CALCULATORS ON-LINE CENTER MATHEMATICS CENTER: CALCULUS

PRE-CALCULUS CALCULATORS, JAVA APPLETS, ANIMATIONS & SIMULATIONS

PRE-CALCULUS COURSES WITH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS


PRE-CALCULUS (JAVA APPLETS & LIVEMATH) – L. Husch,
Department of Mathematics,
University of Tennessee
Multimedia Pre-Calculus Course, Calculators & Applets, etc. (Text & Images)
VERY VERY VERY…EXTENSIVE.

Calculus

“…The basic object of study in calculus is a function. We will start
with the definition of a function and examine the representation
in four modes: symbolic, numerical, graphical and verbal.
The domain and range of a function are also defined; exercises
on finding the domain of a function are provided…”

Examples of “Pre-Calculus” Subject Categories include

Introduction to Functions;

Piecewise Defined Functions;

Even and Odd Functions;

Polynomials;

Rational Functions;

Geometric Transformations of Functions;

Algebra of Functions;

Composition of Functions;

Trigonometric Functions;

Exponential Functions;

Inverses of Functions;

Logarithms;

Parameters and Functions;

Parametric Equations;

Polar Coordinates;

Solving Equations; etc…”

For more information see

Visual Calculus;

Math Archives or the

Department of Mathematics

Examples of Pre-Calculus Calculators include

Transformations of Exponential Functions


Transformations of Logarithmic Functions


Curve Fitting

FUNDAMENTAL THEOREM OF CALCULUS

THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLET) – I.K. Rana,
Mathematics Resource Center,
Department of Mathematics,
Indian Institute of Technology,
Bombay, India
VERY EXTENSIVE.

Fundamental Theorem of Calculus

“…relates the two important
concepts of calculus: Differentiation and Integration…”

For more information see

Calculus;

Mathematics Resource Center;

Department of Mathematics or the

Indian Institute of Technology


THE FUNDAMENTAL THEOREM OF CALCULUS
(JAVA APPLETS & FLASH) – L. Husch,
Department of Mathematics,
University of Tennessee
VERY EXTENSIVE.

The Fundamental Theorem of Calculus:

“…The first part of this theorem tells us how to evaluate a definite integral
provided that f has an indefinite integral. The second part of
the theorem tells us that f has an indefinite integral…”

For more information see

Visual Calculus or the

Department of Mathematics


THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLET) – Asian
Technology Conference in Mathematics (ATCM)
VERY EXTENSIVE.
The Fundamental Theorem of Calculus Applet.
For more information see

Calculus;

Manipula Math With Java or

Math Education and Technology


THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLET) – T. Tao,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
UCLA
VERY EXTENSIVE.
The Fundamental Theorem of Calculus Applet.
For more information see

Java;

Terence Tao’s Home Page;

Analysis Group or the

Department of Mathematics


THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLET) – D.L. Kreider &
C.D. Lahr (Department of Mathematics, Dartmouth College) and
S. Diesel (Department of Mathematics, Norwich University)
VERY EXTENSIVE.

The Fundamental Theorem of Calculus

“…relates derivatives and definite integrals. It also gives a
practical way to evaluate many definite integrals
without resorting to the limit definition…”

For more information see

Principles of Calculus Modeling: Index;

Principles of Calculus Modeling: An Interactive Approach Home Page;

C. Dwight Lahr’s Home Page or the

Department of Mathematics

1ST YEAR CALCULUS COURSES, LECTURES & LESSONS WITH VIDEOS/MOVIES & AUDIO/SOUND

PRINCIPLES OF CALCULUS MODELING: AN INTERACTIVE
APPORACH (REALPLAYER & FLASH) – D.L. Kreider &
C.D. Lahr (Department of Mathematics, Dartmouth College) and
S. Diesel (Department of Mathematics, Norwich University)
Multimedia Calculus Modeling Course (Text, Images,
Animations, Demonstrations, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Examples of “Principles of Calculus Modeling: An Interactive Approach” Course Chapters with over “100” Video Lessons include

“…Modeling Discrete Data;

Modeling Rates of Change;


Modeling with Differential Equations;

Modeling Accumulations; etc…”

