Mathematics Homework Solutions

Solving for Fourier Coefficients

Please see the attached file for the fully formatted problems. Define periodic p=2 function as follows: f(x) = -exp(x) -1

Find the Fourier Series Coefficients.

I have attached two files one being the sketch of the problem and the other containing the questions. Let function f(x) be as sketched. Solve for the fourier series coefficients....

Are the following functions even, odd or neither?

Please see the attached file for the fully formatted problems. Are the following functions even, odd or neither? 1. sin(x) 2. (x^2+1)*sin(x) 3. exp(-x)*cos(x) 4. exp -(|x|)cos(x)

Periodic Function : Solve the Fourier Series

Please see the attached file for the fully formatted problems. See f(x) in the file. 1. sketch f(x) over -3

Fourier Series

I am looking for help with ONLY QUESTION #4 on the pdf file with the questions on it. I have included 3 pdf files that contain notes on how to find the order of coefficients. Also, the average value of g(x) can be found from this link: http://www.efunda.com/math/fourier_series/fourier_series.cfm

1-D Wave Equation with Friction and Free Ends

I have posted a 1-D Wave equation with friction and free ends problem that I could use help with. I have included one pdf file that contains the question, which has parts a-e. Also included are pdf files that contain notes on how to solve a 1-D Wave equation problem, an example of solving one with free-ends and a summary of the ...continues

Wave Equation and Sturm-Liouville Problem with Application to Rayleigh Quotient

I have included a Wave Equation problem with parts a-c, that has variable tension. It involves seperation of variables, the Sturm-Liouville system, and an application to the "Rayleigh Quotient" involving the Eigenvalues. I have included notes on the Sturm-Liouville system with examples and properties. Please refer to these notes ...continues

Geometric Series of a Complex Function

I have the solution to my problem. I just need to understand why it is the solution. I need a step by step outline of how we derive the answer. Please see the attached document.

Fourier Analysis and Rayleigh Quotient

I have posted a total of four questions as well as the "Rayleigh Quotient" that is referenced in problem # 4 part c. Please see the attached files for the fully formatted problems.

Find the fundamental period for this function ...

Find the fundamental period for this function. The function is x(t)= 1 + sin(20t) + cos(30t+(pi/3))

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