MARTINDALE'S CALCULATORS ON-LINE CENTER MATHEMATICS: CALCULUS (Calculators, Applets, Spreadsheets, and where Applicable includes: Courses, Manuals, Handbooks, Simulations, Animations, Videos, etc.)

US/Pacific: Tuesday, May 13, 2008 Sydney, Australia: Wednesday, May 14, 2008 File Download Time Calculator Author, E-Mail, Privacy Policy & Disclaimer Currently the Calculators On-Line Center contains over "23,490" Calculators

CALCULUS Pre-Calculus ~ 1st Year Calculus Advanced Calculus, Infinitesimal Calculus, Multivariable Calculus, etc. Calculus Graphing & Plotting Differential Equations Courses, Lectures, Calculators, etc. Mathematics Calculators Home Page Calculators On-Line Center Home Page

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 Teaching Modules, 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..." Pre-Calculus Subject Categories with Teaching Modules, Calculators & Applets 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; Curve Fitting; Conic Sections. For more information see Visual Calculus; Math Archives or the Department of Mathematics Some examples of Pre-Calculus Calculators & Applets include Transformations of Exponential Functions Transformations of Logarithmic Functions Curve Fitting

First Year Calculus

Fundamental Theorem of Calculus 1st Year Calculus Courses (with Calculators, Applets, Videos/Movies & Audio/Sound) 1st Year Calculus Courses (with Calculus Calculators & Calculus Applets) 1st Year Calculus Calculators & Calculus Applets

1st Year Calculus FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLETS & SHOCKWAVE 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) - 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 APPLET) - T. Tao, Department of Mathematics, UCLA VERY EXTENSIVE. The Fundamental Theorem of Calculus Applet. For more information see Java or the Terence Tao's Home Page 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 THE FUNDAMENTAL THEOREM OF CALCULUS (JAVA APPLETS) - Undergraduate Mathematics Labs, Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada VERY EXTENSIVE. The Fundamental Theorem of Calculus Applet. For more information see UBC Calculus Course Notes Online; UBC Calculus Online Home Page; Undergraduate Mathematics Labs or the Department of Mathematics

1ST YEAR CALCULUS COURSES WITH CALCULATOR, APPLETS, VIDEOS/MOVIES & AUDIO/SOUND PRINCIPLES OF CALCULUS MODELING: AN INTERACTIVE APPORACH (REALPLAYER & SHOCKWAVE) - 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. Calculus Video Chapters with over "100" Videos/Movies 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 WITH CALCULUS CALCULATORS & APPLETS CALCULUS TEXTBOOK (MATH 100) - J. Feldman, Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada Multimedia Calculus Course (Text & Images). VERY VERY VERY...EXTENSIVE. Calculus Chapters with Calculus Calculators, Calculus Applets & Teaching Modules 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 Some examples from over "50" Calculus Calculators & Applets with Teaching Modules include The Function Zoo: Equations of Straight Lines Calculator Tools for Calculating Derivatives: Linear Approximations Calculator Newton's Method Calculator CALCULUS TEXTBOOK (MATH 101) - J. Feldman, Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada Multimedia Calculus Course (Text & Images). VERY VERY EXTENSIVE. Calculus Chapters with Calculus Calculators, Calculus Applets & Teaching Modules include: "...Definite Integrals and the Fundamental Theorem of Calculus; Applications of the Definite Integral: Techniques for Antidifferentiation; Differential Equations & Weighted Averages; Taylor Polynomials and Series, etc..." For more information see Joel Feldman's Home Page; The UBC Calculus Online Homepage or the Department of Mathematics CALCULUS I (MA121) (LIVEMATH) - R.D. Poodiack, Department of Mathematics, Norwich University Multimedia Calculus Course (Text, Images & LiveMath). VERY VERY EXTENSIVE. Examples of Calculus Chapters & Subchapters with Calculus Calculators, Calculus Applets & Teaching Modules include: Chapter 2 "...Numerical Limits; Visualizing Limits; Visualizing Two-sided Limits; Continuity at a point..." Chapter 3 "...Equation of a tangent line; Definition of the Derivative; Derivative Checker; Chain Rule; Implicit Differentiation; Linearization and Differentials..." Chapter 4 "...Critical Numbers; Inflection Points..." For more information see Robert D. Poodiack's Home Page or the Department of Mathematics 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 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..." Calculus Calculators Subject Categories include: "...Single Variable Calculus; Vectors and Algebra; Application to 3D Linear Geometry; Curves; Fields and Surfaces; Complex Numbers and Functions; Integration on Curves; Integration on Surfaces; Differential Equations; Applications..." 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 Some 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 DIFFERENCE EQUATIONS TO DIFFERENTIAL EQUATIONS: AN INTRODUCTION TO CALCULUS (JAVA APPLETS) - D. Sloughter, Department of Mathematics, Furman University Multimedia Difference Equations to Differential Equations: An Introduction to Calculus Course (Text, Images & Applets). VERY VERY EXTENSIVE. Difference Equations to Differential Equations: An Introduction to Calculus 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 Java Applets; Dan Sloughter's Home Page or the Department of Mathematics Some examples from over "8" Calculus Calculators include Affine approximations Numerical integration rules FINITE MATHEMATICS & CALCULUS APPLIED TO THE REAL WORLD - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University Multimedia Applied Calculus & Finite Mathematics Course (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus Resource Page; Finite Mathematics & Applied Calculus; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University Some examples from over "10" Calculus Calculators & Calculus Applets include Function Evaluator and Grapher for Calculus Applied to the Real World Surface Graphing Utility INTRODUCTION TO CALCULUS - Open Learning Initiative (OLI), Carnegie Mellon University Multimedia Introduction to Calculus Course (Text & Images). VERY VERY EXTENSIVE. Examples of Calculus Chapters & Subchapters include: Graphs "...Equations and Their Graphs; Lines; Circles and Semicircles; Ellipses and Semiellipses; Parabolas and Their Branches; Hyperbolas and Their Branches; Polynomial Equations; etc..." Important Functions "...Linear Functions; Power Functions; Quadratic Functions; Polynomials; Rational Functions; Root Functions; Exponential Functions; etc..." Pointwise and Global Properties of Functions Monotonicity; Boundedness; Convexity; The Intermediate Value Property; Pointwise Limits; Continuity; etc..." For more information see Open Learning Initiative (OLI) or Carnegie Mellon VISUAL CALCULUS (JAVA APPLETS & LIVEMATH) - L. Husch, Department of Mathematics, University of Tennessee Multimedia Calculus Course (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..." Calculus Chapters with Calculus Calculators, Calculus Applets & Teaching Modules include: "...Limits and Continuity; Derivatives; Applications of Differentiation; Integration; Applications of Integration; Sequences and Series..." For more information see Department of Mathematics Some example 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

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 APPLIED CALCULUS ON THE WEB - M.S. Pilant, Department of Mathematics, Texas A&M University VERY VERY EXTENSIVE. For more information see Michael S. Pilant's Home Page or the Department of Mathematics Some examples from over "20" Calculus Calculators & Calculus Applets include Slope Applet Modelling Applet Function Analyzing Applet - Qualitative Graphing Interactive Curve Sketching Applet CALCULUS APPLETS - S.A. Sarra, Department of Mathematics, 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 Some 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 (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 - D. Sloughter, Department of Mathematics, Furman University VERY VERY EXTENSIVE. For more information see Dan Sloughter's Home Page or the Department of Mathematics Some examples from over "11" Calculus Calculators & Calculus Applets include Discrete inhibited population growth Applet Affine approximations Applet Trigonometric series approximation of a sound wave 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 Some examples from over "11" Calculus Calculators & Calculus Applets include Morphing Applet SecantTangent Applet Sequences of Functions Applet Riemann Sums: Simpson Rule 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 Calculator "...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 Some 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 Courseware: Projects and worksheets; Mike May, S.J.'s Home Page or the Department of Mathematics and Computer Science Some 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 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 & S.R. Costenoble, 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 Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University INTEGRATION: NUMERICAL INTEGRATION CALCULATOR - S. Waner & S.R. Costenoble, 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 Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University INTEGRATION ERROR: EXAMINATION OF THE MIDPOINT AND TRAPAZOID RULE ERRORS - K.M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell Examination of the Midpoint and Trapezoid Rule Errors "...examines the errors associated with the midpoint and trapazoid rules with n = 1..." For more information see UMass Lowell WebMathematicaScripts; Kenneth M. Levasseur's Home Page; Department of Mathematical Sciences or HostSRV Examples from over "7" other Calculus Calculators & Calculus Applets include Derivatives and Their Approximation Taylor Polynomials A Taylor polynomial "...is a partial sum of a Taylor series. This WebMathematica page will compute and Taylor polynomials of selected functions..." Riemann Integration Riemann Integration "...The integral of a function over an interval is approximated by "Riemann sums" with the limit of these sums being the exact integral..." KARL'S ONLINE INTERACTIVE CALCULUS TUTOR - Karl's Calculus Tutor, Karl Hahn VERY VERY VERY...EXTENSIVE. Karl's Online Interactive Calculus Tutor "...resolve arithmetic expressions in standard infix notation; solve somplex numbers; solve n equations in n unknowns, for n from 2 to 7; generate plot images of functions; generate polar plot images of functions..." For more information see Karl's Calculus Tutor Some examples of Calculus Calculators include Karl's Online Calculator Karl's Online Calculator "...is a powerful calculator that can do multiple operations..." Karl's Online Linear Equation Calculator Karl's Online Linear Equation Calculator "...Solves n equations in n unknowns for n equal 2 to 7..." Karl's Online Complex Calculator Karl's Online Complex Calculator "...does operations on complex numbers..." 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 or the Department of Mathematical, Computing, and Information Sciences Some 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 & S.R. Costenoble, 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 Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University SIMPLE REGRESSION UTILITY - S. Waner & S.R. Costenoble, 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 Resource Page; Steven R. Costenoble'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 & S.R. Costenoble, 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 Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University

