Calculus Applets

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Introduction to Calculus Applets

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. These pages can be explored by students learning calculus, or used by teachers while teaching calculus, and are geared to the topics covered in AB and BC Advanced Placement Calculus. Each applet comes in a version shown on a web page, suitable for viewing in a browser window, and also as a separate resizeable window with larger fonts and line widths, suitable for projection on a screen. Note that this set of pages is not a complete text for calculus, but is intended to supplement a standard textbook or web site. I have used Calculus by Hughes-Hallett, Gleason, McCallum, et al. in my teaching, and I also like Master the AP Calculus AB & BC Tests by Michael Kelley.

See Compatibility, Downloading, and Modifying for more information on computer/OS/browser compatibility, downloading the entire web site, and modifying the web pages. Send comments, questions, and feedback to email.

  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

Creative Commons License
This work by Thomas S. Downey is licensed under a Creative Commons Attribution 3.0 License.

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