Calculus Winplot Files

The following Winplot files can be downloaded. Winplot itself can be downloaded at  https://drive.google.com/file/d/1Nc9lX0DwB4_nbsFnQaDtWwY9EAEuenqq/view?usp=sharing. An online tutorial is also available. To download a one of the files shown below, left click with the mouse and save the file to your local disk. A sample output is shown in the graphic above.
 

Calculus I Examples

Tangent Line to a Circle: Animate on p to Change the Point P, Animate on a to Change the Radius, Animate on h , k to Change the Center.

Geometric Construction of the Tangent Line to a Parabola: Animate on a to Change the Point P, Animate on d to Change the Directrix.

Illustration of Defining a Piece-Wise Function

Illustration of a Limit: Animate on a (the Fixed x Value), e (Epsilon), and p (Varies x) for a Given User Defined Function g(x)

A Second (better!) Illustration of a Limit Authored by John Ganci:  Animate on a (the Fixed x Value), e (Epsilon), and d (Delta) for a User Defined Function FF(x). The parameter p varies x near a.

Illustration of  Problem 19 of Project 1 Animate on a to Change its Value

Calculating the Instantaneous Velocity of a Falling Object  Animate on p to Change the Time, Animate on s to Change Delta Time

The Derivative as the Slope of the Tangent Line: Animate on a to Change the Point on the User Defined Function g(x), Animate on h to change Delta x

Illustration of Problem 1 of Project 2. Animate on a to Change the Point Where the Tangent Line Touches the Curve  y = abs( 4 - x^2)

The Central Difference Approximation to the Derivative: Animate on a to Change the Point on the User Defined Function g(x), Animate on h to change Delta x

Project 3 Problem 1 : Animate on a to move the point on both of y = f(x) and x = f(y)

Mean Value Theorem Illustrated on Project 3 Problem 4a : Animate on A and B to Move the Secant Line

Illustration of the Linear and Quadatic Approximation about a Point on a Curve. Project 3 Problem 6

Illustration of a Cylinder Inscribed in a Sphere (Project 4, Problem 12). This is a Three-Dimensional Plot which Needs to Opened in the 3-dim Window. Vary the Parameter b to Change the Cylinder.

Torus Made by Revolving a Circle of Radius 1 Centered at (0,2) About the x Axis

Torus Made by Revolving a Circle of Radius 1 Centered at (0,2) About the x Axis with an Inscribed Sphere (Volume of Revolution About y Axis!)

A nice view of a Torus: File Generated by John Ganci:

Surface Area of a Sphere Calculated Using a Chord Length

Illustration of the Archimedian Property of a Sphere

Proof of the Archimedian Property of a Sphere
 

Calculus II Examples

Illustration of Slope of Tangent Line to y = 4xln(1 - 2/x)

Illustration of Slope Fields for the Derivative equal to a Piecewise Function (Project 3 Problem 6.d)

Graph of  Lissajous figures (a is the horizontal amplitude, b is vertical amplitude, f is the frequency ratio of the vertical oscillator to the horizontal oscillator)

Graph of the Trochoid (a is the "wheel" radius, b is distance from the center of the "wheel", p is the "time" parameter)

Graph of the Cycloid (a is the "wheel radius", p is the "time" parameter)

Graph of the "Bi-Cycloid (a is the "wheel radius", p is the "time" parameter)

Parameterizing the Unit Hyperbola using sinh and cosh (a is the parameter on the unit circle)

Graph of the Astroid and its Tangent Line as in Problem 3 of Project 6 (a is the Dimension of the Astroid, p is the "angle" parameter)

Graph of the Epicycloid (a is the inner circle radius, b is the rotating circle radius, p is the "time" parameter)

Graph of both the Epicycloid and the Hypocycloid (a is the inner circle radius, b is the rotating circle radius, p is the "time" parameter)

Graph of the "Golden Spiral" showing the limit point as the number of sprials goes to infinity

Three-D Graph of the Intersection of a Cone with a Plane (k is the Cone Angle, Plane is z = a*x + b*y +c )

