Essay: Software Program For Complex Problem Solving With Quadratic Equations.

The application of quadratic equations is boundless; examples that spring to mind are parabolic paths of projectile motion, velocity in a gravitational field, optimization of profit/loss, and the golden ratio being just a few.In this task you are required to design a user interface for the solution of quadratic equations. The quadratic solutions should be clearly shown as well as proof that they do solve the quadratic equation. Feedback should be given to the user if invalid data is entered. 
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Analysis
The following analyses should be completed at the commencement of this project:
User Analysis – who will be using the system
Display Content Analysis – what needs to be displayed
Work Environment Analysis – what is the platform/environment/architecture
Interface Design Steps – what are the interface objects and actions refer to Pressman’s chapters on Interface Design as well as Hix and Hartson.After these analyses have been completed, you should decide on the software tools which you will use. Justify these in your report.

For example, for the graphics you might choose from: Microsoft Word (using the SmartArt, Shapes, Pictures features), Microsoft Paint, Microsoft Powerpoint, GIMP (www.gimp.org), Adobe Acrobat, Enterprise Architect (EA), Inkscape (www.inkscape.org), Photoshop, Paint.net or possibly from Web Tools such as Dreamweaver. Justify your choices in your report. You will need to model the application; you may choose any model discussed in lectures such as
DFD, FSM, SASD, ERD, CSPEC and justify your choice of model or combination of models.Demonstrate the usefulness of your modelling.You will need to provide a State Chart Diagram (State Transition Diagram) of your application as
well.

As there is no programming required in this assignment, you are encouraged - but not obliged to use Wolfram|Alpha (https://www.wolframalpha.com/) to solve your quadratic equations. Wolfram|Alpha is a free-form input computational knowledge engine using natural language. For example you could type “2 + 3” or “what is 2 + 3” or “what is the sum of 2 + 3”.Your GUI should appear to be solving the equations and you may use any relevant output generated from Wolfram|Alpha in your GUI. 

User analysis

  The quadratic equation  is not only a part education  in the high schools or colleges rather it is used  in solving different complex problems in the scientific fields such as measuring the gravity, determining the speed of an object or a  rocket along a projectile.  The proposed application in this assignment we are working on developing a system or a software program that will calculate the roots of a given equation in order to solve other complex problems that depends on the result of the equation.

 The following report contributes to the user analysis, analysis of the content that needs to be displayed on the GUI of application and steps in the design. In addition to that, the steps in the design, modeling of the problem, and the state chart diagram for the proposed application is alos provided in the different sections of this report.          

User analysis

 The user analysis is considered as vital in order to ensure the great product experience for the target audience of the propose application. It helps the developers to have a great insight about the requirements, behavior and expectations from a proposed application. For this specific application the main users will be the school, college students, researchers pursuing researches for complex problems in the field of mathematics and the physics.  In addition to that the application can be used by the different business analysts and experts in order to predict and calculate the profit or loss from the business.

 In order to solve the provided quadratic equation, the application will use the formulas of algebra that states,

Discriminant = b² – 4ac

root1 = (-b + √ (discriminant))/2a

root2 = (-b² - √ (discriminant))/2a

  This formulas are used to determine the real as well as the imaginary roots of the user inputted quadratic equation.

Display content analysis

 There are mainly four GUI’s for the proposed application in order to ensure the efficient use of the application by the user. The home screen of the application is proposed to get the quadratic equation as the input by the users.  There is an “Ok” button on the home screen in order to get the roots of the given quadratic equation.  This instance of the GUI also includes a cancel button that can be used by the user to reset the

In the next part if the user insert any invalid input or equation that cannot be evaluated as a quadratic equation then it will open an error screen indicating “the inserted equation is not a valid quadratic equation”.   This kind of inputs includes the following equations,

Quadratic Equation Formula

X^3+3=0; (or any higher degree of x consisting in the equation)

(a + b) (Or any kind of constant mathematical expression).

Another GUI for this application will show the calculated result for the Quadratic Equation i.e. the roots of the equation. The solution for the inserted equation will be provided in both graphical and numerical form. The roots will be plotted over the real number line or the X axis, if the roots are real.

Design steps

While Designing the GUI for the proposed application we have followed the below described steps,

 Determining the main functionalities required for the application: In this steps we have determined the functionalities for the application.  As the application is desired to calculate the roots of a quadratic equation, thus we have to provide input controls to the GUI.

Adding Controls and selecting the Color scheme for the application:  In this stage we added controls such as “OK” button that will be used by the users to get the roots of a valid quadratic equation provided by the user.

Determining the conditions for the error screens: In this stage the error conditions for which the error window will appear and ask the user to reenter a valid equation.

Modeling of the Problem

 In order to solve the problem or the quadratic equation the user at first have to insert or type the equation in the specified text box of the application (The inserted or the typed application must be of the form ax²+bx+c).  After this, user have to Ok button on the GUI in order to get the result or the root of the equation, else the application will generate an error dialog box asking the user to insert a standard quadratic equation in to the specified field.  

Explanation for the Chosen software tool

Even though there are serval GUI modeling tools but we have used the Enterprise architect to design the GUI for this specific application.  

The design of the user interface or technically known as the GUI in Sparx Systems Enterprise Architect is very easy as well as it helps the designer to fulfil most UI specification requirements for a specific mobile application or a desktop application (This tool can be used for prototyping of a web site or a specific web page).

The design of the GUI of this application can be used to approve the desired functionalities required by the users before the implementation stage of the different functionalities. This helps in the validation of the requirements.  This tool also can be used to define and determine the User Interface along with the traceability links with other modelling elements on the GUI, enabling the developers and the entire team to control the impact of the UI on the business, functional requirements and design aspects of the program and the application.

State chart diagram

(Source: Created by author using Visio)

Conclusion

With an easy and efficient graphical user interface the proposed application can help its target users to achieve its objectives and meet the requirements. When a proposed GUI is described to the users then they can notice the inconsistencies that had to be improved to enhance the usability.  

Consistency of the GUI of the application makes it easy for the end users to explore and utilize the proposed application since they do not need to learn new controls to get the result for their Quadratic Equation. They comprehend or had the idea about what results can be expected from the application as the easier navigation and consistent operation of the application. Actually, this will encourage and help the end users to use the application in order to solve the complex quadratic equations.

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