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Author: Thomas Downey
This file is part of a distribution of the Calculus Applets website (http://www.calculusapplets.com) (v1.1) which has been reformatted for the needs of this OpenCourseware course.

These pages present interactive Java applets for teaching and learning single variable calculus. They use graphs and tables to illustrate concepts in calculus and allow the user to dynamically change the functions involved or the point on the graph that is of interest.  Each applet comes in a version shown on a web page, suitable for viewing in a browser window. Note that this set of pages is not a complete text for calculus, but is intended to supplement a standard textbook or web site.

See Compatibility, Downloading, and Modifying for more information on computer/OS/browser compatibility, downloading the entire web site, and modifying the web pages.

The following list includes topics from Elements of Calculus I and II.  Generally speaking, Elements of Calculus I covers topics in sections 2-6 and some topics in section 7. The topics in sections 8-11 are included in Elements of Calculus II.

This is not the syllabus for Elements of Calculus I, but a listing of interactive activities available to students and teachers studying calculus.

  1. Using the Graphing Tools
    1. Introduction to using the applets.
    2. Limitations of Graphing Software
  2. Continuity and Limits
    1. An Informal, Graphical View of Continuity
    2. Intermediate Value Theorem
    3. Informal View of Limits
    4. One- and Two-Sided Limits and When Limits Fail to Exist
    5. Limits at Infinity
    6. Table View of Limits
    7. Formal Definition of Limits
    8. Definition of Continuity Using Limits
  3. Introduction to the Derivative
    1. Average Velocity and Speed
    2. Instantaneous Velocity
    3. Derivative at a Point
    4. Derivative Function
    5. A Tabular View of the Derivative
    6. Second Derivative
    7. A Tabular View of the Second Derivative
    8. Differentiability
    9. Twice Differentiable
    10. Making a Piecewise Function Continuous and Differentiable
  4. Differentiation Short Cuts
    1. Constant, Line, and Power Functions
    2. Exponential Functions
    3. Trigonometric Functions
    4. Constant Multiple
    5. Combinations: Sum, and Difference
    6. Combinations of Functions: Product and Quotient
    7. Composition of Functions (the Chain Rule)
    8. Transformations of Functions
    9. Inverses of Functions
    10. Hyperbolic Functions
    11. Linear Approximation
    12. Mean Value Theorem
  5. Applications of Differentiation
    1. Curve Analysis: Basics
    2. Curve Analysis: Special Cases
    3. Curve Analysis: Global Extrema
    4. Optimization: Maximize Volume
    5. Extreme Value Theorem
    6. Related Rates
    7. L'Hopital's Rule
    8. Parametric Derivatives
    9. Polar Derivatives
    10. Motion on a Line
    11. Motion in the Plane
  6. Introduction to the Definite Integral
    1. Approximating Distance Traveled With a Table
    2. Approximating Distance Traveled With a Graph
    3. Riemann Sums and The Definite Integral
    4. Fundamental Theorem of Calculus
    5. Average Value
    6. Properties of Definite Integrals
  7. Constructing Antiderivatives
    1. Antiderivatives from Slope and the Indefinite Integral
    2. Accumulation Functions
    3. Basic Antiderivatives
    4. Introduction to Differential Equations
    5. Second Fundamental Theorem of Calculus
    6. Functions Defined Using Integrals
    7. Equations of Motion
  8. Integration Techniques
    1. Substitution
    2. Midpoint and Trapezoid Riemann Sums
    3. Improper Integrals
  9. Applications of Integration
    1. Areas by Slicing
    2. Volumes of Revolution
    3. Volumes of Known Cross Section
    4. Arc Length
    5. Area of Polar Curve
  10. Differential Equations
    1. Slope Fields
    2. Euler's Method
    3. Separation of Variables
    4. Growth, Decay and the Logistic Equation
  11. Sequences and Series
    1. Sequences
    2. Series
    3. Integral Test
    4. Comparison Test
    5. Limit Comparison Test
    6. Ratio Test
    7. Alternating Series and Absolute Convergence
    8. Power Series & Interval of Convergence
    9. Taylor Series & Polynomials
    10. Lagrange Remainder

     

 

For more information on rights and downloading, refer to http://www.calculusapplets.com/download.html.

© Copyright 2001 David J. Eck

© Copyright 2007 Thomas S. Downey

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

You must cause any files that you modify to carry prominent notices stating that you changed the files and the date of any change, and modified files must be put into a Java package different from edu.hws.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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