Graph of the Quadratic Equation x^2/a+y^2/b = 1

Illustration of the Definition of a Parabola: Focus at (0, p), Directrix y = - p

Second Illustration of the Definition of a specific Parabola: y^2 - 8x - 4y = 20 : Focus at (-1, 2), Directrix x = - 5

Graph of the Ellipse x^2/a^2+y^2/b^2  = 1 ( k is the Eccentricity, b = a*sqrt(1-k^2), p Moves the Point on the Ellipse )

Graph of the Ellipse (x-2)^2/9+(y+5)^2/4 = 1 Showing the PF = eccentricity*PD property, p Moves the Point on the Ellipse.

Graph of the Ellipse (x-2)^2/9+(y+5)^2/4 = 1 Showing the reflective property of the two focal points, p Moves the Point on the Ellipse.

Graph of the Hyperbola (y+1)^2/9-(x-3)^2/36 = 1 Showing the PF = eccentricity*PD property, p Moves two Points on the Hyperbola.

Graph of the Hyperbola x^2/a^2 - y^2/b^2  = 1 ( k is the Eccentricity, b = a*sqrt(k^2-1), p Moves Points on the Hyperbola)

Graph of a General Conic Section: ( e is the Eccentricity, k = Distance from Focus to Diretrix, s varies Orientation of Directrix)

Illustration of the "Four Bugs Problem" from Group Project 4: Animate on p to Move the Four Bugs

Illustration of Vector Addition in 2D:  a is the Length of Vector 1, p is its Angle, b is the Length of Vector 2, c is its Angle

Illustration in 2D of Projecting a Vector A (RED) onto a Vector B (BLUE):  a is the Length of Vector A, p is its Angle, b is the Length of Vector B, c is its Angle

Illustration of a Vector in 3D:  a is the Length of the Vector, p is its Polar Angle and c is its Azimuth

Illustration of Vector Addition in 3D:  a is the Length of Vector 1, p is its Polar Angle and c is its Azimuth, b is the Length of Vector 2, with Angles u and v

Illustration of the Geometric Definition of the Vector Cross Product:  < a, b, c> is the BLUE vector A; < e, f, g> is the RED vector B; the PURPLE vector is the projection of B into the plane perpendicular to A at the base of A; the GREEN vector is the rotation of the projected vector 90 degrees CCW about the pole of A; the BLACK vector is the CROSS of A with B.

Illustration of the Vector Cross Product:  a is the Length of Vector 1 (BLUE), p is its Polar Angle and c is its Azimuth, b is the Length of Vector 2 (RED), with Angles u and v

An Elliptic Hyperboloid with Axis Along the z Axis: Animate on a to Change from a one-sheet to a two-sheet Hyperboloid, Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z

An Elliptic Hyperboloid with Axis Along the y Axis: Animate on a to Change from a one-sheet to a two-sheet Hyperboloid, Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z

An Elliptic Hyperboloid with Axis Along the x Axis: Animate on a to Change from a one-sheet to a two-sheet Hyperboloid, Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z

A Hyperbolic Paraboloid (Saddle) with Axis Along the z Axis: Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z

A Hyperbolic Paraboloid (Saddle) with Axis Along the y Axis: Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z

A Hyperbolic Paraboloid (Saddle) with Axis Along the x Axis: Animate on b to Vary Cross Sections at Fixed y , Animate on c to Vary Cross Sections at Fixed x , Animate on d to Vary Cross Sections at Fixed z
 

Calculus III Examples


Illustration of the Equation of a Plane: Ax + By + Cz = D, the Normal, < A, B, C >, and a Parametric Equation of the Line Through the Point (p, q, s) Normal to the Plane (see Project 1 , Problem 5)

Cylindrical Coordinates Showing the Unit Vectors r Hat, Theta Hat and k hat (Animate on E (Theta) and F (z) )

Spherical Coordinates Showing the Unit Vectors Rho Hat, Phi Hat and Theta Hat (Animate on E (Theta) and F (Phi) )

Demonstation that the Intersection of a Plane and a Right Circular Cylinder is an Ellipse (Animate on D to change radius, a and b to rotate plane)

