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


1.1 Functions and the Analysis of Graphical Information

Functions - create your own functions with this Mathematica notebook

1.2Properties of Functions

Functions - create your own functions with this Mathematica notebook

1.3 Graphing Functions on Calculators and Computers: Computer Algebra Systems

Graphics - plotting functions in 2D and altering Mathematica-generated images

1.4 New Functions from Old

Reflections, Symmetry, and Inverses - TI-85/86 activity

Transformation of Functions - TI-85/86 activity

1.5 Mathematical Models; Linear Models

Calculating Velocities I and II - Mathematica notebook on spring-mass systems, equilibrium

1.6 Families of Functions

Power Functions - Mathematica notebook

Horizons Module Chapter 1

Fractals and Chaos
A site dedicated to fractals. A database of numerous fractal diagrams.
A problem dealing with a fractal snowflake
Explains various terms associated with Fractals and Chaos

Iteration and Dynamical Systems
Gives a graphical description of population growth modeling
Population harvesting theory, and models
Describes various concepts of population dynamics such as population growth and life expectancy

Describes the Ackermann function and other concepts of recursion
A Java applet illustrating a recursive function

Deposition in a Bank, and Interest Formula
Describes various accounting principles including principal and simple interest
A problem dealing with lease payments on your Pontiac Sunfire

Fibonacci Sequence
Applications of Fibonacci numbers and further details

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2.1 Limits (An Intuitive Introduction)

Intro to Limits - Graphically and Numerically - TI-85/86 activity

Continuity and Solving Equations - Maple worksheet

Limits - Maple worksheet uses a variety of graphical and numeric methods to study multi-dimensional limits

2.2 Limits (Computational Techniques)

Alternate Intro to Limits - Geometrically, Numerically, Graphically, and Algebraically - TI-85/86 activity

2.4 Continuity

Root-Finding by Intermediate Values Applet - Java applet

Continuity and Solving Equations - Maple worksheet

Horizons Module Chapter 2: No Module

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3.1 Tangent Lines and Rates of Change

Role and Computation of Tangent Lines - Maple worksheet

3.2 The Derivative

The Derivative Function - Mathematica notebook on the relationship between a graph of a function and the graph of its derivative

Discovering the Derivative by Exploration - TI-82/83 activity

3.3 Techniques of Differentiation

Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule

3.4 Derivatives of Trigonometric Functions

Differentiation - Maple worksheet

3.5 The Chain Rule

Symbolic Derivatives - Mathematica notebook on the product rule and the chain rule

Numerically Discovering a Formula for Derivatives - TI-85/86 activity

3.6 Local Linear Approximation; Differentials

Intro to Derivatives - Smooth Curves DonŐt When You Zoom In - TI-85/86 activity

Horizons Module Chapter 3

Calculus of Robotics (Kinematics Equations)
Motion of a piston - an application of differential calculus in robotics
A theoretical explanation of the Radius of Gyration

Cosine, and Sine
Problem about sine and cosine arc lengths
A problem dealing with sine and cosine derivatives
A theoretical view towards various trigonometric principles

Theoretical concepts of maxima and minima
Learn more about the applications of derivatives
A maximum dimensions problem
Application of derivation equations

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4.2 Logarithmic and Exponential Functions

The Natural Logarithm and Exponential Functions - TI-85/86 activity

4.3 Implicit Differentiation

Implicit Differentiation Problems and Plots - Maple worksheet

4.6 Related Rates

Related Average Rates
PDF file - - TI-89/92 activity

Related Average Rates
PDF file - - TI-92 activity

Related Rates - Maple worksheet

Horizons Module Chapter 4: No Module

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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

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

Graphing and Interpreting Graphs - Maple worksheet

Horizons Module: Functions from Data
Least-Squares Data Fitting - TI-85/86 activity

Curve Fitting Applet - Java applet

Least Squares Maple

Horizons Module Chapter 5

An environmental application of interpolation
A theoretical view towards interpolation methods such as Cubic Spline, and Newton’s Algorithm

Fitting curves to data
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
Least Squares Fitting of lines explained using vector principles

Regression Line
A brief description of Linear Regression

Correlation Coefficient
A detailed step- by- step analysis on how to calculate correlation coefficients

