  Description

MathPro is a numerical computing environment and programming language mostly compatible with Matlab. You can implement any numerical method using this program. MathPro is designed in order the user interact more efficiently. Is caracterised by:

• Programs can be viewed or edited using the present famous mobile text editor
• Writing programs more efficiently and solve any mathematical problem.

This Mathematical tool for Mobile Phones and Tablets is a Must-have tool for students, professionals and scientists. MathPro's interface integrate standard mathematical notation, programming statements, and text in a single worksheet. Is very flexible, fast, and more professional. It runs on Android Mobile Phones and Tablets. MathPro is part of MobileMaths. You can get the tool MathPro by downloading MobileMaths.

 Vectors and Matrices linspace(var1,var2,COUNT) vector with COUNT numbers ranging from var1 to var2 length(vector) number of elements in vector zeros(ROWS[,COLUMNS]) create array of all zeros ones(ROWS[,COLUMNS]) matrix of ones eye(ROWS[,COLUMNS]) matrix with diagonal one size(matrix) number of rows and columns sum(var) if var is a vector: sum of elements, if var is a matrix: sum of columns. max(var) largest element in var min(var) smallest element in var det(matrix) determinante eig(matrix) eigenvalues inv(matrix) inverse lu(matrix) LU-decomposition diag(matrix) extracts diagonal elements

 Polynomials ploy(x) creation of a polynomial with specified roots x, poly(x) is a vector whose elements are the coefficients of the polynomial whose roots are the elements of x. Example: y=poly([2,1]). polyval(v,var) generates a new value (estimate) of y at var based on the coefficients vector v found with polyfit.see example 10 polyfit(x,y,n) finds the coefficients of a polynomial p(x) of degree n that fits the data, p(x(i)) is approximately equal to y(i), in a least-squares sense. see example 10
 interp1(x,y,xi) 1-D cubic spline interpolation of x/y-values at xi. yi = interp1(x,y,xi) interpolates to find yi, the values of the underlying function y at the points in the array xi. Example: x=[1,5,15]; y=[15,35,55];xi=6;yi=interp1(x,y,xi) interp2(x,y,z,xi,yi) 2-D cubic spline interpolation of x/y/z-values at xi and yi. zi = interp1(x,y,z,xi,yi) interpolates to find zi, the values of the underlying function z at the points in the arrays xi and yi. Example: x=[1,5,15]; y=[15,35,55];z=[25,66,88]; xi=6;yi=8;z=interp1(x,y,z,xi,yi) sparse(x) create sparse matrix, converts a sparse or full matrix to a sparse form by squeezing out any zero elements. s=sparse(x) fit(x,y,FUNCTION) fit data with arbitrary fitting function, x and y must be vectors of equal length. FIT computes the coefficients of the arbitrary function. Example: x=[1,2,3,4];y=[5,25,30,55];fit(x,y,'y=a*x/(x+b)'); or x=[1,2,3,4];y=[5,25,30,55];fit(x,y,'a*x/(x+b)'); ezfit(x,y,FUNCTION) the same as fit fmin(FUN,x0) starts at x0 and attempts to find a local minimizer x of the function FUN. Example: fmin('sin(x)',3). eval('expression') execute string containing expression. Example: x=3;eval('x^2+3') fzero('expression',x0) single-variuable nonlinear zero finding. Tries to find a zero of the function near x0. Example: fzero('x^2-4',0). roots(p) or roots([coeff]) computes the roots of the polynomial roots. The polynomial is c(1)*x^n+.....+c(n)*x+ c(n+1). solve(expression,x) serach roots for a non linear equation. Example: syms x;y=x^2-1;solve(y,x). syms x;y=x^2+3*x-17*sqrt(3*x^2+6);solve(y,x). syms arg1, arg2, ..... constucting symbolic variables. Example: syms x, y, z. integrate(Function,x) integartes function with respect to the symbolic variable x. Example: syms x;integrate(3*x^2+2*x-5,x). quad('expression',x1,x2) numerically evaluate integral, adaptive Simpson quadrature. Example: quad('sqrt(x)',0,2).

 Plotting plot(x,y) 2-D line plot; x and y being equalsized vectors, which denote the coordinates of the data points to be plotted. see example 13 plot(x,y,option) 2-D line plot; a third optional argument option specifies plot options like colors and symbols. see example 13 loglog(x,y,option) log-log scale plot semilogx(x,y,option) Semilogarithmic plot semilogy(x,y,option) Semilogarithmic plot

 Comparison and Logical Operators Less x < y Less or equal x <= y Larger x > y Larger or equal x >= y Equal x == y Not equal x ˜= y And x & y Or x | y Not ˜x

 Arithmetic Operators Addition x + y Subtraction x - y Multiplication x * y Division x \ y Exponentiation x ˆ y Range x:y:z Assignment x += z Assignment x -= z Assignment x /= z Assignment x *= z Postincrement x++ Postdecrement x--

 Scalar Functions rat(var) var as exact number real(var) real part of var imag(var) imaginary part of var abs(var) absolute value of var sign(var) sign of var conj(var) var conjugate complex sqrt(var) squareroot exp(var) exponential ln(var) natural logarithm log(var) decimal logarithm sinh(var) hyperbolic sine cosh(var) hyperbolic cosine asinh(var) hyperbolic areasine acosh(var) hyperbolic areacosine sin(var) sine (radian) cos(var) cosine (radian) tan(var) tangens (radian) asin(var) arcsine (radian) acos(var) arccosine (radian) atan(var) arctangens (radian) fact(n) factorial n!

Comment statements

MathPro comment statements begin with the percent character, %. All characters from the % to the end of the line are treated as a comment.

Flow Control

MathPro supports the basic flow control constructs found in most high level programming languages, the same as in MathLab language.

Branches if constructs

MathPro supports these variants of the ``if'' construct

• if ... end
• if ... else ... end
• if ... else if ... else ... end end

Jumps
return, continue, break
A function may be prematurely left using return.
continue and break are used in loops: continue jumps back to the start of the loop, and begins another cycle. break permanently leaves the loop.

Loops:
For Loops

The for loop allows us to repeat certain commands. If you want to repeat some action in a predetermined way, you can use the for loop. All of the loop structures in MathPro are started with a keyword such as "for", or "while" and they all end with the word "end".

The for loop is written around some set of statements, and you must tell MathPro where to start and where to end. Basically, you give a vector in the "for" statement, and MathPro will loop through for each value in the vector:

While Loops

If you don't like the for loop, you can also use a while loop.

The while loop repeats a sequence of commands as long as some condition is met.

 Programming in MathPro break Terminate execution of for or while loop continue Pass control to next iteration of for or while loop else Conditionally execute statements end Terminate conditional block of code error Display error message and exit the program disp Display error message and exit the program for Execute block of code specified number of times if Conditionally execute statements return Return to invoking function while Repeatedly execute statements while condition is true> write display text and variables ( ) Pass function arguments % Insert comment line into code eval eval(expression) executes expression, a string containing a valid MathPro expression. see examples 7 and 8 function declare a function. see below examples

 Examples included in MathPro Example 1 Gauss Elimination Example 2 TDMA Solver Example 3 Bisection Example 4 Falsposition Example 5 Secant Example 6 Newton Raphson Example 7 Integral Trapezoid Example 8 Integral Simpson Example 9 Runge Kutta 4 Example 10 Interpolation Example 11 Finite Difference Example 12 Heat Explicit Solver Example 13 Plotting Data