Math Graphica”  -   Quick and Dirty Manual

Version 1.1 (March 2011)

What is Math Graphica ?
Math Graphica Main window
- Calculator
- Functions / operators / constants available
- Equation
- Integration and Double Integration
- Integration
- Double integration
- Graph's
- 3D / 4D Graph's
- 3D Parametric Graph
- 2D Graph's
- System of Equations
- Command Line
User defined Functions
- Variables
- Formulas
- Base number converter
- Matrix
- Contact

• What is Math Graphica ?

Math Graphica aims to be a very easy to use math software. The idea is for you to use it right away without having to read this manual, and yet, give you the flexibility and power to perform more sophisticated calculation in a very easy way.

Some features of Math Graphica: expression parser with real and complex numbers, trigonometric functions, 2D / 3D graphs, integration and equation system.

• Math Graphica main window

• Calculator

If you're lazy to type and like using the mouse, just click on the calculator icon and a advanced calculator will apear. Just click in the buttons to do the calculation you want, and chose the operators and functions available.

You can see all the available functions and start clicking, or typing the expression you want to calculate. Then press Ok. Or you can just use the command line in the main window to write the desired mathematical expression instead.

Next image show the result for the expression "cos(3)+2/5"  (type without the quotes).

The "Calculator" button, down left, is similar to the "Calculator" icon in the menu, the diference is that doesn't calculate the result, only display's the expression in the command line. You should press "Enter" in the command line, or click in the down right "Ok" button to do the calculation.

Math Graphica saves a list of all calculations. Just click to bring then to the command line, or double click them to open the calculator dialog.

You can navigate throw the command line and the calculation list with the Up and Down keys.

• Functions / operators / constants available:

When writing a floting point number use '.' ( 3.2 ok) and not the ',' ( 3,2 wrong)

 Constants pi Pi number, 3.1415... e Nepper number 2.71... (do not use 'E' ) i Imaginary number, use this notation ( 2+3.2i ) do not use ( 2+i3.2 )

 Operators + sum - subtration * multiplication / division ^ Power | Absolute value, e.g. |-10| = 10 (this is not a logical operator) E Same as *10^, e.g . 3E2 = 3*10^2 = 300 (do not use 'e' , 'e' is the Nepper number)

 Trigonometric functions sin, cos, tan, cotg, csc, sec Trigonometric asin, acos, atan, acotg, acsc, asec Inverse trigonometric sinh, cosh, tanh, cotgh, csch, sech hyperbolic asinh, acosh, atanh, acotgh, acsch, asech Hyperbolic inverse

 Other functions sqrt Square root log Natural logarithm ln Exponencial logarithm exp Exponencial, same as e^ sinc Sinc function, sinc(x) = sin(pi*x)/(pi*x) real real part of a complex number, i.e.    real(3-2i) = 3 imag imaginary part of a complex number i. e.  real (3-2i) = -2i abs Equal to the Absolute value, e.g.    abs(-10) = 10

All functions are case insensitive, you can write cos(3) or Cos(3), except for 'e', the Nepper number wich is different from operator 'E'.

• Equation

Plain simple, click this button and equation dialog will appear.

Just write any equation you like in the f(x) and g(x) edit boxes.

You can also use other variable different than 'x', just use 'y', or 'myvar1' the program Math Graphica will automatically detect the variable. The 'min' and 'max' edit are the search intervals, 'step' is the step increment, and 'precision' is the precision result. The default values will be ok for the must common situations.

The solution:

The program will automatically create a variable ''x' and, has in this case, of multiple solution, assign the last value ( x= 6.70156 in this example). Will see more about variable later in the 'command line' section.

Again, you wouldn't need to call the equation dialog, could just write it in the command line. The only thing about the dialog is that will give you more options.

Also if you double click the equation in the mainwindow list, it will bring the equation dialog. If you double click the result t will bring the calculator dialog.

Please do not use equations like:

x=x+1

This is correct only in programming language where '=' is the assignement operator and 'x' is incremented one unit, but mathematically is a equation without solution.

If you do this, Math Graphica will not find a solution. Math Graphica uses a very fast, but experimental search algorithm, but this algorithm looses is speed when dealing with parallel expressions like 'x' and 'x+1' wich are parallel lines. As you probably noticed, Math Graphica solved the early equation 'x^2-4x=3x-2' in almost no time, searching in a interval of 120.000.000 (-1E6 to 1E6 using steps of 0.1). Thatīs very fast.

• Integration and Double Integration

Want to integrate something ? No problem. Simple or double ?

Simple integration:

Notice you can use expressions like 'pi/2' and '-e' in the integration intervals. Also if you don't remember all the available functions Math Graphica has to offer, just click in the f(x) button and it will open the calculator dialog where you can compose your function to integrate. ( in this picture is cos(x) ). 'm' is a quality factor, the higher the slower calculation will be. Actually 'm' is the number of intervals in the Simpson's composite numerical integration rule.

Double integration:

Also notice you can use expressions like 'x^2+3x' and 'x' in the limits of the inner integral. This is very useful. Again you can click the f(x,y) button to bring the calculator dialog to help you compose the integration expression.

There's the solutions:

Please also notice that we could just performed the integrations directly in the command line.

• Graph's

This is the fun part.

3D / 4D Graph's

As you notice by now, all dialog's have predefined values in the edit boxes, to help you fill more confortable in the first time you're using the program. So, we will just use the "cos(x)*sin(y)*cos(t)" and you will see the following picture.

