Calculus: A New Horizon, Sixth Edition
Howard Anton


Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17

CHAPTER 1. FUNCTIONS

1.1 Functions and the Analysis of Graphical Information

Functions - create your own functions with this Mathematica notebook
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

1.2Properties of Functions

Functions - create your own functions with this Mathematica notebook http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

1.3 Graphing Functions on Calculators and Computers: Computer Algebra Systems

Graphics - plotting functions in 2D and altering Mathematica-generated images http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

1.4 New Functions from Old

Reflections, Symmetry, and Inverses - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Transformation of Functions - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

1.5 Mathematical Models; Linear Models

Calculating Velocities I and II - Mathematica notebook on spring-mass systems, equilibrium
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

1.6 Families of Functions

Power Functions - Mathematica notebook
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

Horizons Module Chapter 1


Fractals and Chaos

http://spanky.triumf.ca/
A site dedicated to fractals. A database of numerous fractal diagrams.

http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=18
A problem dealing with a fractal snowflake

http://mathworld.wolfram.com/topics/ComplexSystems.html
Explains various terms associated with Fractals and Chaos

Iteration and Dynamical Systems

http://www.geom.umn.edu/education/calc-init/population/
Gives a graphical description of population growth modeling

http://www.geom.umn.edu/education/calc-init/population/harvest.html
Population harvesting theory, and models

http://mathworld.wolfram.com/topics/PopulationDynamics.html
Describes various concepts of population dynamics such as population growth and life expectancy

Recursion

http://mathworld.wolfram.com/topics/Recursion.html
Describes the Ackermann function and other concepts of recursion

http://www.ies.co.jp/math/java/ser_eq/ser_eq.html
A Java applet illustrating a recursive function

Deposition in a Bank, and Interest Formula

http://mathworld.wolfram.com/topics/Accounting.html
Describes various accounting principles including principal and simple interest

http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=50
A problem dealing with lease payments on your Pontiac Sunfire

Fibonacci Sequence

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
Applications of Fibonacci numbers and further details



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CHAPTER 2. LIMITS AND CONTINUITY

2.1 Limits (An Intuitive Introduction)

Intro to Limits - Graphically and Numerically - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Continuity and Solving Equations - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week2

Limits - Maple worksheet uses a variety of graphical and numeric methods to study multi-dimensional limits
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

2.2 Limits (Computational Techniques)

Alternate Intro to Limits - Geometrically, Numerically, Graphically, and Algebraically - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

2.4 Continuity

Root-Finding by Intermediate Values Applet - Java applet
http://www.wiley.com/college/mat/anton243310/mod2/applets.html

Continuity and Solving Equations - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week2

Horizons Module Chapter 2: No Module



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CHAPTER 3. THE DERIVATIVE

3.1 Tangent Lines and Rates of Change

Role and Computation of Tangent Lines - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week3

3.2 The Derivative

The Derivative Function - Mathematica notebook on the relationship between a graph of a function and the graph of its derivative
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

Discovering the Derivative by Exploration - TI-82/83 activity
http://www.ti.com/calc/docs/act.83calc.htm

3.3 Techniques of Differentiation

Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

3.4 Derivatives of Trigonometric Functions

Differentiation - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week3

3.5 The Chain Rule

Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

Numerically Discovering a Formula for Derivatives - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

3.6 Local Linear Approximation; Differentials

Intro to Derivatives - Smooth Curves DonŐt When You Zoom In - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Horizons Module Chapter 3


Calculus of Robotics (Kinematics Equations)

http://www.scas.bcit.bc.ca/scas/math/examples/ary_16_5/ary_16_5.htm
Motion of a piston - an application of differential calculus in robotics

http://mathworld.wolfram.com/topics/DynamicsandKinematics.html
A theoretical explanation of the Radius of Gyration

Cosine, and Sine

http://forum.swa0rthmore.edu/calcpow/solutions/solution.ehtml?puzzle=44
Problem about sine and cosine arc lengths

http://www.seresc.k12.nh.us/alvirne/gues972.html
A problem dealing with sine and cosine derivatives

http://mathworld.wolfram.com/topics/TrigonometricFunctions.html
A theoretical view towards various trigonometric principles

