Sujaan Kunalan

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These are questions asked by Sujaan Kunalan

I would like to use Newton's Method (the multivariate one) in order to solve a system of equations. From what I understand, fsolve is essentially MAPLE's version of the multivariate Newton's Method. Is there a way to do the multivariate Newton's method any other way, other than fsolve? Also, is there a way to specify our own initial guess and tolerance for the Newton's Method and to get other details such as the number of iterations?

I wish to use closed Newton-Cotes with n=2, also known as Simpson's Rule to numerically integrate an improper integral.


If it matters the integrand is (cos(2x))/(x^1/3), integrating between x=0..1

I've tried a few different (but similar) code but to no avail. Here is some stuff I've tried:





with(Student[Calculus 1]):

Simp1 := ApproximateInt(cos(2*x)/x^(1/3), x = 0 .. 1, method = newtoncotes[2]);


This gives me an output message that says "Float(infinity)".




with(Student[Calculus 1]):

Simp2 := int(exp(-x)/sqrt(1-x), x = 0 .. 1);


This doesn't have Simpson's rule as an option.


I think I'm on the right track with my first try, since I guess it wasn't tecnically an error message, but I'm not sure how to alter the code accordingly to get a numerical value instead. Thanks for any help.







I am trying to numerically double integrate x^2+sqrt(y), with the bounds y=0..x and x=1..1.5.

Then I tried the following code:




I know how to write the code if instead of a 'x' in my upper limit for my integral, I had a real number, but I'm not sure how to remedy to code in order make it work. Any help would be appreciated. Thanks!


I have a coefficient matrix A and the constant matrix b.

I want to find the unknowns x_1,x_2,...,x_8. When I put my code and run it in Maple I get an error. Any ideas as to why this is happening? The code I tried is as follows:




A := Matrix([[-1, 0, 0, (1/2)*sqrt(2), 1, 0, 0, 0], [0, -1, 0, (1/2)*sqrt(2), 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 1/2, 0], [0, 0, 0, -(1/2)*sqrt(2), 0, -1, -1/2, 0], [0, 0, 0, 0, -1, 0, 0, 1], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, -(1/2)*sqrt(2), 0, 0, (1/2)*sqrt(3), 0], [0, 0, 0, 0, 0, 0, -(1/2)*sqrt(3), -1]]);

b := Vector([0, 0, 0, 0, 0, 10000, 0, 0]);

LinearSolve(A, b, maxiterations = 300, method = SOR(1.25), tolerance = 10^(-2));


I also tried it with a SOR variable of 1.5 instead of 1.25, but that gives me the same error.

Is there a way to do the following on Maple:

I want Maple to use Jacobi's method to give an approximation of the solution to the following linear system, with a tolerance of 10^(-2) and with a maximum iteration count of 300.


The linear system is






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