Calculus Applets 

The calculus applets are all based on the Web Components for Mathematics library and developed with the Java programming language. A typical applet, for graphing a function, appears below.
Try the following:
Function Syntax: The syntax for the definition of a function is very similar to that found on common graphing calculators. Binary operators such as + (addition),  (subtraction), * (multiplication), / (division), and ^ (exponentiation) follow the standard rules for precedence. Operators at equal levels are performed left to right, and grouping parentheses are also supported. The following are the symbols and operations allowed in a function definition.
+, , *, /  The standard arithmetic binary operators.
Multiplication is implied if the * is left out (e.g., 2*x and 2x are
equivalent, but note that 2*3 is not the same as 23). Example:
2x1 The – sign can also be used as negation, as in – ( x + 2 ). Use parentheses when an exponent has a  sign, as in e^(1). 
( )  Parentheses are used for grouping and also to delimit the arguments to a function. Examples: (x2)/3 and sin(x) 
x  The independent variable used in all function definitions (some applets support other variables, as noted on those pages) 
^  Exponentiation binary operator. If the exponent is not an integer, the program checks whether it is a rational number. If the reduced denominator is even, or if the program cannot determine that the exponent is rational, then only the nonnegative part of the domain is graphed. If it is rational and the reduced denominator is odd, then the negative part of the domain is also graphed. For example, x^(1/3) will graph a domain of all reals, while x^(pi) will only use nonnegative reals. 
!  Factorial, as in x ! 
e, pi  Builtin constants. 
Builtin Functions: The following builtin functions are provided:
abs(x)  Absolute value 
arccos(x)  Inverse cosine (radians) 
arcsin(x)  Inverse sine (radians) 
arctan(x)  Inverse tangent (radians) 
ceiling(x)  The smallest (closest to negative infinity) real value that is greater than or equal to x and is equal to a mathematical integer. 
cos(x)  Cosine (radians) 
cosh(x)  Hyperbolic cosine 
cot(x)  Cotangent (radians) 
csc(x)  Cosecant (radians) 
cubert(x)  Cube root 
exp(x)  Exponential function (i.e., e^x) 
floor(x)  The largest (closest to positive infinity) real value that is less than or equal to x and is equal to a mathematical integer. 
ln(x)  Natural logarithm (base e) 
log2(x)  Base 2 logarithm 
log10(x)  Common logarithm (base 10) 
round(x)  The closest integer to x 
sec(x)  Secant (radians) 
sin(x)  Sine (radians) 
sinh(x)  Hyperbolic sine 
sqrt(x)  Square root 
tan(x)  Tangent (radians) 
tanh(x)  Hyperbolic tangent 
trunc(x)  Drop any digits after the decimal point 
Piecewise Functions: In addition, a special syntax is provided for conditional expressions, which enables you to graph piecewise functions. A conditional expression is an expression using the ? operator. An example is ((x > 0)? x : x) which says: “if x is greater than 0, then the value is x, otherwise it is – x.” The part before the ? is the condition and compares two quantities using one of the comparison operators =, >, <, >=, <=, or <> (not equal). You can also write more complex expressions using & (the AND binary operator),  (the OR binary operator), and ~ (the NOT unary operator). The part between the ? and the : is the value if the condition is true and can be any valid expression (even another conditional expression). The part after the : is the value if the condition is false. Note that the parentheses surrounding the conditional expression are not required, but are recommended if the conditional expression is part of a larger expression. The false part (after the :) is optional. If it is not present, then when the condition is false the expression evaluates to “not a number,” which will cause nothing to be graphed for that domain value.
Background: These applets are built using the Web Components for Mathematics(WCM) library and the Java programming language. More information on WCM can be found at http://webcompmath.sourceforge.net/
This work by Thomas S. Downey is licensed under a Creative Commons Attribution 3.0 License.
Prev  Home  Next 