| # | Purpose of routine | Input | Output | Example |
|---|---|---|---|---|
| [1] | Graph of function of one variable | showing the origin in center is optional JavaScript syntax is used to enter the function press the plot button |
Graph of function showing maximum and minimum values of f(x) |
x*Math.cos(x) on [-20,20] |
| [2] | First Derivative and Tangent Line | same as [1] various values of x are entered by a slider* |
Graph of function Graph of 1st derivative numerical value of derivative tangent line |
x*Math.cos(x) on [-20,20] |
| [3] | Second Derivative with Osculating Circle |
same as [1] |
Graph of function Graph of 2nd derivative Graph of curvature Osculating circle |
x*Math.cos(x) on [-20,20] |
| [4] | Parametric Equations |
x(t) and y(t) are entered in JavaScript syntax t interval [low, high] slider* to show current t value |
Graph of x(t) Graph of y(t) Graph of [x(t), y(t)] current location |
x(t)=Math.cos(3*t) y(t)=Math.sin(2*t) t: [0, 6.283] |
| [5] | 3-D Space Curves | x(t), y(t), and z(t) and t interval sliders* to animate, rotate, and show view up or down |
graph of parametric curve is shown in 3-D and the view can be changed by sliders |
x(t)=(4+Math.sin(20*t))*Math.cos(t) y(t)=(4+Math.sin(20*t))*Math.sin(t) z(t)=Math.cos(20*t) t: [0, 6.283] |
| [6] | Solids of Revolution | f(x) the outer function g(x) an inner function x interval both are rotated about the x-axis |
the graph in 3-D showing hidden lines as dashed the volume of the revolution |
f(x)=Math.sqrt(x) g(x)=0.2+0.1*(x-3)*(x-3) x: [1, 5] |
| [7] | First Order Differential Equations | y'=f(t, y), initial value t0, no. of pts. | solution including the graph |
y' = 0.2+0.1*(x-3)*(x-3), t0=0 |
| [8] | Prey and Predator Differential Eq. | x'=f(t, x, y), y'=g(t, x, y), initial value t0, initial values of x and y, and no. of pts. |
graph of x(t) and y(t) vs. t graph of x(t) vs. y(t) |
x' = 0.08*x-0.001*x*y y' = -0.02*y+0.00002*x*y x0 = 1000, y0 = 40, and t0 = 0 |
| [9] | Graph of f(x, y) in 3-D Hidden line removal |
function f(x, y), eye position, no. of intervals, x and y domain, transparency level, frames per second, scale |
graph with hidden line removal the graph will rotate back and forth this are stop/resume buttons |
f(x, y) = x*y*Math.exp(-x*x-y*y) eye position (3, 2, 2) x, y each on [-3, 3], scale 2 transparency 0.8, 4 fps |
| [10] | Same as [9] with a tangent plane | same as [9] with a tangent plane at (x, y) |
same as [9] |
same as [9] with tangent plane at (0.71, 0.71) |
| [11] | Same as [9] with polar coordinates | same as [10] with polar coordinates |
same as [9] |
same as [9] |
| [12] | Parametric Surfaces - (examples) | x(u, v), y(u, v), z(u, v) with bounded u, v arbitrary eye position, transparency, no. of intervals |
3-D graph with hidden line removal |
x=4*Math.cos(u)+2*Math.cos(u)*Math.cos(v) y=4*Math.sin(u)+2*Math.sin(u)*Math.cos(v) z=2*Math.sin(v) u, v on [-3.14, 3.14], n = 20. trans. = 0.9 |
| [13] | Parametric
Surface - (examples) with a slider |
same as [12] with eye position determined by theta (angle from x-axis) and phi (angle from z-axis) entered with a slider* |
same as [12] with animation |
same as [12] |
| [14] | String Animation with any initial position |
initial position, speed, no. of subdivisions |
vibrating string with fixed endpts. |
f(x)=x*x*(2-x) on [0, 2] |