I have a multiple integration. I know my integrals exist. When I write procedure for Rimannian sum, Maple gives correct answers for every choice of parameters of my integral. But when I ask Maple to compute it with int(...,numeric) sometimes it shows a correct answer and sometimes it shows a wrong answer. I'm curios to know what is going wrong in Maple, is there any command to see the details and steps of the computation to see where Maple is going wrong? I also increased the number of digits after decimal from 10 to 12 and 14. But Maple just repeats the wrong answers with just two or four digits. So the problem is not related to the approximation arising from number of decimals.

I was calculating the total derivative of a function but maple does not respond to the commands like alias,diff,totaldiff etc.

please see the attached pdf.multiplier.pdfmultiplier.pdf

fsolve does not any answer!!!!

please help me.

fsolve.mw

Dear users!

Hope everyone should be fine here. I need the following simiplification. I did it step by step is there and maple command to do this.

I am waiting your positive answer.

(diff(theta(eta), eta, eta))*(Rd*T[infinity]^3*(`θw`-1)^3*theta(eta)^3+3*Rd*T[infinity]^3*(`θw`-1)^2*theta(eta)^2+(3*(Rd*T[infinity]^3+(1/3)*epsilon*k[nf]))*(`θw`-1)*theta(eta)+Rd*T[infinity]^3+k[nf]) = (-3*Rd*T[infinity]^3*(`θw`-1)^3*theta(eta)^2-6*Rd*T[infinity]^3*(`θw`-1)^2*theta(eta)+(-3*Rd*T[infinity]^3-epsilon*k[nf])*(`θw`-1))*(diff(theta(eta), eta))^2+(-(rho*c[p])[nf]*nu[f]*f(eta)-(rho*c[p])[nf]*nu[f]*g(eta))*(diff(theta(eta), eta))+a*nu[f]*mu[nf]*(diff(f(eta), eta))^2/((-`θw`+1)*T[infinity])-2*a*nu[f]*mu[nf]*(diff(g(eta), eta))*(diff(f(eta), eta))/((`θw`-1)*T[infinity])+a*nu[f]*mu[nf]*(diff(g(eta), eta))^2/((-`θw`+1)*T[infinity])

(diff(theta(eta), eta, eta))*Rd*T[infinity]^3*(theta(eta)*`θw`-theta(eta)+1)^3+(diff(theta(eta), eta, eta))*k[nf]*(epsilon*theta(eta)*`θw`-epsilon*theta(eta)+1)+3*Rd*T[infinity]^3*(`θw`-1)*(theta(eta)*`θw`-theta(eta)+1)^2*(diff(theta(eta), eta))^2+epsilon*k[nf]*(`θw`-1)*(diff(theta(eta), eta))^2

diff((theta(eta)*`θw`-theta(eta)+1)^3*(diff(theta(eta), eta))*Rd*T[infinity]^3, eta)+diff((epsilon*theta(eta)*`θw`-epsilon*theta(eta)+1)*(diff(theta(eta), eta))*k[nf], eta);

when I  have transformed symbol expression  from matlab 2017b to  maple 2018 , maple took a mistake that  "maple kernel connection not available", What  is the  reason？Can anyone help me？Thank you！

fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:

gr:=0.5:pr:=0.71:sc:=0.7:m:=1.0:k:=0.3:
  fcns:=[u(x,y,t),v(x,y,t),h(x,y,t),c(x,y,t)]:
  IC := [u(x,y,0)=0,v(x,y,0)=0,h(x,y,0)=0,c(x,y,0)=0]:
  BC:=[u(0,y,t)=0,h(0,y,t)=0,c(0,y,t)=0,u(x,0,t)=1,v(x,0,t)=0,h(x,0,t)=1,c(x,0,t)=1,u(x,10,t)=0,h(x,10,t)=0,c(x,10,t)=0];
  eq1:={diff(u(x,y,t),t)+u(x,y,t)*diff(u(x,y,t),x)+v(x,y,t)*diff(u(x,y,t),y)=diff(u(x,y,t),y$2)+gr*h(x,y,t)+gr*c(x,y,t)-m*u(x,y,t)
,diff(h(x,y,t),t)+u(x,y,t)*diff(h(x,y,t),x)+v(x,y,t)*diff(h(x,y,t),y)=1/pr*diff(h(x,y,t),y$2),diff(c(x,y,t),t)+u(x,y,t)*diff(c(x,y,t),x)+v(x,y,t)*diff(c(x,y,t),y)=1/sc*diff(h(x,y,t),y$2)-k*c(x,y,t)}:
  pds:= pdsolve(eq1,IC,BC,fcns,numeric):
  pds:= pdsolve(eq1,IC,BC,fcns,numeric,spacestep = 1/100):

for the above problem i made this code.

Lamba is meant to be reserved for liouville function plotting some data i just realized it isn't that, so if the people that make the numtheory package please unprotec lamba in the future, or protec it but changed its proc assignment to the liouville function
function that would really sweet thanks

I wanted to have 3 graphs in 1 coordinate system. The Maple command I used was,

restart;
g := x -> (10*x)/(3+x);

f := x -> (10*x)/(5+x);

h := x -> (8*x)/(5+x);

plots:-display(
  plot( [g(x),f(x), h(x)], x=0..30, color=[red,blue, green], legend = ["k=3,c=10", "k=5, c=10","k=5,c=8"]));

Warning, unable to evaluate 1 of the 3 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

The error comes up. only f(x) and h(x) were shown. How do I fix this? Thank you.

