![]() ![]() To watch my daughter, who just two years ago was so frustrated by algebra, accepting the highest honors in her entire school for her Outstanding Academic Achievement in Mathematics, was no doubt one of the proudest moments of my life. Easy to enter in problems, I get explanations for every step, every step is complete, etc. I must say that I am extremely impressed with how user friendly this one is over the Personal Tutor. Thank you for creating sure a wonderful program! Chuck Jones, LA Algebrator not only allowed me to teach my children algebra, but it also refreshed my knowledge as well. Once they were older, I quickly realized that I was not able to create efficient math lesson plans before I did not have the knowledge to do so. I decided to home school my children at a young age. Subtracting Rational Expressions with the Same DenominatorĪxis of Symmetry and Vertex of a Parabola Simplifying Products and Quotients Involving Square RootsĪdding Rational Expressions with the Same DenominatorĪdding, Subtracting and Multiplying Polynomials Simplifying Square Roots That Contain Variables Quadratic Equations with Imaginary SolutionsĪdding and Subtracting Rational Expressions With Different Denominators Solving Quadratic Equations by Completing the SquareĪdding and Subtracting Rational Expressions with Unlike Denominators Simplifying Square Roots That Contain Whole Numbers Systems of Equations That Have No Solution or Infinitely Many Solutionsĭividing Polynomials by Monomials and Binomials Solving Linear Systems of Equations by Elimination If you have any questions or ideas for improvements to the Derivative Calculator, don't hesitate to write me an e-mail.Solving Quadratic Equations by Using the Quadratic Formula The gesture control is implemented using Hammer.js. poles) are detected and treated specially. For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5). Otherwise, a probabilistic algorithm is applied that evaluates and compares both functions at randomly chosen places. If it can be shown that the difference simplifies to zero, the task is solved. For example, this involves writing trigonometric/hyperbolic functions in their exponential forms. ![]() Their difference is computed and simplified as far as possible using Maxima. The "Check answer" feature has to solve the difficult task of determining whether two mathematical expressions are equivalent. For each calculated derivative, the LaTeX representations of the resulting mathematical expressions are tagged in the HTML code so that highlighting is possible. This, and general simplifications, is done by Maxima. For example, constant factors are pulled out of differentiation operations and sums are split up (sum rule). In each calculation step, one differentiation operation is carried out or rewritten. There is also a table of derivative functions for the trigonometric functions and the square root, logarithm and exponential function. The rules of differentiation (product rule, quotient rule, chain rule, …) have been implemented in JavaScript code. Instead, the derivatives have to be calculated manually step by step. Maxima's output is transformed to LaTeX again and is then presented to the user.ĭisplaying the steps of calculation is a bit more involved, because the Derivative Calculator can't completely depend on Maxima for this task. Like any computer algebra system, it applies a number of rules to simplify the function and calculate the derivatives according to the commonly known differentiation rules. Maxima takes care of actually computing the derivative of the mathematical function. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima. When the "Go!" button is clicked, the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server, where it is analyzed again. ![]() MathJax takes care of displaying it in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. ![]() The Derivative Calculator has to detect these cases and insert the multiplication sign. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". In doing this, the Derivative Calculator has to respect the order of operations. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). For those with a technical background, the following section explains how the Derivative Calculator works.įirst, a parser analyzes the mathematical function. ![]()
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