Differential calculus

[Derivates] [Integration] [Differential equations] [Maximization and minimization]

Visual Calculus: Tutorial in basic calculus, using some java applets.
(University of Tennessee).

Derivates

Derivative: Computes the derivate of any order of an expression.
(Mathserv. CGI)
Computing the derivate implicitly: Takes an implicit equation of x and y, and solves it with respect to y, and then derivates to get dy/dx.
(Mathserv. CGI)
The little deriver: Computes the derivate of an expression with regard to any variable.
Derivative definition: Shows a function and its derivate in a point.
(Copyright California State University. Source code avaliable.)
Derivate: Computes the derivate of any order of a function.
(CAIN (Computer Algebra for Newcomers). CGI-script.)

Integration

[Numerical] [Graphical]

Integral: Solves a definite or indefinite integral.
(CAIN (Computer Algebra for Newcomers), CGI-script.)
The INTEGRATOR: Computes indefinite integrals.
(Wolfram Researc, Inc. CGI-script)
Define Integral of a Function: Computes the value of a definite integral.
(MathServ. CGI-script)
Numerical Integration: Integrating Experimental Data.
(The Geometry Center Calculus Development Team.CGI-script.)
Integration Assistan: Guides you through the process of integration of any expression.
(MathServ.CGI-Script)
Antidifferentiation: Computes the antiderivate of a function.
(MathServ. CGI-script.)

Numerical integration

Numerical integration rules: Demonstrates various rules for integrating a function numerically.
Rieman Sums: Computes the Riemann sum of any function given endpoints and partition.
(MathServ. CGI)
Numerical Integration: Computes the integral over an interval with a given partition.
(MathServ. CGI-script)
Newton cotes Rules: Computes any integral numerically using one of four avaliable methods.
(Copyright Jun Ni. Java Script.)
Gauss Rules: Computes integrals on Hermite or Chebyshev's form.
(Copyright Jun Ni. Java Script)
Simpson's Numerical Integration: Computes numerical integration using Simpson's rule.
(Java script.)
Numerical Integration: Integrates a polynomial using either trapezodial method, Simpson's rule or Romberg.
(Source code avaliable.)

Graphical integration

Volume of a solid of revolution: Visualises how to compute the volume of a solid of revolution.
(International Education Software)
Integrals: Computes the integral under any function. Border can be set both graphically and by numbers.
Numerical Integration Simulation: Shows the graphical interpretation of some numerical methods for integration. Performs on 12 functions.
(Introduction to Scientific Programming.)
Integration definition: Computes the Riemann sum for an integral and shows the graphical interpretation.
(Copyright California State University. Source code avaliable.)

Differential equations

Direction Field of a First Order ODE

Draws a tangent field for an ordinary differential equation on the form dy/dx=f(x,y).
(MathServ. CGI)

Runge-Kutta

Draws a graph over one of the following equations:

y = f(x)
dy/dx = f(x, y)
d²y/dx² = f(x, y, dy/dx)

given initial conditions and ranges, using the Runge-Kutta method.
(Source code avaliable)

Differential equation phase plotter

Draws a vector map and/or tangent lines for a diffential equation where you specify y' and x'.

Find a Particular Solution Using Variation of Parameters

Computes a particular solution to an ODE given two linearly independent solutions to the homogenous equation.
(MathServ. CGI-script)

Solving a Linear Ordinary Differential Equation

Solves linear ODE's written on the form: dy/dx + f(x) y = g(x).
(MathServ. CGI)

Solving an Exact Ordinary Differential Equation

Solves exact ODE's written on the form: f(x,y) dx + g(x,y) dy = 0
(MathServ. CGI)

Solving an Homogeneous Ordinary Differential Equation

Solves homogenous ODE's written on the form: dy/dx = F(y/x).
(MathServ. CGI)

Second-Order DE

Solves second order initial value problems giving a numerical output.

Solving a Bernoulli ODE

Solves a Bernoulli equation on the form : dy/dx = P(x) y + Q(x) y ^r.
(MathServ. CGI)

Solving a Special form

Solves a special kind of DE's that is on the form dy/dx = H(u), where H(u) = (ax + by+ c)/(dx + ey + f).
(MathServ. CGI)

Reduction of order

Finds a second solution to a second order homogenous ODE when one solution is given.
(MathServ. CGI)

Solving an ODE in Standard Form

Solves an ODE on the form : dy/dx = f(x, y).
(MathServ. CGI-Script)

Solution of a Second Order Cauchy-Euler ODE

Given the coefficients of the Cauchy-Euler equation, the general solution is calculated.
(MathServ. CGI-script)

Solving a Separable Ordinary Differential Equation

Solves an equation on the form : f(x) dx + g(y) dy = 0.
(MathServ. GGI-Script.)

Lake pollution solutions

Various solutions to the equation : C'(t) V = Q C_in(t) - Q C(t) - k C(t) V ,
which governs the concentration of contamination in a sea.

Direction Field Java Applet

Draws a direction field and its tangent lines based on an differential equation.

Euler

Calculates the Euler coefficients of the differential equation y' = x + y with initial conditions, and compares them to the correct values.

Second-Order DE

Graphs the solution to a second order DE on the form : y'' = f(t, y, y'), and given initial values.

First-Order DE

Calculates the coefficients for a first order DE on the form : dy/dx = f(x,y).

First-Order DE

Draws the solution to a first order DE on the form : dy/dx = f(x,y).

Phaseplot

Makes a phaseplot of an initial-value problem on the form : y'' = f(t, y, y').

Heat

Draws the solution to the heat equation given initial conditions.

Timesect

Plots discrete points from the phase plot to an equation on the form : y'' = f(t, y, y').

Boundary problem

Plots the solution of the equation : y'' = f(x, y, y') with y(x₀) = y₀ and y(x₁) = y₁.

Direction field

Draws the direction field for a differential equation on the form : y' = f(x, y), and draws a solution graph upon clicking in the field.

Euler coefficents

Diplays the Euler coefficients for a equation on the form : y' = f(x, y), as well as the coefficients for the exact solution.

Maximization and minimization

Simplex Java Applet: Maximizes or minimizes a function under a number of constraints, and shows the process.
(Optimization Tehcnology center)
Genetic algorithm demo: Maximizes a given function by the genetic algorithm method.
Minimization: Minimizes a linear function under any number of linear constraints.
(CGI-script)
Optimization: Optimizes graphically a linear function under three constraints.
( Chris Jones School of Business Administration University of Washington)

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