For more information see

C. Dwight Lahr’s Home Page or the

Department of Mathematics

Some examples from over “40” Calculus Calculators & Applets include


Approximating Areas: Inscribed Polygons


Curve Sketching: Increasing/Decreasing


Limit of sin(x)/x as x approaches 0

1ST YEAR CALCULUS COURSES, TEXTBOOKS & LECTURES

CALCULUS TEXTBOOK (MATH 100) – J. Feldman,
Department of Mathematics,
Faculty of Science,
University of British Columbia,
Vancouver, B.C., Canada
Multimedia Calculus Course, Lessons, Calculators, etc. (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Calculus” Textbook Chapters include

“…Functions;

The Function Zoo;

What is the derivative?;

Tools for Calculating Derivatives;


Applications of the Derivative;


Exponential functions and exponential growth;


Trigonometric and Inverse Trigonometric functions;


Differential equations for periodic behaviour; etc…”

For more information see

Joel Feldman’s Home Page;

The UBC Calculus Online Homepage or the

Department of Mathematics

Examples from over “50” Calculus Calculators include

The Function Zoo: Equations of Straight Lines Calculator


Tools for Calculating Derivatives: Linear Approximations Calculator


Newton’s Method Calculator


CALCULUS TEXTBOOK – Author: Gilbert Strang,
Department of Mathematics (MIT Mathematics),
MIT
Multimedia Calculus Textbook – PDF (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Calculus Textbook” Chapters include

“…Introduction to Calculus;

Derivatives;

Applications of the Derivative;

The Chain Rule;

Integrals;

Exponentials and Logarithms;

Techniques of Integration;

Polar Coordinates and Complex Numbers;

Infinite Series;

Vectors and Matrices;

Motion along a Curve;

Partial Derivatives;

Multiple Integrals;

Vector Calculus; etc…”

For more information see

Calculus Online Textbook Home Page;

Supplemental Resources;

Gilbert Strang’s Home Page;

Department of Mathematics (MIT Mathematics) or

MIT OpenCourseWare


CALCULUS WITH APPLICATIONS TOOLS – Daniel J. Kleitman,
Department of Mathematics & the
MIT OpenCourseWare, MIT
VERY VERY VERY…EXTENSIVE.
Multimedia Calculus Course (Text & Images).

Examples from over “30” “Calculus with Applications Tools” Course Chapters include

The Exponential Function and Trigonometric Functions;

Vectors, Dot Products, Matrix Multiplication and Distance;

Area of a Parallelogram, Determinants, Volume and Hypervolume, the Vector Product;

Computation of Derivatives from their Definition;

Higher Derivatives, Taylor Series, Quadratic Approximations and Accuracy of Approximations;

The Product Rule and Differentiating Vectors;

The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem; etc…”

Examples of “Calculus” Calculators Subject Categories include

“…Single Variable Calculus Calculators;

Vectors and Algebra Calculators;

Application to 3D Linear Geometry Calculators;

Curves; Fields and Surfaces Calculators;

Complex Numbers and Functions Calculators;

Integration on Curves Calculators;

Integration on Surfaces Calculators;

Differential Equations Calculators; etc…”

For more information see

Calculus with Applications;

Department of Mathematics;

Mathematics Courses or the

MIT OpenCourseWare

For MIT’s Online Course see

Calculus Online Textbook: 18.013A

Examples from over “30” Calculus Calculators & Calculus Applets include


Lagrange Multipliers with Two Variables Applet


Curves in Two Dimensions Applet


Complex Functions Applet


Flux Integrals Applet


Static Electric Fields in Three Dimensions Applet


CALCULUS I – P. Chiou,
Department of Mathematics,
College of Arts and Sciences,
Lamar University
Multimedia Calculus I Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Calculus I” Course Chapters & Subchapters include

Limits
“…The Limit;

One-Sided Limits;

Infinite Limits;

Limits At Infinity; etc…”

Derivatives

“…Interpretation of the Derivative;

Derivatives of Trig Functions;

Derivatives of Exponential and Logarithm Functions;

Chain Rule;

Higher Order Derivatives;

Logarithmic Differentiation; etc…”

Applications of Derivatives

“…Critical Points;

Finding Absolute Extrema;

The Mean Value Theorem;

Linear Approximations; etc…”

Integrals; Applications of Integrals; etc.

