MTH 243   Calculus for Functions of Several Variables

Fall   2013

 Instructor: Lubos Thoma Office: Lippitt Hall 101F               Tel: 874.4451 Class schedule: TuTh 8:00am - 9:15am (section 01), Bliss Hall 305 TuTh 11:00am - 12:15pm (section 03), Swan Hall 305

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.

Outcomes:   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.

Syllabus and schedule:     syllabus.