MATH2450 -- Calculus III with Applications

Fall 2014

Instructor: Josh Engwer

"Mathematics, you see, is not a spectator sport." -- George Polya, circa 1969.

Course Calendar:

(DEMOS) -- Visual Demonstrations of Key Concepts. Requires the free Wolfram CDF Player.

DATE:		OUTLINE:	SLIDES:	DEMOS:	NOTES:	DESCRIPTION:
08/25	Mon				[GREEK-ALPHABET], [LOGIC-SETS]	(Course Syllabus)
08/26	Tues	9.2	9.2			Vectors: Algebra
08/27	Wed	9.3	9.3			Vectors: Dot Product
08/29	Fri	9.4	9.4			Vectors: Cross Product
09/01	Mon	********	********	********	LABOR DAY	<< NO CLASS >>
09/02	Tues	9.5	9.5	9.5		Plane Analytic Geometry: 2D Parametric Curves
09/03	Wed	9.5	9.5	9.5		Solid Analytic Geometry: Lines in Space
09/05	Fri	9.6	9.6			Solid Analytic Geometry: Planes
09/08	Mon	9.7	9.7	9.7		Solid Analytic Geometry: Quadric Surfaces (Introduction)
09/09	Tues	9.7	9.7		[EX 9.7.{5,6,9,10} SOLUTIONS]	Solid Analytic Geometry: Quadric Surfaces (Identification)
09/10	Wed	9.7	9.7		[EX 9.7.13 SOLUTIONS]	Solid Analytic Geometry: Quadric Surfaces (Cross Sections)
09/12	Fri	10.1	10.1		[DOMAIN], [LIMITS], [EX 10.1.7 SOLUTIONS]	Vector Functions: Algebra, Limits
09/15	Mon	10.2	10.2	10.2		Vector Functions: Calculus
09/16	Tues	10.2	10.2			Vector Functions: Kinematics
09/17	Wed	10.4	10.4	10.4 10.4		Vector Functions: Arc Length, TNB-Frame, Curvature
09/18	Thurs	********	********	********	Time: 7pm - 11pm Location: SCIENCE 007	LAST-MINUTE HELP SESSION FOR EXAM 1
09/19	Fri	********	********	********	EXAM 1 Info/Logistics/Advice	EXAM 1
09/22	Mon	11.1	11.1			Functions of Several Variables: Intro, Domain
09/23	Tues	11.2	11.2			Functions of Several Variables: Limits
09/24	Wed	11.3	11.3			Functions of Several Variables: Partial Derivatives
09/26	Fri	11.3	11.3		[EX 11.3.10 SOLUTIONS]	Functions of Several Variables: Total Differentials
09/29	Mon	11.5	11.5			Functions of Several Variables: Chain Rules
09/30	Tues	11.5	11.5			Functions of Several Variables: Implicit Differentiation
10/01	Wed	11.6	11.6		[EX 11.6.{3,4,5} SOLUTIONS]	Functions of Several Variables: Gradients
10/03	Fri	11.6	11.6			Functions of Several Variables: Tangent Planes
10/06	Mon	11.7	11.7		[EX 11.7.3 SOLUTIONS]	Optimization: Relative Extrema
10/07	Tues	11.7	11.7		[EX 11.7.6 SOLUTIONS]	Optimization: Absolute Extrema
10/08	Wed	11.8	11.8	11.8	[EX 11.8.{3,4,5,6} SOLUTIONS]	Constrained Optimization: Lagrange Multipliers
10/09	Thurs	********	********	********	Time: 7pm - 11pm Location: CHEM 107	LAST-MINUTE HELP SESSION FOR EXAM 2
10/10	Fri	********	********	********	EXAM 2 Info/Logistics/Advice	EXAM 2
10/13	Mon	12.2	12.2	12.2	[EX 12.2.{5,6} SOLUTIONS]	Double Integrals: Rectangular Coordinates
10/14	Tues	12.2	12.2	12.2	[EX 12.2.8 SOLUTIONS]	Double Integrals: Interchanging Order of Integration
10/15	Wed	12.3	12.3			Graphing Polar Curves (review)
10/17	Fri	12.3	12.3			Double Integrals: Polar Coordinates
