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:

- 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:

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.