Dr. Nestler's Math 11 (Multivariable Calculus) - Spring 2018 - section 4256 - TTh 5:00-7:25pm - Room MC 74

Class information

        Syllabus (8 pages)

Additional resources

        Office hours:  MW 1:30-2:00, T 3:15-4:45, Th 4:15-4:45 in MC 61; Math 11 workshop Th 3:15-4:15 in Math Lab

        Math Lab

        Jeff Miller's History of calculus symbols including "curly d" partial derivative operator and gradient symbol

Class notes

At the start of course you will receive a 39-page packet of notes that you should bring with you to class.  This set of notes is comprised of the following:

Some definitions and theorems from Calculus 1 and 2

Essential Trigonometric and Hyperbolic Identities

Thursday, February 22  Surfaces (4 pages)

Thursday, February 22  Quadric surfaces: pictures (2 pages) from Larson, Hostetler, Edwards "Calculus" 8th Ed. (2006) Houghton Mifflin Co. [These may not have printed correctly in the packet you were given]

Tuesday, February 27  Vector-valued functions and space curves (3 pages)

Tuesday, March 6  Curvature (Part 1) (3 pages)

Thursday, March 8  Curvature (Part 2) (3 pages)

Thursday, March 15  Level curves from Larson, Hostetler, Edwards "Calculus" 8th Ed.

Tuesday, March 27  Differentiable functions (Part 1) (3 pages)

Thursday, March 29  Differentiable functions (Part 2) (2 pages)

Thursday, March 29  Differentials and tangent plane

          Tuesday, April 24  Review of definite integrals

          Thursday, April 26  Double integrals in polar coordinates [These may not have printed correctly in the packet you were given]

          Tuesday, May 1  Inner partition of a solid; definition of triple integral

          Tuesday, May 1  Additional triple integral exercises

          Tuesday, May 8  Triple integrals in spherical coordinates 

          Tuesday, May 15  Vector field examples

          Tuesday, May 22  Independence of path (2 pages)

Thursday, May 24 and Tuesday, May 29  Surface integrals homework [These may not have printed correctly in the packet you were given]

Tuesday, May 29  Divergence theorem homework (2 pages) [These may not have printed correctly in the packet you were given]

          Thursday, May 31  Proof of a special case of the Stokes Theorem

Thursday, May 31  Application of the Stokes Theorem to fluid flow

          Thursday, May 31  Conservative vector fields

          Thursday, May 31  Theorem summary

Optional reading

A simple proof of the right-hand rule (4-page article by Fuchang (Frank) Gao, 2012)

         Direction of normal vector of a smooth plane curve

         A differentiable function with discontinuous first partials

         A differentiable function with discontinuous, unequal second partials (2 pages)

         Two directional derivative examples

        "The History of Stokes' Theorem" (11-page article by Victor J. Katz, Mathematics Magazine, Vol. 52, No. 3, May 1979)

A triple integral in real life

Some examples of non-helix space curves with constant curvature:

http://www.math.uni-bonn.de/people/karcher/ConstantCurvature.pdf

http://math.stackexchange.com/questions/309531/closed-space-curves-of-constant-curvature