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Replace a variable with a function

Hello i hope anyone can help me with the following problem.

i have the following code

T_w,y,T_m,k_f,rho_f,U_0,h_mstar,R, alpha, delta = var('T_w y T_m k_f rho_f U_0 h_mstar R alpha delta') T=T_w+y(-2(T_w-T_m)/delta+rho_fU_0h_mstarcos(Phi)/k_f)+y^2((T_w-T_m)/delta^2-rho_fU_0h_mstarcos(Phi)/(k_fdelta)) u=-6U_0Ry(y-delta)sin(Phi)/delta^3 integralTu=integrate(Tu,y,0,delta)

now i would like to differentiate integralTu with respect to x (diff(integralTu,x)), but delta must be a function of x (i first defined it as a variable because of the integration).

Replace a variable with a function

Hello i hope anyone can help me with the following problem.

i have the following code

T_w,y,T_m,k_f,rho_f,U_0,h_mstar,R, alpha, delta = var('T_w y T_m k_f rho_f U_0 h_mstar R alpha delta')
T=T_w+y(-2(T_w-T_m)/delta+rho_fU_0h_mstarcos(Phi)/k_f)+y^2((T_w-T_m)/delta^2-rho_fU_0h_mstarcos(Phi)/(k_fdelta))
u=-6U_0Ry(y-delta)sin(Phi)/delta^3
integralTu=integrate(Tu,y,0,delta)

T=T_w+y*(-2*(T_w-T_m)/delta+rho_f*U_0*h_mstar*cos(Phi)/k_f)+y^2*((T_w-T_m)/delta^2-rho_f*U_0*h_mstar*cos(Phi)/(k_f*delta)) u=-6*U_0*R*y*(y-delta)*sin(Phi)/delta^3 integralTu=integrate(T*u,y,0,delta)

now i would like to differentiate integralTu with respect to x (diff(integralTu,x)), but delta must be a function of x (i first defined it as a variable because of the integration).

click to hide/show revision 3
No.3 Revision

updated 2014-07-10 08:42:30 -0600

kcrisman gravatar image

Replace a variable with a function

Hello i hope anyone can help me with the following problem.

i have the following code

T_w,y,T_m,k_f,rho_f,U_0,h_mstar,R, alpha, delta delta, Phi = var('T_w y T_m k_f rho_f U_0 h_mstar R alpha delta')
delta Phi')

T=T_w+y*(-2*(T_w-T_m)/delta+rho_f*U_0*h_mstar*cos(Phi)/k_f)+y^2*((T_w-T_m)/delta^2-rho_f*U_0*h_mstar*cos(Phi)/(k_f*delta))

u=-6*U_0*R*y*(y-delta)*sin(Phi)/delta^3

integralTu=integrate(T*u,y,0,delta)

now i would like to differentiate integralTu with respect to x (diff(integralTu,x)), but delta must be a function of x (i first defined it as a variable because of the integration).

click to hide/show revision 4
retagged

updated 2014-07-11 15:04:49 -0600

kcrisman gravatar image

Replace a variable with a function

Hello i hope anyone can help me with the following problem.

i have the following code

T_w,y,T_m,k_f,rho_f,U_0,h_mstar,R, alpha, delta, Phi = var('T_w y T_m k_f rho_f U_0 h_mstar R alpha delta Phi')

T=T_w+y*(-2*(T_w-T_m)/delta+rho_f*U_0*h_mstar*cos(Phi)/k_f)+y^2*((T_w-T_m)/delta^2-rho_f*U_0*h_mstar*cos(Phi)/(k_f*delta))

u=-6*U_0*R*y*(y-delta)*sin(Phi)/delta^3

integralTu=integrate(T*u,y,0,delta)

now i would like to differentiate integralTu with respect to x (diff(integralTu,x)), but delta must be a function of x (i first defined it as a variable because of the integration).