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

Syllabus (8 pages)

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

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

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

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