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The Xmath Calculator

# Xmath Step-by-Step Calculator

The Xmath calculator uses Mathematica packages loaded into webMathematica. The page design and menus are contained in XML files. Expressions are broken down into different levels using the Mathematica object TreeForm. All levels are identified in the output by Level n. On each level different mathematical rules (e.g., the substitution rule) may apply and the rule is identified by the package. Users can determine the number of levels in the input. Level 1 indicates the first hint for eventual further calculation by hand.

This is quite similar to what a professor would do on the blackboard; all rules and intermediate calculations are given. This is quite convenient for ODL applications where a professor is not nearby for face-to-face discussion. This has been tested in distance learning in mathematics for school teachers in Norway; a report may be ordered from anne.norstein@hisf.no.

The Xmath calculator contains a variety of mathematical topics, but not all of them give intermediate results. Some topics are still being developed. The algebra topic includes collecting terms, simplifying expressions, expanding expressions, polynomial factorization, partial fractions, step-by-step partial fractions, equation solving, step-by-step equation solving, solved problems, applications, assessments (mathematical comparison of given and answered expressions), case studies, and student projects.

The function topics include plotting, exact solving, numeric solve limits, step-by-step limits, differentiation, step-by-step differentiation, difference quotients, Newton's method, Taylor series, integration, step-by-step integration, definite integrals, Riemann sums, trapezoidal rule, Simpson's rule, solved problems, applications, assessments, case studies, and student projects.

Other topics will be plane curves, functions with several variables, and differential equations. Many of these will have step-by-step facilities.

## Examples from the Calculator

The calculator can integrate, differentiate, solve equations, and so on for a wide range of expressions. Different levels are shown by scrolling and focusing only on the first level will give the user the first hint in a hand calculation. The program has discovered expressions the calculator can solve for integration but Mathematica cannot (certain substitutions).

Figure 2. webMathematica output for integration.

Here is another example focusing on the first level.

Figure 3. Integration with the first hint for further calculation by hand.

The third example from Xmath uses partial fractions.

Figure 4. webMathematica output for partial fractions.