For more information see

Paul Chiou’s Home Page or the

Department of Mathematics


CALCULUS II – P. Chiou,
Department of Mathematics,
College of Arts and Sciences,
Lamar University
Multimedia Calculus II Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Calculus II” Course Chapters & Subchapters include

Integration Techniques
“…Partial Fractions;

Integrals Involving Quadratics;

Improper Integrals;

Approximating Definite Integrals; etc…”

Parametric Equations and Polar Coordinates

“…Parametric Equations and Curves;

Arc Length with Parametric Equations;

Polar Coordinates;

Area with Polar Coordinate; etc…”

Sequences and Series

“…Sequences;

Series;

Alternating Series Test;

Ratio Test;

Strategy for Series;

Power Series;

Taylor Series; etc…”

Three Dimensional Space

“…The 3-D Coordinate System;

Equations of Lines;

Quadric Surfaces;

Vector Functions;

Calculus with Vector Functions;

Velocity and Acceleration;

Cylindrical Coordinates; etc…”

Vectors; etc.

For more information see

Paul Chiou’s Home Page or the

Department of Mathematics


CALCULUS III – P. Chiou,
Department of Mathematics,
College of Arts and Sciences,
Lamar University
Multimedia Calculus III Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Calculus III” Course Chapters & Subchapters include

Partial Derivatives
“…Limits;

Partial Derivatives;

Higher Order Partial Derivatives;

Chain Rule;

Directional Derivatives; etc…”

Multiple Integrals

“…Double Integrals;

Iterated Integrals;

Double Integrals over General Regions;

Triple Integral;

Triple Integrals in Spherical Coordinates; etc…”

Line Integrals;

Surface Integrals; etc.

For more information see

Paul Chiou’s Home Page or the

Department of Mathematics


CALCULUS: VISUAL CALCULUS (JAVA APPLETS & LIVEMATH) – L. Husch, Department of Mathematics, University of Tennessee
Multimedia Calculus Course with Calculators (Text & Images).
VERY VERY VERY…EXTENSIVE.

Visual Calculus

“…includes tutorials, interactive modules (MathView, Java, and Javascript)
which can be used by either students or faculty…”

Examples of “Visual Calculus” Course Chapters include

“…Limits and Continuity;

Derivatives;

Applications of Differentiation;

Integration;

Applications of Integration;

Sequences and Series…”

For more information see

Department of Mathematics

Examples from over “80” Calculus Calculators & Calculus Applets include


Numerical Exploration of Limits Calculator


Bisection Method to Find Roots of Third Degree Polynomials Calculator


Finding the Derivatives of Inverses of Trigonometric Functions Calculator


Tangent Lines Calculator


DIFFERENCE EQUATIONS TO DIFFERENTIAL EQUATIONS: (JAVA APPLETS) – D. Sloughter,
Department of Mathematics, Furman University
Multimedia Difference Equations to Differential Equations Course (Text, Images & Applets).
VERY VERY VERY…EXTENSIVE.

Examples of “Difference Equations to Differential Equations” Course Chapters include

“…Sequences, limits, and difference equations;


Functions and their properties;


Best affine approximations;

Integration;


Polynomial approximations and Taylor series; etc.

For more information see

Dan Sloughter’s Home Page or the

Department of Mathematics

Examples from over “15” Calculus Calculators include


Affine approximations


Numerical integration rules


FINITE MATHEMATICS & APPLIED CALCULUS – Stefan Waner (Emeritus),
Department of Mathematics,
Hofstra University
Multimedia Finite Mathematics & Applied Calculus Course (Text & Images).
VERY VERY VERY…EXTENSIVE.
For more information see

Finite Mathematics & Applied Calculus Home Pge;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University

Examples from over “10” Calculus Calculators & Calculus Applets include


Function Evaluator and Grapher for Calculus Applied to the Real World


Surface Graphing Utility

1ST YEAR CALCULUS CALCULATORS, APPLETS & SPREADSHEETS (XLS)

APPLETS IN CALCULUS – I.K. Rana,
Mathematics Resource Center,
Department of Mathematics,
Indian Institute of Technology,
Bombay, India
VERY VERY EXTENSIVE.

Examples from over “20” Calculus Calculators & Calculus Applets include

“…One-One/Onto Function Calculator;

Composition of Functions Calculator;

Vector Fields Calculator;

Differentiability Calculator;

Derivative of Function with Different Parameters Calculator;

Derivative of the Inverse Function Calculator;

Convexity/Concavity Calculator; etc…”

For more information see

Resources in the Center;

Mathematics Resource Center;

Department of Mathematics or the

Indian Institute of Technology


CALCULUS APPLETS – S.A. Sarra,
Department of Mathematics,
College of Science,
Marshall University
VERY VERY EXTENSIVE.

