University of Rhode Island Department of Mathematics Fall 2011

**MTH 243-200 (Providence) Calculus for Functions of Several Variables**

**Text**: 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 the official Calendar and Problems sheet . 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.
- Represent and interpret plots of vector fields (including flow lines)
- Use vector valued functions to do calculations of line integrals, and apply Green's theorem.

**Evaluation** There will be two exams (Oct. 6 and Nov. 10) and a comprehensive final exam (Dec 15). 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, 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).

**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.