I 'm solving asystem of equations and one of the result are Hfloat what does it means and how i convert it to number???

how to find skin friction value below code

restart

PDEtools[declare]((U, W, T, C)(y), prime = y):

R1 := .1; R0 := .1; m := .1; a := .1; Ha := .1; Nt := .1; Nb := .1; Pr := 6.2; Le := .6; Bi := 1; Ec := .1; k := 1; r := .1; A := 1;

sys := diff(U(y), `$`(y, 2))+(R1*(diff(U(y), y))-2*R0*W(y))*exp(a*T(y))-a*(diff(U(y), y))*(diff(T(y), y))-Ha = 0, diff(W(y), `$`(y, 2))+(R1*(diff(W(y), y))+2*R0*U(y))*exp(a*T(y))-a*(diff(W(y), y)) = 0, diff(T(y), `$`(y, 2))+R1*Pr*(diff(T(y), y))+Pr*Ec*exp(-a*T(y))*((diff(U(y), y))*(diff(U(y), y))+(diff(W(y), y))*(diff(W(y), y)))+Pr*Ha*Ec*((U(y)+m*W(y))*(U(y)+m*W(y))+(W(y)-m*U(y))*(W(y)-m*U(y)))/(m^2+1)^2+Nb*(diff(T(y), y))*(diff(C(y), y))+Nt*(diff(T(y), y))*(diff(T(y), y)) = 0, diff(C(y), `$`(y, 2))+Pr*Le*R1*(diff(C(y), y))+Nt*(diff(C(y), `$`(y, 2)))/Nb = 0:

ba := {sys, C(0) = 0, C(1) = 1, T(1) = 0, U(0) = 0, U(1) = 0, W(0) = 0, W(1) = 0, (D(T))(0) = Bi*(T(0)-1)}:

r1 := dsolve(ba, numeric, output = Array([0., 0.5e-1, .10, .15, .20, .25, .30, .35, .40, .45, .50, .55, .60, .65, .70, .75, .80, .85, .90, .95, 1.00])):

with(plots); 

p1u := odeplot(r1, [y, U(y)], 0 .. 1, numpoints = 100, labels = ["y", "U"], style = line, color = green); 

plots[display]({p1u})

restart; with(plots);
G := 1; M := .1; R := 1; P := .72; alpha := .1; phi := 1; K := 1; n := 2; beta := 1;
                               1
                              0.1
                               1
                              0.72
                              0.1
                               1
                               1
                               2
                               1
ode1 := {(1+(4/3)*R)*(diff(theta(x), x, x))+(1/2)*P*f(x)*(diff(theta(x), x))+alpha*theta(x) = 0, n*(diff(f(x), x, x))^(n-1)*(diff(f(x), x, x, x))+f(x)*(diff(f(x), x, x))/(n+1)+G*theta(x)-M*(diff(f(x), x)) = 0, f(0) = 0, theta(10) = 0, (D(f))(0) = beta*K*((D@@2)(f))(0), (D(f))(10) = 1, (D(theta))(0) = -phi*(1-theta(0))};
 /7  d  / d          \                     / d          \
{ - --- |--- theta(x)| + 0.3600000000 f(x) |--- theta(x)|
 \3  dx \ dx         /                     \ dx         /

                         / d  / d      \\ / d  / d  / d      \\\
   + 0.1 theta(x) = 0, 2 |--- |--- f(x)|| |--- |--- |--- f(x)|||
                         \ dx \ dx     // \ dx \ dx \ dx     ///

     1      / d  / d      \\                  / d      \      
   + - f(x) |--- |--- f(x)|| + theta(x) - 0.1 |--- f(x)| = 0,
     3      \ dx \ dx     //                  \ dx     /      

  f(0) = 0, theta(10) = 0, D(f)(0) = @@(D, 2)(f)(0),

                                           \
  D(f)(10) = 1, D(theta)(0) = -1 + theta(0) }
                                           /
dsol := dsolve(ode1, numeric, method = bvp[midrich], range = 0 .. 10);
Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

Hello,

I need a little help...

what I want to do, if i have 3 equations  with multiple variables and i want to get derivative of some of these variables wrt other variables while setting others as constants

here in the example

1st i thought the last equation should have partial m / partial f ... how can i get that

2nd if ,another problem, i wanted to set z as a constant so it won't consider getting its derivative, how do i get that

diff_test.mw

Download diff_test.m

hope i was clear in my explanation. thank you

Hello,

So my questions is fairly simple but I am not sure if Maple can do this. I want to create a Matrix full of partial derivatives (Jacobian), but computing this Jacobian is maxing out my RAM. So I would like to create each row (or column) of the Jacobian seperately and save each row (or column) in a Matrix that has already been saved to a file. Basically I would like to store values in a file (in a loop) without overwriting the file.