You can zoom it with the mouse wheel or with the keyboard '+' and '-'. Just rotated it by click and drag. It will create a very nice animation rotation movement that will eventually stop. To stop it right now click and release withou moving the mouse. Also you can rotate the graph with the keyboard keys Left, Right, Up, Down, '8' and '9' (rotation in x, y, and z axis).

This is a 4D graph, matematically defined as  z=f(x,y,t).

We can bring a context menu with four options:

- "New 3D Graph" : this will show the new graph dialog, wich will allow you to add new graphs to the current window. The maximun graph number is only limited by the computer memory.

- "Play/Stop Graph Animation" : This will activate the movement in time, it will show a legend with "t = xxxx s" updating constinuosly the seconds, and animating the graph with a very nice movement.

- "Background color" : Will show a color dialog to choose a new color for the background.

- "Save image as" : will save a png file with the graph image.

Next image show you the window with new added graph with animation.

3D Parametric Graph's

This is similar to normal 3D graph, you just have to write functions of the type: x=f1(t) ; y=f2(t); z=f3(t), like in the following example

The corresponding graph:

2D Graph's

The "12*cos(x-t)" graph:

Use the whell mouse for zoom, and click and drag to move the graph. Notice we could have clicked the 'GraphColor' button
to choose a color for the graph. If we don't click it, 'Math Graphica' will choose a pre defined color for us.

We can also right clik for more options:

• Play / Stop Graph Animation : Starts the animation by activating the movement in time.
• Background color : changes the background color.
• Save as image :  save the graph as a PNG image format.
Actually, this is a 3D graph of type y = f(x,t), it's a 2D with movement in time t.

We could add as many graphs as we like to the window, as long has your memory system can handle.

Next image shows several graphs:

To create a graph in a new window just click in the main window icon 'Graph 2D'.

• System of Equations

Just select the number of equations you want to calculate, then enter the values or if you want press the random button, that will generates numbers for yuor equation system. Then press solve, and there's your solution.

This is very powerfull because you can use complex numbers and expression's in the equation system.

• Command line

We can use the command line to create variables. Just type 'y=3.2' and we have a variable named y with value 3.2. Now you can define z = y+3, and we have a z variable with 6.2 value.

You also can type expressions like 'z+2*y' and Math Graphica will show you the result.

Also you can use names for variables like 'myvar2', 'xx_3'. Remember it must start with a letter, then use letters, underscores and numbers.

You can navigate throw the command line and the list of calculations by pressing the arrows key up and down.
Pressing "Enter" in the command line is the same as clicking the "Ok" button, calcutes the expression in the command line and displays the result in calculation list.

If you exit Math Graphica and start it again, it will retain the variables and their values, so you can use it again.

• Variables

To manaje the variables created in the command line we have the above dialog. It will show all the variables created so far.
We can set new names and values by editing. Plus, by righ clicking it
we have a context menu with options:
• Add Variable: it will apperar another line were we can define a new variable and the respective value.
• Remove Variable: choose this option to permanently delete a variable.
• Remove All: all variables from the list wll be deleted.

• User defined Functions

Imagine you want to define a mathematical function like f(x) = 2*x+3, and them you want to evalute for x= 3, something like f(3) = 2*(3)+3 = 9

Then just type in the command line:

f(x)=2*x+3

to calculate the function to the value of x= 3, just type in the command line:

f(3)

This is as simples as it gets. You can play around with expressions embebeding functions like:

2*f(4+3i)+7

Thats right, you can use an expression, or a complex number, as an input for the function, you can define all the function you want and use it as a argument to other functions.

We can create a function called media with two arguments that return the medium value of those arguments, like

media(a, b) = (a+b)/2

We called the arguments , "a" and "b", but we can name them something more descriptive, as "my_first_argument" or "argument_2".

To manage all this functions you have a dialog wich will help you, just click in the main window "functions" icon:

It displays the two functions defined so far. Right clicking will bring a pop up menu that allows you to add a new function (but you can do this directly in the command line, as seen so far), you can remove function you clicked, or remove all.

Please avoid doing stupid things like creating two functions with the same name.

• Formulas

This is a very powerfull feature.

Just write any formula you want (in this example 'P*V=n*R*T' ). Then double click on it, or press the 'Validate' button. Math Graphica will automatically grab the variables for you:

Suppose you want to assign values to 'P', 'n', 'R' and 'T' and want to calculate the value of 'V'. So, just edit those values and assign a '?' to 'V' like that:

Now just press the 'Solve' button and Math Graphica will give you the solution.

We can also right click in the formulas list and a popup menu will appear, with some options:

• New Formula: add's a new line so we can edit a new formula.
• Delete current formula: deletes the clicked formula.
All formulas and values assigned to the variables are saved between sessions of Math graphica.

• Base number converter

Base number converter performs conversions between decimal, binary, octal and hexadecimal numbers.

Just type any number in any base, and the other bases are automatically converteded.

• Matrix

Matrix Editor lets you define two matrixes and perform sum, subtraction and multiplication

Define the two upper matrices, define the operation (sum, subtraction or multiplication) in the combo box, and clik 'Calculate'.
The result will appear in the lower matrix. By right clicking in the matrixes, a context menu will give you some options: fill a random matrix, a matrix with ones, a matrix with zeros and a diagonal matrix.

All said, Math Graphica is really a powerful tool, so enjoy.

• Contact
You can contact me, for bugs, suggestions, comments, feature requests at:

Email:
math.graphica@gmail.com

Web:
soft-ingenium.planetaclix.pt

or

http://www.math-graphica.tk