gradient_sym.m

function gradientSym = gradient_sym(V,X,coordinate_system)
%% gradient_sym
% Copyright (c) 2018, mohamed fekry
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%This Function calculates the gradient of 3D scalar function in Cartesian, Cylindrical, and Spherical coordinate system.
%function gradientSym = gradient_sym(V,X,coordinate_system)
%V is the 3D scalar function
%X is the parameter which the gradient will calculate with respect to.
%coordinate_system is the kind of coordinate system at which the vector field is specified.
%the gradient is calculated according to (Engineering Electromagnetics Sixth Edition William H. Hayt, Jr. . John A. Buck)
%Example (1):
%V=24*cos(pi*y/3)*sin(2*pi*z/3)
%gradient_sym(V,[x,y,z],'Cartesian')
%Example (2):
%V=Vo*exp(-2*r)*sin(3*phi)
%gradient_sym(V,[r,phi,z],'Cylindrical')
%Example (3):
%V=Vo*a/R*cos(2*th)
%gradient_sym(V,[R,th,phi],'Spherical')

%%
switch coordinate_system
    case {'cartesian','Cartesian'}
        gradientSym=gradient(V,X);
    case {'cylindrical','Cylindrical'}
        gradientSym=[diff(V,X(1)),1/X(1)*diff(V,X(2)),diff(V,X(3))];
    case {'spherical','Spherical'}
        gradientSym=[diff(V,X(1)),1/X(1)*diff(V,X(2)),1/(X(1)*sin(X(2)))*diff(V,X(3))];
end
end