Dr. Nestler's Math 11 (Multivariable Calculus) - Fall 2017 - section 4305 - TTh 7:35-10:00pm - Room MC 73

Class information

Syllabus (6-page PDF)

Additional resources

Office hours: MW 1:30-2:00, M 3:45-4:45, TTh 3:15-3:45 in MC 61; Math 11/15 workshop W 3:45-4:45 in Math Lab

Study suggestions (PDF)

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

Some definitions and theorems from Calculus 1 and 2 (PDF)

**Documents in PDF form (1 page unless noted): Please print and bring them to class.**

Thursday, September 7 Surfaces (4 pages)

Thursday, September 7 Quadric surfaces: pictures (2 pages) from Larson, Hostetler, Edwards "Calculus" 8th Ed. (2006) Houghton Mifflin Co.

Tuesday, September 12 Vector-valued functions and space curves (3 pages)

Tuesday, September 19 Curvature (Part 1) (3 pages)

Tuesday, September 19 Curvature (Part 2) (3 pages)

Tuesday, September 26 Level curves from Larson, Hostetler, Edwards "Calculus" 8th Ed.

Thursday, October 5 Differentiable functions (Part 1) (3 pages)

Tuesday, October 10 Differentiable functions (Part 2) (2 pages)

Tuesday, October 10 Differentials and tangent plane

Tuesday, October 10 Implicit differentiation

Tuesday, October 24 Review of definite integrals

Tuesday, October 31 Double integrals in polar coordinates

Thursday, November 2 Inner partition of a solid; definition of triple integral

Thursday, November 2 Additional triple integral exercises

Thursday, November 9 Triple integrals in spherical coordinates

Tuesday, November 14 Vector field examples

Tuesday, November 28 Independence of path

Thursday, December 7 Proof of a special case of the Stokes Theorem

Thursday, December 7 Conservative vector fields

Thursday, December 7 Theorem summary

Optional reading (PDF documents)

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