MapleFans001

when calculating the following equations

int( exp(t*int( (m/2*(diff(x, t))^2-exp(x)), t)), x)

maple give

-Ei(1, t^2*exp(x))

what is Ei? how to show result normally?

i follow

http://www.maplesoft.com/applications/view.aspx?SID=4706

and edit existing code to solve a equation and got some questions and error, How to solve pde with finite difference in maple?

r := 0.03;
K := 20;
Smax := 20;
T := 1;
ex1 := diff(y(x,t), t) + r*x*diff(y(x,t), x) + 1/2*sigma^2*x^2*diff(y(x,t), x$2) + x*diff(y(x,t), x)*diff(y(x,t), t) = r*y(x,t);

bc1 := y(0,0)=K*exp(-r), y(Smax,0)=0;
a := 0;
b := 1;
N := 10;

ex1 := {
evalDG( d(x) = w1*e1 + w2*e2),
evalDG(d(e1) = w12*e2 + w13*e3),
evalDG(d(e2) = -w12*e1 + w23*e3),
evalDG(d(e3) = -w13*e1 - w23*e3)
};
ExteriorDerivative(ex1);


> ex1 := {evalDG(d(e1) = w12*e2+w13*e3), evalDG(d(e2) = -w12*e1+w23*e3), evalDG(d(e3) = -w13*e1-w23*e3), evalDG(d(x) = w1*e1+w2*e2)}; ExteriorDerivative(ex1);
{d(e1) = w12 e2 + w13 e3, d(e2) = -w12 e1 + w23 e3, d(e3) = -w13 e1 - w23 e3,

  d(x) = w1 e1 + w2 e2}

Could you give examples of differentiate differential form or integrate differential form using maple?

k := 1:
alpha := vector([x*cos(theta), x*sin(theta), k*x]);

e1 := map(diff, alpha, theta);
e2 := map(diff, alpha, x);

G := matrix([[simplify(e1[1]^2 + e1[2]^2 + e1[3]^2), 0],[0, simplify(e2[1]^2 + e2[2]^2 + e2[3]^2)]]);

inv_e1 := evalm(1/G[1,1]*e1);
inv_e2 := evalm(1/G[2,2]*e2);

e11 := map(diff, e1, theta);
e12 := map(diff, e1, x);
e22 := map(diff, e2, x);

gamma_1_11 := simplify(evalm(e11&*inv_e1));
gamma_1_12 := simplify(evalm(e12&*inv_e1));

How to interpolate in terms of any form of algebra in maple?

For example, to interpolate a time series in terms of exponential or mixed with cos and sin?

r := 1;
c := 1;
G := 1;
M := 1;
theta := 90;

ex1 := {
Diff(f1(t), t$2)
+ 2*(-G*M/(r*(-r*c^2+2*G*M)))*Diff(f(t), t1)*Diff(f2(t), t) = 0,

Diff(f2(t), t$2)
+ (-(-r*c^2+2*G*M)*G*M/(r^3*c^4))*Diff(f1(t), t)^2
+ (G*M/(r*(-r*c^2+2*G*M)))*Diff(f2(t), t$2)
+ ((-r*c^2+2*G*M)/c^2)*Diff(f3(t), t$2)
+ ((-r*c^2+2*G*M)*sin(theta)^2/c^2)*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)
+ (-sin(theta)*cos(theta))*Diff(f4(t), t)^2 = 0,

Diff(f3(t), t$2)

How to solve a set or a system of differential equations in maple for motion with Schwarzchild metric?

************** Schwarzchild metric *****************
with(tensor):
coord := [t, r, theta, Phi]:

g_compts:=array(symmetric,sparse,1..4,1..4):

g_compts[1,1]:=1 - 2*G*M/(r*c^2):
g_compts[2,2]:=-(1 - 2*G*M/(r*c^2))^(-1):
g_compts[3,3]:=-r^2:
g_compts[4,4]:=-(r^2)*sin(theta)^2:

g1 := create([-1,-1], eval(g_compts)):

alpha := vector([cos(theta), sin(theta), sin(k*theta)]);

alpha1 := map(diff, alpha, theta);
alpha11 := map(diff, alpha1, theta);

with(linalg):
cr := multiply(alpha1, alpha11)/simplify(multiply(alpha1, alpha1));

F := vector([0, 0, -m*g]);
c := multiply(F, alpha1/simplify(multiply(alpha1, alpha1)))/m;

motion := diff(f(theta), theta$2) + cr*diff(f(theta), theta)^2 = c;

pdsolve and dsolve not work, how to solve above motion equation with maple?

g(theta) := array([[cos(theta), -sin(theta)],[sin(theta), cos(theta)]]);
dg := map(diff, g(theta), theta);
invg := inverse(g(theta));
w := multiply(invg, dg);
w := map(simplify, w);

crossprod(-w, w); <- have error?

How to cross product between matrix?

As i know wedge product is cross product, so i use cross product