## What is Ostad Mathematical Software? Briefly, we can say that Ostad is an intelligent software that can analyze user mathematical questions and gives step by step solution to them. The way that Ostad describes solutions, is in mathematical form and notations. In other words, Ostad software is an intelligent mathematical tool for education that can help students to find the answer to their math questions.

### Abilities and Features

Ostad Mathematical software has very powerful tools for answering questions of students of high school and college degree. Some of capabilities of Ostad mathematical software are as follow:

• Solving equalities and inequalities in the form of trigonometric, logarithmic, exponential, polynomial, radical, inverse trigonometric, absolute value, floor and other forms with many excellences in each form in comparison to other symbolic tools available in market. For example, in solving trigonometric equations, Ostad can find solution of equations in the general k form and even can say conditions of each variable for being a valid solution.
• Calculating domain of functions. Ostad can find domain of functions and demonstrate the way of calculation step by step.
• Calculating period of a periodic trigonometric function. By a couple of heuristic and analytic approaches, Ostad can explain about period of a trigonometric function and also can determine the principal period of function.
• Finding inverse of an invertible function.
• Numerical and analytical drawing of functions. With this feature one can find domain of functions, axes intersections, horizontal, vertical and slant asymptotes, inclination point, maximum and minimum points or ranges and finally Ostad can show all information about falling and rising ranges of function in a relative table.
• Calculating limit of functions, derivative and integral of functions step by step.
• User can simplify a formula by using simplify tool. This tool implements simplification rules to pack the formula and shrink it.
• User friendly and easy to use.

## The comparison between Ostad and Maple As everyone knows, Maple software has a very powerful and rapid base (Kernel) which makes it the most powerful and flexible mathematical software for algebraic and symbolic calculations in different engineering branches. but it has many problems in educational purpose. some of these problems are as follow :

### Attractive interface

Ostad Interface is developed for students to be attractive for these students and easy to use and understand. But in Maple and other common mathematical softwares you should learn syntax, commands, functions and etc., to enter your request in a command line. Although command line feature gives flexibility to engineers and advanced users, but can be confusing for intermediate students. So in design of Ostad, we have used special effects, colors, and dialogs for a particular action to make the software enjoyable and easier to use.

### Solving Equalities and inequalities

With this powerful feature, users can solve polynomial equations in the general form up to degree 4. Also this tool can give the solution of trigonometric equations in general k form, for example k(Pi) for equation sin(x)=0. Also the solution to absolute value and floor equations are given in the range form. For more examples see another page of persian site. it is worthy to mention that all parts of this application explain the solution step by step. Ostad software solves equations and not only gives the solution to inequalities of a specified inequality, but also gives table of changes of the given function. Ostad benefits from a human-like Solver. Therefore solutions of Ostad are the same as human solution and can be useful for education. Common mathematical tools solve trigonometric equations numerically but Ostad solves it like a human and gives the solution in algebraic notation.

As one can infer, Maple only finds the solution when k = 0 but Ostad finds general form of solution. Not only Ostad can give general form of solutions, but also it can explain condition of a particular variable for being the solution of equation. For example equation(a)(sin(x)+cos(x)) = 0, has two solutions, one for second parenthesis, one for the first parenthesis. So one solution is a = 0 and it is independent of variable x.

In inequality section, Ostad draws table of changes of inequality to explain clearly about range of changes in the given function.

### Calculating Domain

Domain calculation is one of the important parts of mathematics which is not considered well in common mathematical softwares such as Matlab, Mupad and Maple. Ostad can calculate domain of functions with step by step explanation of the solution.

### Numerical drawing

Ostad has an eligible and robust drawing engine because it profits from an algebraic function analyzer. To explain its difference, suppose y = 1/(sin(x)) as input function in Maple. As one can perceive, vertical asymptotes, originated from mistakes in implementation of plot function, are shown and the plot of function seems to be continuous and there is no difference between actual values of function and vertical asymptotes. On the other hand, Ostad depicts function values exactly and does not show vertical asymptotes.

With Algebraic Function Analyzer (AFA), Ostad draws floor functions discontinuous and takes advantage of a heuristic numerical algorithm in finding points of discontinuity.

### Analytical drawing

In analytical drawing section, requested functions are drawn with full analysis. With this feature one can find domain of functions, axes intersections, horizontal, vertical and slant asymptotes, inclination points, maximum and minimum points or ranges and finally all information about falling and rising ranges of function drawn in a relative table. Analytical drawing does not exist in any other software except Wolfram Alpha which is a computational engine.

## Services Overview

Chief goals of G.A. comapny could be mentioned as follow :