1) Consider the followin Integral:

int(cosh(a*x)*cos(b*x),x)

How can I tell maple to give the results in terms of hyperbolic and harmonic funtions?
The maple returns the answer in term of exponentials with imaginary powers.
Also, I could not use the "simplify" command to turn the answer returned by maple into an answer in terms of what I want! Please see the code below.


2) Is there a way that I can update the maple integration database manaully?

Example.mw

Consider the following sum:


We know that if k is between 1 and N, the result will be



and otherwise the sum is zero.

How can I tell maple to compute this sum in each case without giving numerical values to the parameters "N" and "k"?

Thanks. :)

I want to draw a contour plot like the pic below which the relating value of each curve is specified on several parts of the curve. Can anyone suggest a way? :)

As an example do it with the following function:

f(x,y)=x^2+y^2-5

I have a complicated equation which you can find in the file below. I want to multiply both sides of equaiton by cos(beta[1,j__1]*z) and integrate from 1 to L. I have many such similar equations so I decided to write a procedure to do these staffs for me.

Can you give me simple suggestions on how to write such a procedure. The procedure will take the "equation", "multiplier" and "limits of integration" as inputs and gives the "integrated equation" as the output. Integration is perfomed by the inert function "Int".

Many thanks.

Equation.mw

Consider the following two variable funtion:

f(x,y)=x^2+y^2-5

then we want to draw a contourplot:

contourplot(f,x=-10..10,y=-10..100)

My problem is that I want maple to diplay the value of the function "f" relating to each curve on the contour plot!
How can I do this?

Please see the following code.

Example.mw