Mathematics Problems

Show that u=x^3-3xy^2+3x^2-3y^2+1 is harmonic and find its harmonic conjugate. Also find the corresponding analytic function f (z) Problem Question Show that u=x^3-3xy^2+3x^2-3y^2+1 is harmonic and find its harmonic conjugate. Also find the corresponding analytic function f (z)   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps…

Construct the analytic function whose real part is r^2 cos 2theta Problem Question Construct the analytic function whose real part is r^2 cos 2theta   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type…

Determine the analytic function f (z) =u+iv given that the real part u=e^2x (x cos(2y-y sin2y)) Problem Question Determine the analytic function f (z) =u+iv given that the real part u=e^2x (x cos(2y-y sin2y))   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate…

Find the analytic function f (z) given u=e^ (-x) [(x^2-y^2) cosy+2xy siny] Problem Question Find the analytic function f (z) given u=e^ (-x) [(x^2-y^2) cosy+2xy siny]   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex…

Find the analytic function f (z) whose imaginary part is e^x (x siny + y cosy) Question Question Find the analytic function f (z) whose imaginary part is e^x (x siny + y cosy)   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate…

Construct the analytic function whose real part is u=log(sqrt((x^2+y^2)) Problem Question Construct the analytic function whose real part is u=log(sqrt((x^2+y^2))   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for…

Show that f (z)=(r+k^2/r cosθ+i (r-k^2/r) sinθ, r≠0 is a regular function of z=r e^ (iθ) Also find f'(z) Problem Question Show that f (z)=(r+k^2/r cosθ+i (r-k^2/r) sinθ, r≠0 is a regular function of z=r e^ (iθ) Also find f'(z)   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3…

Given that f(z)= (x^3 (1+i )-y^3 (1-i))/(x^2+y^2 ) if z≠0 and f(z) =0 if z=0, Show that f(z) satisfies Cauchy-Riemann equations at the origin Problem Question Given that f(z)= (x^3 (1+i )-y^3 (1-i))/(x^2+y^2 ) if z≠0 and f(z) =0 if z=0, Show that f(z) satisfies Cauchy-Riemann equations at the origin   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function…

Find the derivative of the analytic function z^z Problem Question Find the derivative of the analytic function z^z   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for Analytic Functions…

Show that f (z) =e^x (cos y + i sin y) is analytic function in complex variable Problem Question Show that f (z) =e^x (cos y + i sin y) is analytic function in complex variable   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find…

Show that w=z z(bar) is not analytic function in complex variables Problem Question Show that w=z z(bar) is not analytic function in complex variables   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type…

Show that f (z) =z^n where n is a positive integer is analytic and hence find its derivative Problem Question Show that f (z) =z^n where n is a positive integer is analytic and hence find its derivative   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps…

Show that f (z) =cos hz is analytic and hence find f’(z) Problem Question Show that f (z) =cos hz is analytic and hence find f’(z)   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex…

Show that f(z)=sin z is analytic and hence find f’(z) Question Question Show that f(z)=sin z is analytic and hence find f’(z)   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 -…

Solve the equation u_ (n+2)-5 u_ (n+1) +6 u_n=36 using Z-transforms with u_0=u_1=0 Problem Question Solve the equation u_ (n+2)-5 u_ (n+1) +6 u_n=36 using Z-transforms with u_0=u_1=0 Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms…

Solve the difference equation using Z-transform, y_ (n+2) +4 y_ (n+1) +3 y_n=3^n with the initial conditions y_0=0 & y_1=1 Problem Question Solve the difference equation using Z-transform, y_ (n+2) +4 y_ (n+1) +3 y_n=3^n with the initial conditions y_0=0 & y_1=1 Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_…

Solve the difference equation y_(n+2)+6y_(n+1)+9y_n=2^n with y_0=y_1=0 using Z-transform Problem Question Solve the difference equation y_(n+2)+6y_(n+1)+9y_n=2^n with y_0=y_1=0 using Z-transform Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Solve the difference equation y_(n+2)+6y_(n+1)+9y_n=2^n with y_0=y_1=0 using…

Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Problem Question Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Solve the difference equation y_(n+2)+6y_(n+1)+9y_n=2^n with y_0=y_1=0 using Z-transform Solve the difference…

Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Problem Question Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0   Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Solve…

Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Problem Question Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2   Topic Steps to find the solution of Difference equations using Z-transforms Steps to find the solution of Differential equations using Z-transforms Differential equations Problems Solve using Z-transforms y_n+2-4y_n=0 given that y_0=0 and y_1=2 Solve by using z-transform y_ (n+1) +1/4 y_n= (1/4) ^n, (n≥0), y_0=0 Solve the difference equation y_(n+2)-6y_(n+1)+9y_n=3^n using Z-transforms Solve the difference equation y_(n+2)+6y_(n+1)+9y_n=2^n with y_0=y_1=0…