Linear Model/Nonlinear
Minimize your gas costs by applying calculus to real- life situations

Exponential Models
Problems based on exponential models

Logarithmic Models
An application of logarithms to mechanical technology in the area of belt friction
Example exercises and solutions to logarithmic differentiation

Newton’s law of Cooling
A warming, cooling, and urban ozone pollution example based on Newton’s law of Cooling.
An example of how Newton’s law of Cooling applies to a mug of hot chocolate

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6.2 Applied Maximum and Minimum Problems

Fermat's Principle - Maple worksheet

Finding Maxima - Maple worksheet

Finding Maxima with Finite Points - Maple worksheet

6.4 Newton's Method

Newton's Method - Mathematica notebook

Newton's Method Applet - Java applet

Solving Equations by Newton's Method - Maple worksheet

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.
A Java applet illustration Rolle’s Theorem and the Mean Value theorem
An in-depth tutorial on Newton’s Method

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7.2 The Indefinite Integral; Integral Curves and Directions Fields

How Do You Graph Derivatives and Antiderivatives?
PDF file - TI-85/86 activity

How Do You Graph Derivatives and Antiderivatives?
PDF file - - TI-82/83 activity

Comparing Graphs - Maple worksheet

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

Area Functions - Riemann sums and area TI-85/86 activity

Area by Chance - Maple worksheet

Horizons Module Chapter 7

Elevation Angle
A calculus problem relating to the rate of change of shadows
A tricky question relating to the burglary of a museum.

Equations of Motion
Using calculus to predict the motion of a windsurfer
An equation of motion problem relating to a thrown bridal bouquet
An equation of motion question with multiple objects on a straight path

A trajectory question relating to tracking a fired rocket with radar

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8.1 Area Between Two Curves

Rotations - Maple worksheet

8.3 Volumes by Cylindrical Shells

Circular Cylinder and Planes- An introductory worksheet using the 3D Region Plot Package and other Maple tools

8.4 Length of a Plane Curve

Length and Speed Along a Curve - Maple worksheet

Horizons Module Chapter 8: No Module

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9.7 Numerical Integration; Simpson's Rule

Intro to Integration - Numerically and Statistically - TI-85/86 activity

Numerical Integration Applet - Java applet

Approximating Definite Integrals Numerically - - Maple worksheet

Approximation Errors and Simpson's Rule - Maple worksheet

Horizons Module Chapter 9
Railroad Design (Integration)

An additional application of integral calculus to surveying

Simpson’s Rule
An interactive tool for integrating functions using Simpson’s Rule

Calculating the volume of Mount Washington given the radius of the base.
A problem dealing with calculating the volume given a graph

Riemann Sums
A site providing further details to Riemann Sums

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10.1 First-Order Differential Equations and Applications

Understanding Differential Equations - TI-85/86 activity

10.3 Modeling with Differential Equations

Growth, Decay, and Exponential Functions - Maple worksheet

Horizons Module Chapter 10: No Module
A real-life example based on First and Second Order Chemical Kinetics applied to radio- active decay

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11.5 Taylor and Maclaurin Series

Taylor and Maclaurin Series Approximations - TI-85/86 activity

Taylor Series - Maple worksheet explores multivariate Taylor series. Compares graphically various Taylor polynomials to the original function.

Horizons Module Chapter 11: No Module

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12.3 Area in Polar Coordinates

Polar Coordinates - Maple worksheet

12.4 Conic Sections in Calculus

Hyperbolae and Loran C Navigation - Maple worksheet

Horizons Module Chapter 12

Arc Length
An interactive explanation of Arc Lengths using definitions and examples

Find out if Joe Physics can save himself from the wrath of the hand grenade in this application of curved paths
Distance of a space colony orbiting around the earth

A theoretical explanation of Ellipses

Polar Co- ordinate Systems
A theoretical view towards Polar Co-ordinates
Examples explaining areas bounded by Polar Co- ordinate Systems
A detailed description of all aspects of Polar Co- ordinate Systems

Kepler’s Law II

An interactive examples demonstration Kepler’s Law

Conic Sections
A definition of Conic Sections, explaining the differences between various types of conic sections
A detailed view towards conic sections outlining their history, and various graphical examples and links