Derivative

http://mathworld.wolfram.com/topics/MaximaandMinima.html
Theoretical concepts of maxima and minima

http://www.mnsinc.com/hylton/dept/math/calculus/page4.htm
Learn more about the applications of derivatives

http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=35
A maximum dimensions problem

http://www.seresc.k12.nh.us/alvirne/ap99p10.html
Application of derivation equations



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CHAPTER 4. LOGARITHMIC AND EXPONENTIAL FUNCTIONS

4.2 Logarithmic and Exponential Functions

The Natural Logarithm and Exponential Functions - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

4.3 Implicit Differentiation

Implicit Differentiation Problems and Plots - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week4

4.6 Related Rates

Related Average Rates
PDF file - - TI-89/92 activity
http://www.ti.com/calc/docs/act.89calc.htm

Related Average Rates
PDF file - - TI-92 activity
http://www.ti.com/calc/docs/act.92calc.htm

Related Rates - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week6

Horizons Module Chapter 4: No Module



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CHAPTER 5. ANALYSIS OF FUNCTIONS AND THEIR GRAPHS

5.2 Analysis of Functions II: Relative Extrema; First and Second Derivative Tests

The First Derivatives and Graphing: Extrema - Mathematica notebook on local and global extrema
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

5.3 Analysis of Functions III: Applying Technology and the Tools of Calculus

Little Red Corvette - analyzing functions with graphing calculators
PDF file - - TI-89/92 activity
http://www.ti.com/calc/docs/act.89calc.htm

Graphing and Interpreting Graphs - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week6

Horizons Module: Functions from Data
Least-Squares Data Fitting - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Curve Fitting Applet - Java applet
http://www.wiley.com/college/mat/anton243310/mod2/applets.html

Least Squares Maple
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

Horizons Module Chapter 5

Interpolation

http://grandmac.calpoly.edu/docs/math/diffcalc/wobegon.html
An environmental application of interpolation

http://mathworld.wolfram.com/topics/Interpolation.html
A theoretical view towards interpolation methods such as Cubic Spline, and Newton’s Algorithm

Fitting curves to data

http://www.geocities.com/SiliconValley/2902/curve-fi.htm
An interactive curve fitting tool. It allows you to vary the degrees of the polynomial, the number of data points and the coefficients of the polynomial.

Least Squares

http://mathworld.wolfram.com/LeastSquaresFitting.html
Least Squares Fitting of lines explained using vector principles

Regression Line

http://mathworld.wolfram.com/LinearRegression.html
A brief description of Linear Regression

Correlation Coefficient

http://mathworld.wolfram.com/CorrelationCoefficient.html
A detailed step- by- step analysis on how to calculate correlation coefficients

Linear Model/Nonlinear

http://grandmac.calpoly.edu/docs/math/diffcalc/rentalcar.html
Minimize your gas costs by applying calculus to real- life situations

Exponential Models

http://www.sosmath.com/algebra/logs/log5/log53/log53.html
Problems based on exponential models

Logarithmic Models

http://www.scas.bcit.bc.ca/scas/math/examples/ary_9_4/ary_9_4.htm
An application of logarithms to mechanical technology in the area of belt friction

http://math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/LogDiff.html
Example exercises and solutions to logarithmic differentiation

Newton’s law of Cooling

http://www.math.duke.edu/education/ccp/materials/diffcalc/ozone/ozone1.html
A warming, cooling, and urban ozone pollution example based on Newton’s law of Cooling.

http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=48
An example of how Newton’s law of Cooling applies to a mug of hot chocolate



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CHAPTER 6. APPLICATIONS OF THE DERIVATIVE

6.2 Applied Maximum and Minimum Problems

Fermat's Principle - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week5

Finding Maxima - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week5

Finding Maxima with Finite Points - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week5

6.4 Newton's Method

Newton's Method - Mathematica notebook
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

Newton's Method Applet - Java applet
http://www.wiley.com/college/mat/anton243310/mod2/applets.html

Solving Equations by Newton's Method - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week7

Horizons Module Chapter 6: No Module

Although there is no Module for this Horizons Module Chapter, these are two good links that relate to the Horizons Module Chapter.

http://www.ies.co.jp/math/java/rolhei/rolhei.html
A Java applet illustration Rolle’s Theorem and the Mean Value theorem