Calculus Calculators & Calculus Applet Subject Categories include

“…Calculus;

Ordinary Differential Equations and Difference Equations;


Partial Differential Equations;

Numerical Analysis;

Numerical Partial Differential Equations; etc…”

For more information see

Scott A. Sarra’s Home Page or the

Department of Mathematics

Examples from over “20” Calculus Calculators & Calculus Applets include


Epsilon Delta Limits Calculator

Epsilon Delta Limits Calculator is

“…designed to help users
understand the epsilon/delta definition of a limit. The
definition states that the limit of f(x) as x approaches a is L…”


Secant and Tangent Lines Calculator

Secant and Tangent Lines Calculator

“…shows secant lines converging to tangent lines…”


CALCULUS APPLETS & CALCULATORS – D. Sloughter,
Department of Mathematics,
Furman University
VERY VERY VERY…EXTENSIVE.
For more information see

Dan Sloughter’s Home Page @ synechism.org;

Dan Sloughter’s Home Page @ dananne.org or

Department of Mathematics

Examples from over “11” Calculus Applets include


Trigonometric series approximation of a square wave Applet


Affine approximations Applet


Numerical integration rules Applet


CALCULUS (JAVA APPLETS) – Asian Technology Conference in Mathematics (ATCM)
VERY VERY EXTENSIVE.
For more information see

Manipula Math With Java or

Math Education and Technology

Examples from more than “64” Calculus Applets with Simulations include

Volume of a Solid of Revolution Applet


Cycloids Applet


Visualization of limits Applet


CALCULUS APPLETS – R.J. Pruim,
Department of Mathematics and Statistics,
Calvin College,
Grand Rapids, MI
VERY VERY EXTENSIVE.
For more information see

Math 162 B, Calculus II Home Page;

Randall J. Pruim’s Home Page or the

Department of Mathematics and Statistics

Examples from over “11” Calculus Calculators & Calculus Applets include

Morphing Applet


SecantTangent Applet


Sequences of Functions Applet


CALCULUS DEMONSTRATIONS (JAVA APPLETS) – D. Austin,
Department of Mathematics, Grand Valley State University,
Allendale, Michigan
VERY VERY EXTENSIVE.

Calculus Calculators & Calculus Applet Subject Categories include

Functions Calculators
“…Transformations Calculator;

Families of functions Calculator;

Parametric Curves Calculator;

Inverse Functions Calculator; etc…”

Derivatives Calculators

“…Secant Lines Calculator;

The Derivative as a Function Calculator; etc…”

Summations Calculators

“…Arithmetic series Calculator;

Geometric series Calculator;


Sum of odds Calculator;

Sum of cubes Calculator; etc…”

Integration Calculators;

Taylor Series Calculator; etc…”

For more information see

David Austin’s Home Page or the

Department of Mathematics


CALCULUS: FLASH MATHLETS (FLASH) – Barbara Kaskosz,
Department of Mathematics,
University of Rhode Island
VERY VERY VERY…EXTENSIVE.
For more information see

Barbara Kaskosz’s Home Page or the

Department of Mathematics

Examples from over “22” Calculus Calculators include


Multivariable Calculus: Motion in 3D


Multivariable Calculus: Parametric Surfaces in Cylindrical Coordinates


Multivariable Calculus: Parametric Surfaces in Spherical Coordinates


Multivariable Calculus: 3D Function Grapher


Single Variable Calculus: Sequence and Series Plotter


Single Variable Calculus: Accumulated Change and Antidervative Plotter


Graphing the Cantor Function


CALCULUS MATH APPLETS AT SLU – Mike May, S.J.,
Department of Mathematics and Computer Science,
Saint Louis University
VERY VERY VERY…EXTENSIVE.

