Multivariable Calculus Online
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| (supported in part by National Science Foundation grant DUE-9950600) |
Under Construction: Please go to the main site at
math.etsu.edu/multicalc .
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1: Vector-Valued
Functions
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1.1 Vectors
in 2 and 3 dimensions
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1.2 The
Dot Product
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1.3 The
Cross Product
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1.4 Equations
of Planes
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1.5 Parametric
Equations
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1.6 Velocity
and Acceleration
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1.7 Speed
and Arclength
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1.8 Components
of Acceleration
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Summary
and Review
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2: Partial
Differentiation
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2.1 Functions
of 2 Variables
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2.2 Limits
and Continuity
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2.3 Partial
Derivatives
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2.4 Partial
Differential Equations
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2.5 Differentiability
and Approximation
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2.6 The
Chain Rule
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2.7 Gradients
and Level Curves
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2.8 Optimization
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2.9 Lagrange
Multipliers
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Summary
and Review
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3: Surfaces
and Transformations
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3.1 Surfaces
and Tangent Planes
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3.2 Parametric
Surfaces
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3.3 Coordinate
Transformations
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3.4 Polar
Coordinates
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3.5 The
Jacobian
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3.6 Curvilinear
Coordinates
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3.7 Normals
and Geodesics
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3.8 The
Fundamental Form
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3.9 DIFF
GEOM: Curvature
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Summary
and Review
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4.1 Iterated
Integrals
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4.2 Double
Integrals
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4.3 Applications
of the Double Integral
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4.4 Change
of Variables
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4.5 Double
Integrals in Polar Coordinates
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4.6 Triple
Integrals
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4.7 Cylindrical
and Spherical
Coordinates
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Summary
and Review
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5.1 Vector
Fields
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5.2 Line
Integrals
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5.3 Potentials
of Conservative Fields
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5.4 Green's
Theorem
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5.5 Surface
Integrals
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5.6 The
Divergence Theorem
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5.7 Stoke's
Theorem
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5.8 Differential
Forms
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Summary
and Review
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Capstone: The Inverse
Square Law
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C.1. Uniform
Circular Motion
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C.2. Conservation
Laws
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C.3. Kepler's
Laws
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C.4. Satellites
and Planets
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C.5. Electric and Magnetic Fields
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C.6. Maxwell's Equations
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C.7. Maxwell's Equations and
Special Relativity
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C.8. General Relativity - An Overview
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Individual
Sections
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Maple
Worksheets
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Online
Tools
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Answers to Selected Odd
Exercises
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The
Entire Course
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Introduction
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FAQ's
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Contributors
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Instructor's
Guide
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Optimized for 1024 X 768 resolution
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Developed for Windows IE 6.0 or greater
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Patch for Netscape and Mozilla
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MacIntosh Users
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MATHML Version -- Coming Soon
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Mathematica Notebooks --
Coming Soon
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© Copyright 2001 by Jeff Knisley,
Dept. of Math., East Tennessee
State University. Free for individual use only. No portion of this
textbook may be altered or sold.
Multivariable Calculus Online is adapted from the
textbook Calculus: A Modern
Approach by Kevin Shirley and Jeff Knisley.
Development of Multivariable
Calculus Online was funded in part by National Science Foundation grant DUE-9950600.
Many of the applets and images were prepared with Javaview,
an excellent web-based visualization tool which is free for
download and can be used with Maple 6 through 9.
Additional applets were
prepared with LiveGraphics3d,
an excellent complement to Mathematica featuring parameterized graphics.
Sections written in LaTeX2e and converted to html with TTHGold.
Final editing
was performed with Microsoft Frontpage and Eversoft
1stPage2000.
A special thanks to
my wife, Debra, for all her support, suggestions, guidance, and encouragement.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the
author and do not necessarily reflect the
views of the National Science Foundation.
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Eversoft
1stPage2000. |