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

Three-Dimensional Graphics - Maple worksheet

13.2 Vectors

Learning About Vectors and Vector Operations - Java applet

Vectors - using Maple to computer addition of vectors, magnitudes, angles

Lines and planes with Maple

The distance from a point to a plane Maple routine

13.3 Dot Products; Projections

Projections Onto Lines and Planes - Maple worksheet

13.4 Cross Product

The Volume of a Parallelepiped - Maple worksheet

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

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

13.8 Cylindrical and Spherical Coordinates

A Water Whirl (revolution of a cylinder) - Maple worksheet

Finding points and the distance from a point to a line with Maple

Horizons Module Chapter 13: No Module

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14.1 Introduction to Vector-Valued Functions

Limits and Continuity - introducing vector functions with Maple

14.2 Calculus of Vector-Valued Functions

The derivative of a vector function with Maple

14.3 Change of Parameter; Arc Length

Arc length and curvature with Maple

14.4 Unit Tangent, Normal, and Binormal Vectors

Unit tangent and Unit normal - what they are, how to with Maple

14.5 Curvature

Arc length and curvature with Maple

14.6 Motion Along a Curve

Length and Speed Along a Curve - Maple worksheet

Horizons Module Chapter 14: No Module

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15.1 Functions of Two or More Variables

Contour lines -Java Applet

Functions of several variables in Maple

15.2 Limits and Continuity

Computing limits with Maple

15.3 Partial Derivatives

Computing partial derivatives with Maple

15.4 Differentiability and Chain Rules

The Chain rule - Maple routine

15.5 Tangent Planes; Total Differentials for Functions of Two Variables

Tangent Planes and Normal Lines - Maple worksheet

Tangent planes with Maple

15.8 Maxima and Minima of Functions of Two Variables

Finding extrema with Maple

15.9 Lagrange Multipliers

Maximization with Constraints - Maple worksheet

Lagrange Multiplier Maple routine

Lagrange multipliers - The geometry of Lagrange multipliers is explored with Maple

Constrained maxima and minima with LagrangeŐs Method - Mathematica lecture

Horizons Module Chapter 15: No Module

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16.1 Double Integrals

Double integrals, approximating Riemann sums with Maple.

Computing volumes of solids with Maple

Random Riemann sums with Maple - shows how such can be computed for double integrals.

16.2 Double Integrals over Nonrectangular Regions

Double integrals over general regions Maple routine

16.3 Double Integrals in Polar Coordinates

Transformation to polar coordinates with Maple

Integration in Polar Coordinates - Maple lecture

16.4 Parametric Surfaces; Surface Area

Examples of surface areas computations with Maple

Surface area of the intersection of 2 cylinders with Maple

16.6 Centroid, Center of Gravity; Theorem of Pappus

Distribution of Weights - Maple worksheet

Moments and Centroids - Java Applet

Centroids and Averages - Maple lecture

The Theorem of Pappus - Maple lecture

16.7 Triple Integrals in Cylindrical and Spherical Coordinates

Integration in cylindrical and spherical coordinates - Mathematica lecture

Integration in 3 dimensions - Maple lecture

Horizons Module Chapter 16: No Module

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17.2 Line Integrals

Numerical Evaluation of Line Integrals - PDF file TI-85/86 activity

Definition of a line integral with Maple

Computing line integrals with Maple

17.3 Independence of Path; Conservative Vector Fields

A Potential for Being Conservative - Maple lecture

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.

Vector fields, line integrals, and the theorems of Green and Gauss - Mathematica lecture

Green's Theorem - Maple lecture

17.5 Surface Integrals

Surface integrals - Mathematica lecture

Sample surface integrals - Maple lecture

17.6 Applications of Surface Integrals; Flux

Flux and Circulation in Two Dimensions - Maple lecture

17.7The Divergence Theorem

The Divergence Theorem - Maple lecture

Horizons Module Chapter 17

Hurricane Modeling

Fluid dynamics
Examples of Vector Fields

Superposition principle
A definition of the Superposition Principle

Uniform sink flow

An interactive exercise explaining the flow of vector fields

Stream lines
Learn about vectors and vector operations by sketching and playing with them

Radial Unit Vector
A theoretical description of Radial Curves

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