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/newton.html
An in-depth tutorial on Newton’s Method



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CHAPTER 7. INTEGRATION

7.2 The Indefinite Integral; Integral Curves and Directions Fields

How Do You Graph Derivatives and Antiderivatives?
PDF file - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

How Do You Graph Derivatives and Antiderivatives?
PDF file - - TI-82/83 activity
http://www.ti.com/calc/docs/act.83calc.htm

Comparing Graphs - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week1

7.5 The Definite Integral

Riemann Sum Pictures and Calculating Riemann Sums - Mathematica notebooks on making pictures of left and right rectangle estimates of area, and calculating values of Riemann sums
http://calculuslab.sjdccd.cc.ca.us/CalcIMMA/CalcIMMA-h.html

Area Functions - Riemann sums and area TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Area by Chance - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week2

Horizons Module Chapter 7

Elevation Angle

http://www.seresc.k12.nh.us/alvirne/ap99p9.html
A calculus problem relating to the rate of change of shadows

http://www.kent.wednet.edu/pcpow/questions/calc/museum0/index.html
A tricky question relating to the burglary of a museum.

Equations of Motion

http://grandmac.calpoly.edu/docs/science/physics/wind_surf.html
Using calculus to predict the motion of a windsurfer

http://www.seresc.k12.nh.us/alvirne/gues994.html
An equation of motion problem relating to a thrown bridal bouquet

http://www.seresc.k12.nh.us/alvirne/ap98p9.html
An equation of motion question with multiple objects on a straight path

Trajectory

http://www.netsrq.com/~hahn/pr8_2-4.html
A trajectory question relating to tracking a fired rocket with radar



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CHAPTER 8. APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

8.1 Area Between Two Curves

Rotations - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week3

8.3 Volumes by Cylindrical Shells

Circular Cylinder and Planes- An introductory worksheet using the 3D Region Plot Package and other Maple tools
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

8.4 Length of a Plane Curve

Length and Speed Along a Curve - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week4

Horizons Module Chapter 8: No Module



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CHAPTER 9. PRINCIPLES OF INTEGRAL EVALUATION

9.7 Numerical Integration; Simpson's Rule

Intro to Integration - Numerically and Statistically - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Numerical Integration Applet - Java applet
http://www.wiley.com/college/mat/anton243310/mod2/applets.html

Approximating Definite Integrals Numerically - - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week8

Approximation Errors and Simpson's Rule - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week1

Horizons Module Chapter 9
Railroad Design (Integration)

Surveying

http://www.scas.bcit.bc.ca/scas/math/examples/ary_17_6/ary_17_6.htm
An additional application of integral calculus to surveying

Simpson’s Rule

http://www.geocities.com/SiliconValley/2902/simpson.htm
An interactive tool for integrating functions using Simpson’s Rule

Volume

http://www.seresc.k12.nh.us/alvirne/ap98p17.html
Calculating the volume of Mount Washington given the radius of the base.

http://www.seresc.k12.nh.us/alvirne/ap98p20.html
A problem dealing with calculating the volume given a graph

Riemann Sums

http://mathworld.wolfram.com/RiemannSum.html
A site providing further details to Riemann Sums



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CHAPTER 10. MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS

10.1 First-Order Differential Equations and Applications

Understanding Differential Equations - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

10.3 Modeling with Differential Equations

Growth, Decay, and Exponential Functions - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week6

Horizons Module Chapter 10: No Module
http://grandmac.calpoly.edu/docs/science/chem/kinetics.html
A real-life example based on First and Second Order Chemical Kinetics applied to radio- active decay



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CHAPTER 11. INFINITE SERIES

11.5 Taylor and Maclaurin Series

Taylor and Maclaurin Series Approximations - TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Taylor Series - Maple worksheet explores multivariate Taylor series. Compares graphically various Taylor polynomials to the original function.
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

Horizons Module Chapter 11: No Module


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CHAPTER 12. ANALYTIC GEOMETRY IN CALCULUS

12.3 Area in Polar Coordinates

Polar Coordinates - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week5

12.4 Conic Sections in Calculus

Hyperbolae and Loran C Navigation - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c1program.html#week9

