Advanced Math

Question : Calculate the div and curl of the vector field \[F\left(x,y,z\right)=(3x^2z+ye^x)\hat{i}+(e^x)\hat{j}+ (x^3)\hat{k}\] Is the vector field conservative? Solution : (a) To Find Div (divergence) of the Vector Field \[F\left(x,y,z\right)=(3x^2z+ye^x)\hat{i}+(e^x)\hat{j}+…

Question : Calculate the div and curl of the vector field \[F\left(x,y,z\right)=x^2z\hat{i}+sin(yz)\hat{j}+ xyz\hat{k}\] Is the vector field conservative? Solution : (a) To Find Div (divergence) of the Vector Field \[F\left(x,y,z\right)=x^2z\hat{i}+sin(yz)\hat{j}+…

is {(1, 1, 0),(1, 0, 1),(0, 1, 1)} a set of linearly dependent or linearly independent vectors ? Answer : Linearly Dependent Set : A set S of elements or…

Question : What is conservative force? Prove that the following force is conservative. \[\vec{F_1}=\left(x^2-y^2+x\right)\hat{i}-\left(2xy+y\right)\hat{j}\] Solution : Conservative Force : A force field vector F written as \[\vec{F\left(x,y,z\right)}=f_1\left(x,y,z\right)\hat{i}+f_2\left(x,y,z\right)\hat{j}+f_3\left(x,y,z\right)\hat{k}\] which is defined…

Question : Find real and imaginary parts of tan(z) Solution : Let z=x+iy be any complex numbers where x and y are real numbers. Since tan(z)=sin(z)/cos(z) Hence we first expand…