Motion with Constant Angular Velocity = w (Animate on w) The Position, Velocity and Acceleration Vectors are Illustrated: Circular Motion

Motion with Constant Angular Velocity = w (Animate on w) The Position, Velocity and Acceleration Vectors are Illustrated: r = 3cos(2theta)

The Evolute of the Parabola y = x^2 : Animate on Parameter P to Move on the Parabola and Move the osculating Circle

The Evolute of the Parabola y = bx^2 : Animate on Parameter P to Move on the Parabola and Move the osculating Circle

Unit Tangent and Normal Vectors for a Curve in the x-y plane. The osculating Circle is also Displayed: Curve 1: A Circle. Animate on the Parameter P

Unit Tangent and Normal Vectors for a Curve in the x-y plane. The osculating Circle is also Displayed: Curve 2: A Parabola. Animate on the Parameter P

Unit Tangent and Normal Vectors for a Curve in the x-y plane. The osculating Circle is also Displayed: Curve 3: A Sine Wave. Animate on the Parameter P

Unit Tangent and Normal Vectors for y = sin(x) . The Osculating Circle and the Evolute are both Displayed. Animate on the Parameter P

Unit Tangent and Normal Vectors for y = Acos(bx) . The Position Vector, the Unit Tangent Vector, the Unit Normal Vector and the Osculating Circle are all Displayed. Animate on the Parameters P, A and b

Unit Tangent and Normal Vectors for y = Asin(bx) . The Position Vector, the Unit Tangent Vector, the Unit Normal Vector and the Osculating Circle are all Displayed. Animate on the Parameters P, A and b

TNB Vectors for Problem 4 on Project 2. Animate on the Parameter P

A Second View of the TNB Vectors for Problem 4 on Project 2 Showing the Osculating Circle. Animate on the Parameter A

TNB Vectors for a Circular Helix

Example of Using Unit Vectors to Solve for Angular Acceleration in Dynamics

Illustration of the Motion in Group Project 1, Problem 1 : Animate on A (time)

Illustration of the Motion in Group Project 1, Problem 4 (The Ant) : Animate on P (to see the ant move counter clockwise up the parabola)

Example of a Tangent Plane and Normal to the surface z = f(x, y) = 3x^2y + x^3

Example of a Tangent Plane and Normal to the Sphere z = f(x, y) = sqrt(16-x^2- y^2)

Example of a Tangent Plane and Normal to a surface z = f(x, y) = exp(-x^2-y^2)

Example of a Tangent Plane and Normal to a surface z = f(x, y) = x^2 + 2x + y^2 - 6y

Example of a Tangent Plane and Normal to a surface z = f(x, y) = xsin(xy)

Project 3 Problem 5 on the Electric Field in a Metal Animate on a (Lamda), b (Omega), F (E nought), u , v to vary a "point" on the surface

Project 3 Problem 8 on the Intersection of a Sphere with a Saddle

Project 3 Problem 10 on the Maximum/Minimum on a Closed Region

Fall 2007 Exam 2: Illustation of Finding Max/Min of f(x, y) = -2xy^3 on a circle of radius a

Group Project 2 Problem 3 on the Steepest Ascent of the Droid on the Glacier

Group Project 2 Problem 4 on the Tangent Plane to a Cone

Group Project 2 Problem 4 on the Tangent Plane to a Curve z = y f(y/x) for f(x) = 3x

Group Project 2 Problem 4 on the Tangent Plane to a Curve z = y f(y/x) for f(x) = sin(x)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) z, y, x : Animate on (a, b, c) for (x, y, z)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) y, z, x : Animate on (a, b, c) for (x, y, z)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) z, x, y : Animate on (a, b, c) for (x, y, z)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) x, z, y : Animate on (a, b, c) for (x, y, z)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) y, x, z : Animate on (a, b, c) for (x, y, z)

An Illustration of Integrating under the Plane x + y + 2z = 6 in the First Octant in the Order (Inside to Outside) x, y, z : Animate on (a, b, c) for (x, y, z)