Horizons Module Chapter 12

Arc Length

http://archives.math.utk.edu/visual.calculus/5/arclength.1/index.html
An interactive explanation of Arc Lengths using definitions and examples

Orbital

http://www.seresc.k12.nh.us/alvirne/gues9814.html
Find out if Joe Physics can save himself from the wrath of the hand grenade in this application of curved paths

http://www.kent.wednet.edu/pcpow/questions/calc/colony2/index.html
Distance of a space colony orbiting around the earth

Ellipses

http://mathworld.wolfram.com/Ellipse.html
A theoretical explanation of Ellipses

Polar Co- ordinate Systems

http://mathworld.wolfram.com/PolarCoordinates.html
A theoretical view towards Polar Co-ordinates

http://archives.math.utk.edu/visual.calculus/5/polar.1/index.html
Examples explaining areas bounded by Polar Co- ordinate Systems

http://www.ping.be/math/polar.htm
A detailed description of all aspects of Polar Co- ordinate Systems

Kepler’s Law II

http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.html
An interactive examples demonstration Kepler’s Law

Conic Sections

http://mathworld.wolfram.com/ConicSection.html
A definition of Conic Sections, explaining the differences between various types of conic sections

http://www.best.com/~xah/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html
A detailed view towards conic sections outlining their history, and various graphical examples and links



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CHAPTER 13. THREE-DIMENSIONAL SPACE; VECTORS

13.1 Rectangular Coordinates in 3-space; Spheres; Cylindrical Surfaces

Three-Dimensional Graphics - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

13.2 Vectors

Learning About Vectors and Vector Operations - Java applet
http://www.frontiernet.net/~imaging/vector_calculator.html

Vectors - using Maple to computer addition of vectors, magnitudes, angles
http://omega.albany.edu:8008/calc3/vectors-maple-dir/vector-maple.html

Lines and planes with Maple
http://omega.albany.edu:8008/calc3/Lines-Planes-dir/lines-plans-maple.html

The distance from a point to a plane Maple routine
http://omega.albany.edu:8008/calc3/intro2-ga-toc.html

13.3 Dot Products; Projections

Projections Onto Lines and Planes - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

13.4 Cross Product

The Volume of a Parallelepiped - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

13.5 Parametric Equations of Lines

The distance from a point to a line, and the equation of the plane containing two given lines - Maple routines
http://omega.albany.edu:8008/calc3/intro2-ga-toc.html

13.6 Planes in 3-space
The plane through 3 points - Maple routine

http://omega.albany.edu:8008/calc3/intro2-ga-toc.html

13.8 Cylindrical and Spherical Coordinates

A Water Whirl (revolution of a cylinder) - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

Finding points and the distance from a point to a line with Maple
http://omega.albany.edu:8008/calc3/intro2-ga-toc.html

Horizons Module Chapter 13: No Module


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CHAPTER 14. VECTOR-VALUED FUNCTIONS

14.1 Introduction to Vector-Valued Functions

Limits and Continuity - introducing vector functions with Maple
http://omega.albany.edu:8008/calc3/vector-funcs-toc.html

14.2 Calculus of Vector-Valued Functions

The derivative of a vector function with Maple
http://omega.albany.edu:8008/calc3/vector-funcs-toc.html

14.3 Change of Parameter; Arc Length

Arc length and curvature with Maple
http://omega.albany.edu:8008/calc3/vector-funcs-toc.html

14.4 Unit Tangent, Normal, and Binormal Vectors

Unit tangent and Unit normal - what they are, how to with Maple
http://omega.albany.edu:8008/calc3/vector-funcs-toc.html

14.5 Curvature

Arc length and curvature with Maple
http://omega.albany.edu:8008/calc3/vector-funcs-toc.html

14.6 Motion Along a Curve

Length and Speed Along a Curve - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week4

Horizons Module Chapter 14: No Module


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CHAPTER 15. PARTIAL DERIVATIVES

15.1 Functions of Two or More Variables

Contour lines -Java Applet
http://www.math.gatech.edu/~bourbaki/c3program.html

Functions of several variables in Maple
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.2 Limits and Continuity

Computing limits with Maple
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.3 Partial Derivatives

Computing partial derivatives with Maple
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.4 Differentiability and Chain Rules