Advanced Calculus ADVANCED CALCULUS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ADVANCED CALCULUS COURSES WTIH CALCULATORS & APPLETS Calculus II, III, & IV CALCULUS (JAVA APPLETS) - E.A. Carlen, School of Mathematics, Georgia Tech VERY VERY EXTENSIVE. For more information see Mathematicians of the Day Resources; Resources; Eric A. Carlen's Home Page or the School of Mathematics Some examples from over "40" Calculus Calculators & Calculus Applets include Calculus II Applets Calculus III Applets Calculus IV Applets Infinitesimal Calculus INTRODUCTION TO INFINITESIMAL CALCULUS (WEBMATHEMATICA, LIVEGRAPHICS3D & JAVA APPLETS) - K.D. Stroyan, Department of Mathematics, University of Iowa Multivariable Infinitesimal Calculus Course (Text, Images & Simulations). VERY VERY EXTENSIVE. Multivariable Infinitesimal Calculus Chapters & Subchapters include Some Intuitive Proofs with "Small" quantities; "...Continuity & Extreme Values; The Fundamental Theorem of Integral Calculus; Continuity of the Derivative; Leibniz's Formula for Radius of Curvature; etc..." Keisler's Foundations for Infinitesimal Analysis "...Small, Medium, and Large Hyperreal Numbers; Keisler's Function Extension Axiom; Continuity & Extreme Values; Second Differences and Higher Order Smoothness; etc..." Local Linearity and Infinitesimal Microscopes; etc. For more information see Interactive Multivariable Calculus Course; Keith D. Stroyan's Home Page or the Department of Mathematics FOUNDATIONS OF INFINITESIMAL CALCULUS (PDF) - K.D. Stroyan, Department of Mathematics, University of Iowa Multivariable Foundations of Infinitesimal Calculus Book - 182 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Foundations of Infinitesimal Calculus" Book Chapters include "...Chapter 1: Numbers; Chapter 3: The Theory of Limits; Chapter 5: The Theory of Derivatives; Chapter 8: Higher Order Derivatives; Chapter 11: Theory of Initial Value Problems; Chapter 12: The Theory of Power Series; etc..." For more information see Interactive Multivariable Calculus Course; Keith D. Stroyan's Home Page or the Department of Mathematics Multivariable Calculus MULTIVARIABLE CALCULUS (PDF) - 18.02 - M. Manapat, Department of Mathematics, MIT Multimedia Multivariable Calculus Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "25" Multivariable Calculus Course Lectures include "...Matrices, inverse matrices; Planes, parametric equations for lines and curves; Partial derivatives, tangent plane approximation; Summary of global max-min, boundaries and infinity, chain rule, differentials; Lagrange multipliers; Changing order of integration, double integrals, applications; General change of variables; Fundamental theorem for line integrals, grad test, potential functions; Triple integrals, cylindrical coordinates; Surface area and flux across cylinders and spheres, divergence theorem; Stokes' theorem; etc..." For more information see Michael Manapat's Home Page or the Department of Mathematics MULTIVARIABLE CALCULUS (WEBMATHEMATICA, LIVEGRAPHICS3D & JAVA APPLETS) - K.D. Stroyan, Department of Mathematics, University of Iowa Multimedia Multivariable Calculus Course (Text, Images & Simulations). VERY VERY VERY...EXTENSIVE. Multivariable Calculus "...includes over "50" Calculus Calculators & Calculus Applets. For more information see Interactive Multivariable Calculus Course; Keith D. Stroyan's Home Page or the Department of Mathematics Multivariable Calculus with Vector Analysis MULTIVARIABLE CALCULUS WITH VECTOR ANALYSIS (MATHEMATICA, LIVEGRAPHICS3D & JAVA APPLETS) - J. Rogness, School of Mathematics, University of Minnesota Multimedia Multivariable Calculus with Vector Analysis Course & Applets (Text & Images). VERY VERY VEVY...EXTENSIVE. For more information see Jonathan Rogness' Home Page; Institute of Technology Center for Educational Programs (ITCEP) or the School of Mathematics Some examples from over "20" Vector Calculus Calculators & Calculus Applets include Interactive Gallery of Quadric Surfaces Lagrange Multipliers

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