Precalculus, Single Variable Calculus Applets
Slope Field Applet
The applet plots the slope field for any ordinary differential equation of the form dy/dx=f(x,y)
entered by the user. The user controls the x and y ranges as well. Approximate solutions
based on the slope field can be drawn with the mouse.
Practice Sketching Derivative
The applet illuminates the relationship between graphs
of functions and their derivatives. A graph of
a randomly generated function f(x) is provided. The student attempts to sketch the graph
of the derivative f '(x) by dragging and shaping a curve. The answer is evaluated for correctness
at a click of a button providing instant feedback.
Implicit Equations Grapher
This applet graphs user-defined implicit equations of the form
f(x,y)=g(x,y) in a user-defined x,y ranges. The syntax used for input
is the same as graphing calculator syntax and the applet is very easy to use.
The results are comparable with those provided by CAS like Maple.
- Matching Formulas to Data Plot points,
enter any parametric family of functions, dynamically change parameters while observing the
changes in the least square error. Provides a quick and easy way of matching formulas to data points.
- Parametric Curves on the Plane Graph
parametric curves in rectangular as well as polar coordinates. Curves can be traced showing the direction of motion
and the way a curve is traversed. The x and y ranges adjust automatically.
- Two Function Graphers
Graph two or three arbitrary functions at a time and trace them.
- Derivative Plotter
Enter a formula for an arbitrary function, the applet will plot it. Try sketching the derivative by drawing
on screen. Reveal the real derivative dynamically by dragging a slider while the lineal element corresponding to the tangent line
and its slope are displayed. Many demo examples.
- Accumulated Change and Antiderivative Plotter
Enter a formula for an arbitrary function, the applet will plot it. Try sketching the antiderivative with a given initial condition by drawing
it on screen. Reveal the real antiderivative dynamically by dragging a slider while the area corresponding to the value of the antiderivative
is dynamically shaded. The applet will draw antiderivatives of functions hand-drawn by the user!
- Sequences and Series of Functions Plotter
Enter a formula for a sequence or a series of functions, the applet will plot consecutive terms or partial sums at a click
of a button. In particular, you can enter Taylor series or Fourier series.
You can also enter a piecewise defined limit function to be plotted. Many demo examples are provided.
- Sequences and Series of Constants Plotter
Enter a formula for a sequence or a series of constants, the applet will plot consecutive terms or partial sums at a click
of a button or automatically in the autorun mode. The applet illustrates many concepts associated with convergence and divergence of sequences and series, including
the speed of convergence, subsequences, and Weyl's Theorem on Uniform Distribution. Examples and practice problems are provided.
- Familes of Functions and Points Plotter, Matching Functions to Data
This applet tackles a similar topic as Matching Formulas to Data above. This applet takes a different pedagogical approach, though.
You enter data points and then choose from a list of families of functions: linear, surge, trigonometric, logistic, polynomial etc. to match the data
points. Current values for parameters in each family are placed right in the formula for the family and change dynamically as the arrows above and below them
are pressed. Thus, one level of abstraction with parameters, a, b, c, d present in each formula is removed.
- The Definite Integral in Terms of Areas You will find this applet to be simple and appealing. The applet uses many examples to dynamically illustrate the Fundamental Theorem of Calculus and the meaning of the definte integral in terms of areas. The areas are shaded and the value of the integral changes as you drag a slider.