Enter a computation above or click on an example below.

Statistics

• Calculate basic statistics of a data set: statistics {25, 35, 10, 17, 29, 14, 21, 31}
  (includes mean, median, standard deviation... click on "more" for more)
• Calculate a curve of best fit (sequence): cubic fit {20.9, 23.2, 26.2, 26.4, 16.3, -12.2, -60.6, -128.9}
• Calculate a curve of best fit (data points): quadratic fit { (1.3, 2.2), (2.1, 5.8), (3.7, 10.2), (4.2, 11.8) }
• Other available curve fits include: linear, quadratic, cubic, quartic, quintic, sextic, exponential, logarithmic, periodic

Logic

• Truth tables: truth table P && (Q || R) implies S
• Multiple truth tables, side-by-side: P implies Q, (~Q) implies (~P)
  (can be used to check for logical equivalency)
  
• Lots of information: A and B or not C
  (Truth tables, Venn diagrams, Logic circuits, Minimal forms - when possible)

Sequences and Series

• Determine sequence formula: 1, 4, 9, 16, ... 
• Calculate value of a finite series: 3 + 6 + 9 + ... + 99
• Calculate value of an infinite series: 1/2 + 1/4 + 1/8 + ... , 1 + 1/3 + 1/5 + ... , 1/2 + 1/3 + 1/5 + ...
  (also performs multiple series tests for convergence and divergence)
  
• Calculate value of a finite product: 2 * 5 * 8 * ... * 17
• Solve recurrence relation: f(n+1) = n^2 + f(n)
• Solve recurrence relation with initial conditions: f(n) = -f(n - 2), f(1) = 1, f(2) = 2

Calculus

• Limits: lim (sin x)/x as x->0
• Summation Notation: sum j^2, j=1 to 100
  
• Derivatives: (x^3)'
• Complicated Derivatives, alternate notation: d/dx 4*x*sin(x^2) + e^(tan(x))
  Also Try: click on "Show Steps" in the upper-right corner of the W|A window.
• Antiderivatives/Indefinite Integrals: integrate x^3
• Definite Integrals: integrate x^3 from 1 to 2
  
• Improper Integrals: integrate (sin x)/x dx, x=0..infinity
  
• Taylor Series: taylor series sin x
• Vector Derivatives: d/dt (3t^3, sin(sqrt(t)), t^337)
  
• Gradient: grad sin(x^2 y)z
• Divergence of a vector field: div (x^3-y^2, 2xy, z)
• Curl of a vector field: curl (x^3-y^2, 2xy, z)
• Fourier Series (function x^3, degree 4 approx.): FourierSeries[x^3, x, 4]

Differential Equations

• Differential equation: y' = x^2y 
• Alternate notation: dx/dt = 2x
• Differential equation with initial condition: y' = x^2y , y(1) = 2
  
• Second-order equation:  y''(t) + y(t) = sin t
• System of differential equations: x'(t) = x + y, y'(t) = 2x - 3y
• Vector field/integral curves: (x+2y, 3y -2x)
• Laplace transforms: Laplace transform 2*sin(7t)
  

Linear Algebra

• Solve system of linear equations: solve 2x + 3y = 4, 3x + 4y = 5, 3x + 5y + z = 6
• Example, no solution: solve 2x + 3y = 4, 2x + 3y = 5
  
• Example, many solutions: solve 2x + 3y = 4, x + y + z = 1, 2x + 2y + 2z = 2
• 2D vector properties: vector {3, 4}
  (graph, length, unit vector, polar coordinates)
• 3D vector properties: vector {3, 3, 7}
  (graph, length, unit vector, spherical coordinates)
• Dot product: {3, 3, 7} dot {1, 2, 3}
• Cross product: {3, 3, 7} cross {1, 2, 3}
• Matrix arithmetic: {{2,-3},{4,5}} . {{1,2},{3,4}} + {{2,-1},{-1,2}}
• Solving matrix equations: solve {{1,2},{-2,3}}.{x,y} = {5,7}
• Matrix arithmetic with parameters: inverse {{a, b}, {c, d}}
• Properties of a square matrix: {{2,3,3},{4,5,4},{1,1,1}}
  (dimensions, determinant, trace, characteristic polynomial, inverse, eigenvalues, eigenvectors)
• Matrices of Geometric Transformations: rotate 30 degrees , rotate 30 degrees with center (4,3) , reflect across y=x+1

Abstract Algebra

• Addition and Multiplication Tables: Z/7Z
  Note: using large groups, such as Z/15Z, with result in a graphical display
  
• Quaternion Group Operation Table: quaternion group

For lots more examples of mathematical computations:  http://www.wolframalpha.com/examples/Math.html
Also, don't forget that Wolfram|Alpha does more than just math... for example: Adelphi University