivariable Calculus, 7th Edition 
Prerequisites: MTH 142 or equivalent 
Calculators: A graphing calculator is required 
Office Hours: TuTh 12:302 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 (8742098) 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

