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

        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