The Chain rule - Maple routine
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.5 Tangent Planes; Total Differentials for Functions of Two Variables

Tangent Planes and Normal Lines - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

Tangent planes with Maple
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.8 Maxima and Minima of Functions of Two Variables

Finding extrema with Maple
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

15.9 Lagrange Multipliers

Maximization with Constraints - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c3program.html

Lagrange Multiplier Maple routine
http://omega.albany.edu:8008/calc3/funcs-severalvars-toc.html

Lagrange multipliers - The geometry of Lagrange multipliers is explored with Maple
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

Constrained maxima and minima with LagrangeŐs Method - Mathematica lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Horizons Module Chapter 15: No Module


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CHAPTER 16. MULTIPLE INTEGRALS

16.1 Double Integrals

Double integrals, approximating Riemann sums with Maple.
http://omega.albany.edu:8008/calc3/int-severalvar-toc.html

Computing volumes of solids with Maple
http://omega.albany.edu:8008/calc3/int-severalvar-toc.html

Random Riemann sums with Maple - shows how such can be computed for double integrals.
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

16.2 Double Integrals over Nonrectangular Regions

Double integrals over general regions Maple routine
http://omega.albany.edu:8008/calc3/int-severalvar-toc.html

16.3 Double Integrals in Polar Coordinates

Transformation to polar coordinates with Maple
http://omega.albany.edu:8008/calc3/int-severalvar-toc.html

Integration in Polar Coordinates - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

16.4 Parametric Surfaces; Surface Area

Examples of surface areas computations with Maple
http://omega.albany.edu:8008/calc3/surface-area-dir/examples-m2h.html

Surface area of the intersection of 2 cylinders with Maple
http://omega.albany.edu:8008/calc3/surface-area-dir/two-cyls-m2h.html

16.6 Centroid, Center of Gravity; Theorem of Pappus

Distribution of Weights - Maple worksheet
http://www.math.gatech.edu/~bourbaki/c2program.html#week4

Moments and Centroids - Java Applet
http://www.math.gatech.edu/~bourbaki/c2program.html#week4

Centroids and Averages - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

The Theorem of Pappus - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

16.7 Triple Integrals in Cylindrical and Spherical Coordinates

Integration in cylindrical and spherical coordinates - Mathematica lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Integration in 3 dimensions - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Horizons Module Chapter 16: No Module


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CHAPTER 17. TOPICS IN VECTOR CALCULUS

17.2 Line Integrals

Numerical Evaluation of Line Integrals - PDF file TI-85/86 activity
http://www.ti.com/calc/docs/act.85calc.htm

Definition of a line integral with Maple
http://omega.albany.edu:8008/calc3/vector-calculus-toc.html

Computing line integrals with Maple
http://omega.albany.edu:8008/calc3/vector-calculus-toc.html

17.3 Independence of Path; Conservative Vector Fields

A Potential for Being Conservative - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

17.4 Green's Theorem

Green's Theorem for a Triangle - Maple worksheet does a variety of things related to Green's theorem for an infinitesimal triangle.
http://mathlab.cit.cornell.edu/local_maple/mvc/lecguide.html

Vector fields, line integrals, and the theorems of Green and Gauss - Mathematica lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Green's Theorem - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

17.5 Surface Integrals

Surface integrals - Mathematica lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Sample surface integrals - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

17.6 Applications of Surface Integrals; Flux

Flux and Circulation in Two Dimensions - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

17.7The Divergence Theorem

The Divergence Theorem - Maple lecture
http://www.math.gatech.edu/~carlen/newton/html/c4program.html

Horizons Module Chapter 17

Hurricane Modeling

Fluid dynamics

http://mathworld.wolfram.com/VectorField.html
Examples of Vector Fields

Superposition principle

http://mathworld.wolfram.com/SuperpositionPrinciple.html
A definition of the Superposition Principle

Uniform sink flow

http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Flow/flow.html
An interactive exercise explaining the flow of vector fields

Stream lines

http://www.frontiernet.net/~imaging/vector_calculator.html
Learn about vectors and vector operations by sketching and playing with them

Radial Unit Vector

http://mathworld.wolfram.com/RadialCurve.html
A theoretical description of Radial Curves



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