Calculus Applets

Grapher

Allows graphing of equations on the Cartesian coordinate system.

Graphical and Numeric Limits

Demonstrates how limits are found using graphical and numerical techniques. Includes functionality to support piecewise defined functions.

Tangent to a Circle

Demonstrates how a tangent line to a circle looks.

Tangent and Secant Lines

Illustrates the relationship between tangent lines and secant lines to a given graph.

Derivatives of Inverse Functions

Demonstrates the relationship between a function and it's inverse with respect to the slopes of tangent lines.

Absolute Extrema

Demonstrates the how to find an absolute extrema on a closed interval.

First Derivative Graph

Demonstrates how the graph of the first derivative is obtained from a given function.

First Derivative Test

Shows how the graph of the derivative of a function can be used to determine where a function is increasing or decreasing.

Second Derivative Test

Shows how the graph of the second derivative of a function can be used to determine where a function is concave up or concave down.

Curve Sketching

Demonstrates how the first and second derivatives can be used in conjunction in order to produce graph of the original function.

Area of a Circle

Demonstrates how the area of a circle can be approximated using inscribed regular polygons.

Integrals and Approximations

Demonstrates how to approximate the area under a curve using either left endpoint rectangles, right endpoint rectangles, lower sums, upper sums, midpoint rectangles, trapezoids or parabolas. Compares the approximation to the exact area under the curve.

General and Particular Solutions

Demonstrates the concept of a general solution to a differential equation and a particular solution.

Definite Integrals

Calculates a definite integral between two different functions so that properties of definite integrals can be displayed.

Average Value of a Function

Demonstrates how the average value of a function is computed using limits and allows users to take a guess at what the average value of a function is to compare to the real result.

Slope Fields

Allows the user to input a first degree differential equation in order to see the slope field associated with it. A function that represents a particular solution can also be drawn so that students can see the relationship between the particular and general solutions.

Area Between Curves

Allows user to draw up to four boundary functions, and can either move a base rectangle within that region, or view approximating rectangles within the region. The rectangles can either be oriented vertically or horizontally. A vertical or horizontal axis can also be drawn to help illustrate the disk and shell methods.

Disks and Shells

Demonstrates the object created in 3D by rotating a user-defined path in the xy plane around the x or y axis.

Arc Length

Demonstrates how the approximation of arc length is calculated along a function on a given interval.

Sequences and Series

Allows the user to graph sequences and partial sums of series in order to visually see how some series converge and others diverge. Allows comparison tests to be used in order to see how these work as well.

Taylor and MacLaurin Series

Demonstrates how Taylor and MacLaurin Polynomials can be used to make approximations to transcendental functions.

Vector Rotation

Demonstrates the effect of rotating vectors 90 degrees clockwise or counter-clockwise.

Points in Space

Demonstrates plotting a point in 3D.

3D Vector Sum

Illustrates the geometric relationship of the sum of two vectors in 3D.

Collinear Points

Illustrates the concept of how three points can lie on a line in 3D.

Parallelogram Points

Demonstrates how to show that 4 points in space form a parallelogram.

Sphere

Allows the user to draw spheres in different center points and radii.

Horizontal and Vertical Planes

Demonstrates some basic horizontal and vertical planes in 3D.

Vector Projections

Demonstrates what a vector projection and an orthogonal vector projection look like.

Dot Products

Allows user to visually see the result of the dot product.

Intersecting and Skew Lines

Demonstrates the difference between lines that intersect in space and lines that are skew.

Intercepts of Planes

Demonstrates what the intercepts of a plane looks like in space.

Graphing Vector-Valued Functions in the Plane

Demonstrates how vector-valued functions are graphed in the plane. The applet can also show the relationship between the function and it's first and second derivative vectors.

Graphing Vector-Valued Functions

Demonstrates how vector-valued functions are graphed in space.

Velocity and Acceleration

Demonstrates the relationship between the velocity and acceleration vectors with respect to a point on a 3D vector-valued function.

Curvature

Demonstrates how curvature works on a 2D curve.

Graphing Surfaces

Demonstrates how surfaces are drawn in three dimensions.

Graphing Traces

Demonstrates how graphs can be produced in three dimensions using traces.

A Limit that Exists

Shows a limit in 3D that exists, and demonstrates different paths that can be taken to get to it.

A Limit that Does Not Exist

Demonstrates a limit in 3D that does not exist and the different paths that can be taken to prove this.

Partial Derivatives and Gradients

Shows how to interpret a partial derivative, directional derivative, and gradient in three dimensons.

4D Graph

Demonstrates a graph of a 4-dimensional surface by allowing a 3d surface to change over time.

3D Grapher

Allows user to plot points, vector-valued functions and z=f(x, y) functions in a 3-dimensional system.

Absolute Extrema

Demonstrates the necessity of testing for absolute extrema along the boundaries of a region, at the intersection of a region and within a region for extreme values of a function.

LaGrange Multipliers

Demonstrates the concept of finding a minimum distance using LaGrange Multipliers.

Calculating Volume Using a Double Integral

Demonstrates how the volume of a solid trapped between a surface and the x-y plane can be calculated using a double-integral.

Linear Transformations

Allows the user to see the effect of a linear transformation on a defined region in order to view the effect of the Jacobian on that region.

Non-Linear Transformations

Allows the user to see the effect of a non-linear transformation for points and relations within a system based on given transformation functions.

Path Integration

Demonstrates the integral of a surface subject to a path within the x-y plane.

Vector Fields

Graphs 2-dimensional vector fields and allows the user to explore how particles are affected within these systems and see the value of the curl and divergence for different points on the field.

3D Vector Field

Shows a vector field in 3D that you can rotate around.

Parameterized Paths

Demonstrates how paths can be constructed in 2D. Helps the student visualize what a parameterized path represents graphically.

Intersection of Three Planes

Demonstrates what the intersection of three planes at a single point looks like.

Intersection of Two Planes

Demonstrates what the intersection of two planes in space looks like.