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• Users: greisen
• In Calculus and Beyond Homework Help
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1. Derivate of generalized function

Hi, I have to show that if the derivate f'(x) of a generalized function f(x) is defined by the sequence f'_n(x) where f(x) is defined f_n(x)[\tex] then \int_{-\infty}^{\infty}f'(x)F(x) dx = - \int_{-\infty}^{\infty}f(x)F'(x) dx I use the limits for generalized functions and...
2. Write as sum of real and imaginary part

Hi, I have to write the 1/(a+ib) as a sum of a real part and an imaginary part. I was thinking of using the complex conjugate (a-ib) and multiply with this (a-ib) / (a^2 + b^2) I am a little bit lost on what to do next - any help appreciated thanks in advance Best
3. Find a general formula

Thanks yes I have tried integration by parts but that got very messy. I don't quite understand how to rewrite the equation involving the anti-derivative? Best,
4. Find a general formula

Hi, I have to find a general formula for the function 1/(2n)!\int_{-\inf}^{\inf}x^{2n}*e^{-ax^2} I am a little bit lost in how to proceed - any hints appreciated thanks in advance
5. Coordinate transformation and multiplying with size of J

Hi, So if I transform and the volume of the transform is preserved the size of |J| is one?
6. Coordinate transformation and multiplying with size of J

Hi, I am using the book "Advanced Engineering Mathematics" by Erwin Kreyszig where I am reading on the transformation of coordinates - when changing from \int f(x,y) to \int f(v(x,y),v(x,y) it is necessary to multiply with the size of the jacobian, |J| - I cannot find the proof in the book...
7. Eigenvector and eigenvalues

to see if I understand correctly - let's assume that the matrix A har the eigenvalues {1,2,2} and the matrix B has the eigenvalues {-1,1,1} - then it is possible to construct the eigenvectors of B according to the common unique pairs of A and B( (1,1),(2,1),(2,-1)) giving the following...
8. Differential Equations.

Have you tried to solve the equation directly y'' = -k^2*cos(kt) y = cos(kt) than you get two values of k +/-.
9. Eigenvector and eigenvalues

Sorry not H but A the same matrix
10. Eigenvector and eigenvalues

Hey all, I have two matrices A,B which commute than I have to show that these eigenvectors provide a unique classification of the eigenvectors of H? From these pairs of eigenvalue is it possible to obtain the eigenvectors? I don't quite know how to procede any suggestions? Thanks...
11. Elementary matrix

I don't know if I understand you correctly M will be 3x2 matrix and EM will 2x2 matrix where with a summation of the each row in M - a(11) summation of first row and a(12) of second row. Rest will be zero
12. Linear Algebra

hey rigth method but wrong eigenvalues P = 1/sqrt(2) [i -1;i 1] this will help