Examples by Topic

Calculus & Analysis

Mathematics
Calculus & Analysis

Integrals »

compute an indefinite integral

integrate x^2 sin^3 x dx

compute a definite integral

integrate sin x dx from x=0 to pi

compute an improper integral

Derivatives »

calculate the derivative of a function

derivative of x^4 sin x

compute higher derivatives

second derivative of sin(2x)

compute partial derivatives

Limits »

compute a limit

limit (1+1/n)^n as n->infinity

compute a one-sided limit

Sequences »

analyze a sequence

sequence of Fibonacci numbers

compute a possible formula and continuation for a sequence

1, 4, 9, 16, 25, ...

solve a recurrence

Sums »

compute an indexed sum

sum j^2, j=1 to 100

compute an infinite sum

Products »

compute an indexed product

product (k+2)/k, k=1..25

compute an infinite product

Series Expansions »

find a Taylor series expansion

taylor series sin x

specify the center point and the order of the expansion

Coordinate Geometry »

compute the area bounded by two curves

compute the area between y=|x| and y=x^2-6

locate inflection points of a function

Differential Equations »

solve a linear ordinary differential equation

y'' + y = 0

specify initial values

y'' + y = 0, y(0)=2, y'(0)=1

solve a nonlinear equation

Complex Analysis »

compute properties of a function of a complex variable (use the variable z)

e^z

compute the residue of a function at a point

Vector Analysis »

compute the gradient of a function

calculate alternate forms of a vector analysis expression

Integral Transforms »

compute a Fourier transform

Fourier transform exp(-x^2)

compute a Laplace transform

Domain & Range »

compute the domain of a function

domain of f(x) = x/(x^2-1)

compute the range of a function

Continuity »

determine whether a function is continuous

is sin(x-1.1)/(x-1.1)+heaviside(x) continuous

locate discontinuities of a function

Numerical Analysis »

find roots of an equation using Newton's method

using Newton's method solve x cos x = 0

numerically integrate functions that cannot be integrated symbolically