10/20	Mon	12.3	12.3		[EX 12.3.8 SOLUTIONS]	Double Integrals: Polar Coordinates
10/21	Tues	12.4	12.4			Double Integrals: Surface Area
10/22	Wed	12.5	12.5			Triple Integrals: Rectangular Coordinates
10/24	Fri	12.5	12.5		[EX 12.5.6 SOLUTIONS]	Triple Integrals: Rectangular Coordinates
10/27	Mon	12.7	12.7		[EX 12.7.3 SOLUTIONS] LAST DAY TO DROP	Triple Integrals: Cylindrical Coordinates
10/28	Tues	12.7	12.7		[EX 12.7.5 SOLUTIONS]	Triple Integrals: Spherical Coordinates
10/29	Wed	12.8	12.8			Multiple Integrals: Change of Coordinates
10/31	Fri	12.8	12.8		[EX 12.8.4 SOLUTIONS]	Multiple Integrals: Change of Coordinates
11/03	Mon	********	********	********		REVIEW FOR EXAM 3
11/04	Tues	********	********	********		REVIEW FOR EXAM 3
11/04	Tues	********	********	********	Time: 7pm - 11pm Location: PETRE 121	LAST-MINUTE HELP SESSION FOR EXAM 3
11/05	Wed	********	********	********	EXAM 3 Info/Logistics/Advice	EXAM 3
11/07	Fri	13.1	13.1			Vector Fields: Intro, Div, Curl
11/10	Mon	13.1	13.1		[EX 13.1.6 SOLUTIONS]	Vector Fields: Intro, Div, Curl
11/11	Tues	13.2	13.2	13.2		Line Integrals: Intro & Computation
11/12	Wed	13.2	13.2		[EX 13.2.3 SOLUTIONS]	Line Integrals of Scalar Fields
11/14	Fri	13.2	13.2		[EX 13.2.6 SOLUTIONS]	Line Integrals of Vector Fields
11/17	Mon	13.3	13.3		[EX 13.3.1 SOLUTIONS]	Line Integrals: Gradient Fields, Scalar Potentials
11/18	Tues	13.3	13.3		[EX 13.3.3 SOLUTIONS]	Line Integrals: Path Independence, Simpler Paths
11/19	Wed	13.4	13.4		[EX 13.4.2 SOLUTIONS]	Green's Theorem
11/21	Fri	13.4	13.4			Green's Theorem
11/24	Mon	13.5	13.5			Surface Integrals
11/25	Tues	13.5	13.5			Flux Integrals
11/26	Wed	********	********	********	THANKSGIVING	<< NO CLASS >>
11/28	Fri	********	********	********	THANKSGIVING	<< NO CLASS >>
12/01	Mon	13.6	13.6		[EX 13.6.2 SOLUTIONS]	Stokes' Theorem
12/02	Tues	13.7	13.7		[EX 13.7.2 SOLUTIONS]	Gauss' Theorem (Divergence Thm)
12/03	Wed	11.2	11.2		[EX 11.2.15 SOLUTIONS]	Functions of Two Variables: Continuity
12/08	Mon	********	********	********	EXTENDED OFFICE HOURS: 10am - 4pm	EXTENDED OFFICE HOURS
12/09	Tues	********	********	********	FINAL EXAM Info/Logistics/Advice	FINAL EXAM

EPILOGUE: (Assorted CalcIII topics that were not covered due to time but useful for higher math courses)

Multivariable Chain Rules: 2nd-order Derivatives (PDF Slides)
The Laplacian Operator in Polar Coordinates (PDF Slides)
An example of computing an infinite sum using only double integrals:
- T.M. Apostol, "A Proof that Euler Missed: Evaluating ζ(2) the Easy Way", The Mathematical Intelligencer, 5 (1983), 59-60.
An example of establishing irrationality of an infinite sum using double/triple integrals & geometric series:
- F. Beukers, "A Note on the Irrationality of ζ(2) and ζ(3)", Bulletin of the London Mathematical Society, 11 (1979), 268-272.

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