University of Rhode Island    Department of Mathematics   Fall 2009

MTH 243  Calculus for Functions of Several Variables

EXAM 2: Tuesday November 24, from 6 pm to 7:30 pm in CBLS 100 (Center for Biotechnology and Life Sciences Auditorium) (14.6-17.2)

FIINAL EXAM : Friday, December 18, 7:00-10:00 pm, Swan Auditorium

Calendar with Exam Dates and Suggested
Problems: mth243f09syll.pdf

Maple Projects: Project 1, Project 2, Project 3

Instructors:   O. Merino (Secs. 1, 200) ,   V. Dobrushkin (Secs. 2 and 4) ,   R. Beauregard (Sec. 3)

TextMc 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 Maple software, which is available in computer labs at URI. Our work with Maple will be organized into Maple projects. As sections are covered in class, you are expected to work out at least the problems listed in mth243f09syll.pdf . At the conclusion of this semester 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 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 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.
  5. Calculate double and triple integrals algebraically, change variables in integrals  from rectangular coordinates to polar, cylindrical, spherical coordinates and viceversa.
  6. Use the concept of parametrization.
  7. Represent and interpret plots of vector fields (including flow lines)
  8. Use vector valued functions to do calculations of line integrals, and apply Green's theorem.

Evaluation There will be two COMMON exams and a comprehensive final exam.  The two exams will be given outside normal class time, on OCT 13 and NOV. 24, from 6 pm to 7:30 pm in CBLS 100 (Center for Biotechnology and Life Sciences Auditorium). The final exam is common, and it will be given at a date/time to be determined. The course grade will be computed as follows:

Course grade =  ( 100 E1 + 100 E2 +  150 FE + 150 CW ) / 500

Key: E1 and E2 correspond to Exams, FE = Final Exam, CW = Class Work.
Class Work may include collected homework, quizzes, Maple assignments or special projects.
The course material discussed after the second exam will be heavily represented in the final exam.

How to get help See your instructor during office hours.

Special Accomodations Students who need special accomodations and who have documentation from Disability Services (874-2098) should make arrangements with the instructor as soon as possible.

Illness due to Flu The H1N1 Flu Pandemic may impact classes this semester. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify your instructor of your status, and we will communicate through the medium we have established for the class. We will work together to ensure that course instruction and work is completed for the semester. The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view UrI information on the H1N1 will be posted on the URI website at, with links to the site.