## MTH 243   Calculus for Functions of Several Variables

### Summer   2012

 Instructor: Lubos Thoma Office: Lippitt Hall 101G               Tel: 874.4451 Class schedule: MTuWTh 8:00 - 9:45am, Lippitt Hall 204

Description:   MTH 243 is a third calculus course, with the focus on functions of 2,3, and more variables and the extensions of the ideas of elementary calculus to higher dimensions.

Objectives:   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 vice versa,
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.

Textbook:   McCallum, Hughes-Hallet, et. al., Calculus: Multivariable (5th Edition) with WileyPlus, Wiley, ISBN: 978-0-470-13158-9.

WileyPlus:   We will be using WileyPlus online homework system this semester. To sign up for the WileyPlus system, you will need a WileyPlus registration code. If you buy a copy of our textbook at the URI Bookstore, a registration code for WileyPlus will be included with the book at no additional cost. If you buy a copy somewhere else and it does not include WileyPlus code, you will need to purchase a WileyPlus code separately. The cost of a registration code at the Wiley site: WileyPlus is about \$50.
To register for our section on WileyPlus, follow the following link http://edugen.wileyplus.com/edugen/class/cls272792/

Calculator:   A graphing calculator is required.

Prerequisites:   MTH 142  or equivalent.

Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.