Project 4 Problem 1e on the Integral of xy over the Region Bounded by the Coordinate Planes and the Plane 2x + y + 3z = 6

Project 4 Problem 1f on the Integral of xy over the Region Bounded by the Coordinate Planes, the Cylinder r = 2 and the Plane  x + z = 3

Project 4 Problem 2b Showing the Three Dimensional Region: 0 < z < pi - x^2 ; 0 < y < x ; 0 < x < sqrt (pi)

Project 4 Problem 7b Showing the Three Dimensional Region defined as "Crystal": Animate on a and b to Vary Over the Domain

Project 4 Problem 7c Showing the Three Dimensional Region in the First Octant between the two Planes: x + y + z = 1 and 2x + 2y + z = 2

An Illustration of the Element of Volume in Cylindrical Coordinates: dV = r d(r) d(theta) d(z) : Animate on the Parameters Listed in the File

An Illustration of the Element of Volume in Spherical Coordinates: dV = rho^2 sin(phi) d(rho) d(phi) d(theta) : Animate on the Parameters Listed in the File

The Intersection of a Sphere of Radius a and the Half Space z > b : r on the "outside", z on the "inside" : Animate on the Parameters Listed in the File

The Intersection of a Sphere of Radius a and the Half Space z > b : z on the "outside", r on the "inside" : Animate on the Parameters Listed in the File

The Intersection of a Sphere of Radius a and the Half Space z > b : Spherical Coordinates : Animate on the Parameters Listed in the File

A cored Sphere: The Intersection of a Sphere of Radius a and the Cylinder r = b : r on the "outside", z on the "inside" : Animate on the Parameters Listed

A Cylinder Inscribed Inside of a Sphere with the Height of the Cylinder as a Variable Parameter

The Sphere Game: Group Project Problem 3

Miscellaneous Examples


Transformation of a Rectangle into a Square of Equal Area. The parameter p (range of zero to one) controls the movement of the "cut" pieces while the parameters a and b are the dimensions of the rectangle. Only values of b > a should be used.

Torus with axis along x: Animate on a to change the mean radius of the torus about the axis, animate on b to change the "tube" radius, animate on c to move along the axis

Torus with axis along z: Animate on a to change the mean radius of the torus about the axis, animate on b to change the "tube" radius, animate on c to move along the axis

Torus with axis along y: Animate on a to change the mean radius of the torus about the axis, animate on b to change the "tube" radius, animate on c to move along the axis

Double Torus: Animate on a to change the mean radius of the torus about the axis, animate on b to change the "tube" radius

Triple Torus: Animate on a to change the mean radius of the torus about the axis, animate on b to change the "tube" radius

Two Toruses (wheels) with an axle: animate on D to spin the wheels

Four Toruses (wheels) with a axles: animate on D to spin the wheels

Stereographic_Projection_z_and_theta_input  Animate on S and O to move the source point

Stereographic_Projection_to Z and 1/Z_z and_theta_input  Animate on S and O to move the source point

Projection of a Circle on Unit Sphere to a Circle in C  Animate on O to rotate the source point

Projection of a Circle in C onto a Circle on Unit Sphere  Animate on O to rotate the source point

Projection of a Polar Circle on Unit Sphere to a Line in C  Animate on O to rotate the source point

Projection of a Line (Cartesian Input) in C to a Polar Circle on Unit Sphere  Animate on P to move the source point

Projection of a Line (Polar Input) in C to a Polar Circle on Unit Sphere Animate on P to move the source point

Construction of the Centroid of a Triangle as the Intersection of the Medians: Vertices at (0,0), (a,b), (c,0). Animate on a, b and c

Construction of the In Center of a Triangle as the Intersection of the Angle Bisectors: Sides of length a, b and c. Animate on a, b and c

Construction of the Circum Center of a Triangle as the Intersection of the Perpendicular Bisectors of the Sides: Vertices at (0,0), (a,b), (c,0). Animate on a, b and c

Construction of the Ortho Center of a Triangle as the Intersection of the Altitudes: Vertices at (0,0), (a,b), (c,0). Animate on a, b and c

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