Calculus Calculators & Calculus Applets Categories & Subcategories include

Single Variable Calculus
“…Graphers;

Continuity;

Differentiation;

Integration;

Sequences and Series; etc…”

Multivariable Calculus

“…Understanding surfaces and graphs of several variables;


Vectors; Continuity in several variables;


Differentiation of functions of several variables;


Integration in vector fields…”

For more information see

Mike May, S.J.’s Home Page or the

Department of Mathematics and Computer Science

Examples from over “30” Calculus Calculators & Calculus Applets include


Continuity: A Single Variable Continuity Applet


Differentiation: First Derivatives Applet


Sequences and Series: Functions Defined by Series Applet


DERIVATIVES: STEP BY STEP DERIVATIVES – Wolfram Research Inc.
VERY VERY VERY…EXTENSIVE.

Derivatives Calculator

“…Evaluates Derivatives Step-by-Step…”

For more information see

webMathematica or

Wolfram Research Inc.


DERIVATIVES CALCULATORS – eFunda
VERY VERY EXTENSIVE.

Derivatives Calculators include:

Derivatives in General Calculator;

Higher Derivatives of Products Calculator;

Derivatives of Trigonometric Functions Calculator;

Derivatives of Hyperbolic Functions Calculator;

Derivatives of Exponential and Logarithmic Functions Calculator.

For more information see

Calculus;

Engineering Mathematics or

eFunda


FUNCTION CALCULATOR (ENGLISH) – Xiao Gang,
Laboratoire J.-A. Dieudonné,
Université de Nice, Nice, France
English & Français.
VERY VERY VERY…EXTENSIVE.

Function Calculator is

“…an interactive calculator to plot,
compute and test numbers…”

For more information see

WIMS


FUNCTION EVALUATOR & GRAPHER: A UTILITY FOR APPLIED
CALCULUS, FINITE MATHEMATICS & APPLIED
CALCULUS (JAVA APPLET) – S. Waner (Emeritus),
Department of Mathematics,
Hofstra University
VERY VERY EXTENSIVE.

Function Evaluator & Grapher

“…Creates a table of values and graph for any function you
specify…”

For more information see

Online Utilities & Software – Calculators;

Finite Mathematics & Applied Calculus;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University


INTEGRATION: NUMERICAL INTEGRATION CALCULATOR – S. Waner (Emeritus),
Department of Mathematics,
Hofstra University
VERY VERY EXTENSIVE.

Numerical Integration Calculator

“…Graphs, and computes left-, right-, trapezoid, and
Simpson’s rule sums. Also computes integrals to the
accuracy you specify using an adaptive quadrature algorithm…”

For more information see

Online Utilities & Software – Calculators;

Finite Mathematics & Applied Calculus;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University


MATHLETS: JAVA APPLETS FOR MATH EXPLORATIONS – T. Leathrum,
Department of Mathematical, Computing, and Information Sciences,
Jacksonville State Univertsity, Alabama
VERY VERY VERY…EXTENSIVE.
For more information see

Tom Leathrum’s Home Page;

Tom Leathrum’s Faculty Home Page or the

Department of Mathematical, Computing, and Information Sciences

Examples from over “30” Calculus Calculators & Calculus Applets include


Derivative Calculator Applet


Newton’s Method Applet


The Technique of Substitution for Definite Integrals Applet


Exploring Jacobians and Changes of Variables Applet

Regression Calculators & Applets


MULTIPLE LINEAR REGRESSION – S. Waner (Emeritus),
Department of Mathematics,
Hofstra University
VERY VERY EXTENSIVE.

Multiple Linear Regression Calculator
“…instantly gives you the best-fit (regression) linear function
of up to 4 independent variables and up to 16 data points (10 digit accuracy)…”

For more information see

Online Utilities & Software – Calculators;

Finite Mathematics & Applied Calculus;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University


SIMPLE REGRESSION UTILITY – S. Waner (Emeritus),
Department of Mathematics,
Hofstra University
VERY EXTENSIVE.

Simple Regression Utility

“…The algorithm is written to round all output to no
more than 11 significant digits…”

For more information see

Online Utilities & Software – Calculators;

Finite Mathematics & Applied Calculus;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University


RIEMANN SUM (SPREADSHEET OPENS ONLINE WITH EXCEL, iWORK-NUMBERS, IBM LOTUS SYMPHONY, NEOOFFICE, OPENOFFICE CALC, ETC.) – S. Waner (Emeritus),
Department of Mathematics,
Hofstra University
VERY VERY EXTENSIVE.

Riemann Sum Calculator

“…Shows a graph along with the area corresponding to
the left-sum approximation of the integral…”

For more information see

Online Utilities & Software – Calculators;

Finite Mathematics & Applied Calculus;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University