University of Rhode Island
Department of Mathematics Fall 2010
MTH 243-200 (Providence) Calculus for Functions of Several Variables
Mc Callum, Hughes-Hallet, et al, Calculus Multivariable
5th edition, Wiley. ISBN: 987-0470-13158-9
Prerequisites: MTH 142 or equivalent
Calculators: A graphing calculator is recommended
About the course
MTH 243 is a third calculus
course, with focus on functions of several variables,
and extensions of the ideas of elementary calculus to higher
dimension. In this course we will use the Mathematica software, which
is available in computer labs at URI.
As sections are covered in class, you are expected to work out
at least the problems listed in mth243f10 schedule .
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
- 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
- Calculate double and
triple integrals algebraically, change variables in integrals
from rectangular coordinates to polar, cylindrical, spherical
coordinates and viceversa.
- Use the concept of
- Represent and interpret
plots of vector fields (including flow lines)
- Use vector valued
functions to do calculations of line integrals, and apply Green's
There will be two exams
and a comprehensive final exam.
The course grade will be computed
Course grade =
( 100 E1 + 100 E2 + 150 FE + 150 CW ) / 500
and E2 correspond to Exams, FE = Final Exam, CW
= Class Work.
Class Work may include
collected homework, quizzes, Mathematica assignments or special projects.
The course material discussed after the second exam will be heavily represented
in the final exam.
How to get help
I will be coming to the classroom 1/2 hour early
in order to answer questions. Also, URI has free tutoring
in room 222 of the Shepard building (schedule is posted on the door).
Students who need special
accomodations and who have documentation from Disability Services
(874-2098) should make arrangements with the instructor as soon as