Version 1.1 (March 2011)
 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.
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.
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.
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(32i) = 3 
imag  imaginary part of a complex number i. e. real (32i) = 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'.
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^24x=3x2' in almost no time, searching in a interval of 120.000.000 (1E6 to 1E6 using steps of 0.1). Thatīs very fast.
Want to integrate something ? No problem. Simple or double ?
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.
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.
Please also notice that we could just performed the integrations directly in the command line.
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.
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:
The "12*cos(xt)" graph:
We can also right clik for more options:
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'.
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.
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.
If you exit Math Graphica and start it again, it will retain the variables and their values, so you can use it again.
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: