MTH 243   Calculus for Functions of Several Variables

Fall   2010

 Instructor: Lubos Thoma Office: Lippit Hall 101G,   tel: 874.4451 Class Schedule: TuTh 8.00 -- 9.15am, Washburn Hall 219 (Section 0001)                            TuTh 12.30 -- 1.45pm, Lippitt Hall 204 (Section 0003) Find the volume of cool and unusual geometric shapes. Fluid flow velocity is a vector field. Vortices are localized regions of high curl.

Final Exam:   The final exam is a comprehensive exam and will be given on Thursday December 16, 7.00 -- 10.00 pm (common slot), in Quinn auditorium as scheduled by the Registrar. This time is valid for both Sections 01 and 03.

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.