## Calculus: A New Horizon, Sixth Edition Howard Anton

 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6Chapter 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 1.2 Properties 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 Chaoshttp://spanky.triumf.ca/A site dedicated to fractals. A database of numerous fractal diagrams. http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=18A problem dealing with a fractal snowflake http://mathworld.wolfram.com/topics/ComplexSystems.htmlExplains 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.htmlPopulation harvesting theory, and models http://mathworld.wolfram.com/topics/PopulationDynamics.htmlDescribes various concepts of population dynamics such as population growth and life expectancy Recursion http://mathworld.wolfram.com/topics/Recursion.htmlDescribes the Ackermann function and other concepts of recursion http://www.ies.co.jp/math/java/ser_eq/ser_eq.htmlA Java applet illustrating a recursive function Deposition in a Bank, and Interest Formula http://mathworld.wolfram.com/topics/Accounting.htmlDescribes various accounting principles including principal and simple interest http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=50A problem dealing with lease payments on your Pontiac Sunfire Fibonacci Sequence http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.htmlApplications of Fibonacci numbers and further details

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

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 Don�t 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.htmMotion of a piston - an application of differential calculus in robotics http://mathworld.wolfram.com/topics/DynamicsandKinematics.htmlA theoretical explanation of the Radius of Gyration Cosine, and Sine http://forum.swa0rthmore.edu/calcpow/solutions/solution.ehtml?puzzle=44Problem about sine and cosine arc lengths http://www.seresc.k12.nh.us/alvirne/gues972.htmlA problem dealing with sine and cosine derivatives http://mathworld.wolfram.com/topics/TrigonometricFunctions.htmlA theoretical view towards various trigonometric principles Derivative http://mathworld.wolfram.com/topics/MaximaandMinima.htmlTheoretical concepts of maxima and minima http://www.mnsinc.com/hylton/dept/math/calculus/page4.htmLearn more about the applications of derivatives http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=35A maximum dimensions problem http://www.seresc.k12.nh.us/alvirne/ap99p10.htmlApplication of derivation equations

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

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.htmlAn environmental application of interpolation http://mathworld.wolfram.com/topics/Interpolation.htmlA 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.htmAn 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.htmlLeast Squares Fitting of lines explained using vector principles Regression Line http://mathworld.wolfram.com/LinearRegression.htmlA brief description of Linear Regression Correlation Coefficient http://mathworld.wolfram.com/CorrelationCoefficient.htmlA detailed step- by- step analysis on how to calculate correlation coefficients Linear Model/Nonlinear http://grandmac.calpoly.edu/docs/math/diffcalc/rentalcar.htmlMinimize your gas costs by applying calculus to real- life situations Exponential Models http://www.sosmath.com/algebra/logs/log5/log53/log53.htmlProblems based on exponential models Logarithmic Models http://www.scas.bcit.bc.ca/scas/math/examples/ary_9_4/ary_9_4.htmAn application of logarithms to mechanical technology in the area of belt friction http://math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/LogDiff.htmlExample exercises and solutions to logarithmic differentiation Newton�s law of Cooling http://www.math.duke.edu/education/ccp/materials/diffcalc/ozone/ozone1.htmlA warming, cooling, and urban ozone pollution example based on Newton�s law of Cooling. http://forum.swarthmore.edu/calcpow/solutions/solution.ehtml?puzzle=48An example of how Newton�s law of Cooling applies to a mug of hot chocolate

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.htmlA Java applet illustration Rolle�s Theorem and the Mean Value theorem http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/approx/newton.htmlAn in-depth tutorial on Newton�s Method

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.htmlA 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.htmlUsing calculus to predict the motion of a windsurfer http://www.seresc.k12.nh.us/alvirne/gues994.htmlAn 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.htmlA trajectory question relating to tracking a fired rocket with radar

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

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.htmAn additional application of integral calculus to surveying Simpson�s Rule http://www.geocities.com/SiliconValley/2902/simpson.htmAn interactive tool for integrating functions using Simpson�s Rule Volume http://www.seresc.k12.nh.us/alvirne/ap98p17.htmlCalculating the volume of Mount Washington given the radius of the base. http://www.seresc.k12.nh.us/alvirne/ap98p20.htmlA problem dealing with calculating the volume given a graph Riemann Sums http://mathworld.wolfram.com/RiemannSum.htmlA site providing further details to Riemann Sums

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

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

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.htmlAn interactive explanation of Arc Lengths using definitions and examples Orbital http://www.seresc.k12.nh.us/alvirne/gues9814.htmlFind 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.htmlA theoretical explanation of Ellipses Polar Co- ordinate Systems http://mathworld.wolfram.com/PolarCoordinates.htmlA theoretical view towards Polar Co-ordinates http://archives.math.utk.edu/visual.calculus/5/polar.1/index.htmlExamples explaining areas bounded by Polar Co- ordinate Systems http://www.ping.be/math/polar.htmA detailed description of all aspects of Polar Co- ordinate Systems Kepler�s Law II http://SunSITE.UBC.CA/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.htmlAn interactive examples demonstration Kepler�s Law Conic Sections http://mathworld.wolfram.com/ConicSection.htmlA definition of Conic Sections, explaining the differences between various types of conic sections http://www.best.com/~xah/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.htmlA detailed view towards conic sections outlining their history, and various graphical examples and links

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

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

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 Lagrange�s Method - Mathematica lecture http://www.math.gatech.edu/~carlen/newton/html/c4program.html Horizons Module Chapter 15: No Module

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