Convergence of series

Application of the ratio, root or integral test on a series.

Calculation of the Taylor series

Calculates and draw the graph of the first n elements of the Taylor series for an entered function.

Calculation of the Fourier series

Calculates and draw the graph of the first n elements of the Fourier series for an entered function.

Direction field

Draws the direction field for a differential equation $y'=f(x,y)$.

Direction field for a system of equations

Draws the direction field for a system of two differential equations

$y_1'=f(y_1,y_2)$

$y_2'=g(y_1,y_2)$

Solution in the direction field

Draws the direction field and several different solutions for a differential equation $y'=f(x,y)$.

Separation of variables

General solution of a differential equation which can be written in the form $y'=f(x)g(y)$.

Linear differential equation of the first order

General solution of a differential equation which can be written in the form $y'+py=q$.

Homogeneous linear ODEs with constant coefficients

Calculation of the basis of the space of solutions of a homogeneous linear ODE with constant coefficients.

Finite difference method for the Poisson equation

Boundary value problem.

$-\frac{\partial^2 u}{\partial x^2}-\frac{\partial^2 u}{\partial y^2}=f(x,y)$ inside the square $\Omega = [0,1]x[0,1]$,

$u=0$ on the boundary $\partial \Omega = \Gamma$,

is being solved by the finite difference method.

$n$ inner nodes on the side of the square generates a system of $n^2$ linear equations.