§ 4: Algebraic Calculations and Re-Calculations on the WWW

• Basic Calculations and Re-calculations
• More Complex Re-calculations
• Solving Polynomial Equation With Associated Graph!
• Simplifying the Difference Quotient from Calculus

Basic Calculations and Re-calculations As the author, you may set up for your readers the ability to conduct algebraic and numerical experiments with expressions. Although the readers do not have control over the setup of the calculation, they may change the input parameters to see how the steps and the outputs are changed by different inputs. Go ahead and experiment with this interactive that expands a simple trinomial to a power. You may change the trinomial (to anything), and the power of the expression.

More Complex Re-calculations As the author, you may set up for your readers the ability to conduct complex algebraic and numerical recalculations. This is a bit tricky to author, but with practice you can make rather interesting recalculation interactives, choosing which steps you readers will see. Go ahead and experiment with this interactive that solves a polynomial equation. You may change polynomial to any polynomial in x (not too big so that it stays on the screen!). All solutions will be numerical, of course.

Solving Polynomial Equation With Associated Graph! In this interactive, the user may change the polynomial equation to be solved, and the associated graph of the polynomial function whose roots are the solutions of this equation is shown in a graph. The graph changes depending on the user input equation. (The equation with the symbol shows which equation is the input equation.) Go ahead and experiment with this interactive that solves a polynomial equation. You may change polynomial to any polynomial in x (not too big so that it stays on the screen!). All solutions will be numerical, of course.

Simplifying the Difference Quotient from Calculus One age-old calculation from calculus is the simplification of the difference quotient which leads to the calculation of the derivative. While MathView can certainly calculate the algebraic derivative of any (algebraic) function using the built-in differential operator, and also calculate the numerical derivative of any function (and graph it), this interactive below emulates a whole host of examples of "hand calculations" that have haunted even the best calculus students! The following interactive calculates and simplifies the difference quotient for polynomials. It will not work on all functions. The symbol is a wildcard variable, and must be used in the definition of the function F(x). To obtain it, the keystrokes are: = ? x

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Official Website of www.calculus.net  • Webcast on a DEC Alpha on a T-1 line from •   • Webster, Massachusetts, USA •   • Web Construction and Management by WebPrimitives •  Core Development Team Robert R. Curtis Phil R. Smith Christopher A. Barker Diane Welden Housken Tim Lance Bob Stein Donald Hartig Lee Wayand Charlene Beckmann Bill Davis Paul Latiolais Dennis Sentilles Carmen Artino Michael Colvin

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