Differential calculus

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

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

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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.)

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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.)

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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: 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 Cin(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.

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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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