Examples
Built-in Functions and Constants for Demo Software
| Notation |
Meaning |
| pi |
π=3.14159265 |
| e |
2.71828183 |
| + - * / |
Standard arithmetic functions -
Warning: Always put a * in between two values you want mulitplied. Always remember your order of operations and use parentheses as necessary. |
| x^n |
xn |
| ln(x) |
Natural log (log base e) of (x) |
| a^x |
ax |
| sin(x) |
Sine of x |
| cos(x) |
Cosine of x |
| tan(x) |
Tangent of x |
| asin(x) |
Arcsine or inverse sine of x |
| acos(x) |
Arccosine or inverse cosine of x
|
| atan(x) |
Arctangent or inverse tangent of
x |
| sinh(x) |
Hyperbolic sine of x |
| cosh(x) |
Hyperbolic cosine of x |
| tanh(x) |
Hyperbolic tangent of x |
| sqrt(x) |
√x |
| abs(x) |
|x| |
| f'(x) |
The first derivative of f(x) |
| f''(x) |
The second derivative of f(x) |
| f_x(x,y) |
The first partial derivative of
f with respect to x |
| f_x_y(x,y) |
The partial derivative with
respect to y of the partial derivative of f with respect to x. Can be
used for further partial derivatives. |
| length(x,y) |
The distance of the point (x,y)
from the origin. Also works in higher dimensions |
| dot(x,y) |
The dot product of x and y. |
| cross(x,y) |
The cross product of x and y. |
| unit(x,y) |
Returns a unit vector in the
direction of the vector (x,y) |
| arg(x,y) |
The angle from the positive
x-axis to the vector (x,y) |
| x_a |
The ath coordinate of
the vector x |
| integral(integrand, variable,
lower, upper, [resolution]) |
The integral of
integrand with respect to variable from lower to upper - e.g. for ∫01x2dx,
type integral(x^2, x, 0, 1) The resolution is optional input that can be used to increase the accuracy of the integral approximation. |
| t_max |
The maximum value of the
interval or variable t |
| t_min |
The minimum value of the
interval or variable t |
| t_res |
The number of steps of the
interval or variable t |
| scale(t) |
Converts the value of t to a
point in the 0-1 range |
| ipart(x) |
The integer part of x |
| fpart(x) |
The fractional par of x |
| max(a,b,....,h) |
The maximum of the set |
| min(a,b,....,h) |
The minimum of the set |
| random |
A random number between 0 and 1
(Note that this takes no argument) |
| and, or, <, >, =, true,
false |
Logical operators that return 1
if true and 0 if false. |
