Purchase Solution

Fourier Series of a Periodic Fuction : Convergence

Not what you're looking for?

Ask Custom Question

Work out the Fourier series of f, given over one period as follows.
At which values of x does the series fail to converge to f(x)? To what values does it converge at those points?

(h) |cos x| for all x
(k) x on 0<x<1, 1<x<2.

See the attached file.

Attachments
Purchase this Solution
Solution Summary

Convergence of Fourier Series of Periodic Fuctions is investigated. The solution is detailed and well presented.

Solution Preview

Please see the attached file for the complete solution.

Solution. By a theorem which states, if y=f(x) is a periodic function and y=f(x) is continuous at x=a, then its Fouries series converges to x=a; if y=f(x) is NOT continuous at x=b, then its Fouries series fails to converge to x=b. So,

(a) Its Fourier series converges to all points in and ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Fourier series

    348307 Dirichlet's Test for Convergence of a Series Verify that (1/2i)sum {(e^(inx))/n} (where n does not equal zero in the sum) is the Fourier series of the 2 Pi periodic function defined by f(0)=0 and f(x)=-Pi/2-x/2 for between -pi and 0 and f(x

  • Wave equation

    Second, I want to point out that when is an odd periodic function on R, then its Fourier Series is of the form ( By Fourier Convergence Theorem) ( is continuous at x) where (since is an odd function over [-L,L

  • Fourier Series Expansion

    ): For 30 terms it looks like: And after 100 terms we see a good convergence except at the points of discontinuity where we see the manifestation of the Gibbs phenomenon The 5 pages solution includes all derivations needed to find the Fouriere

  • Express Fourier series in sine-cosine form and complex form and find convergence.

    A Fourier series iis expressed in sine-cosine form and complex form and the convergence is found. The solution is detailed and well presented.

  • Fourier Series of the Periodic Function

    30765 Fourier Series of the Periodic Function The answer is provided - please provide step by step work and explaination and solution. 4. Find the Fourier series of the periodic function attached...

  • Fourier Series and Convergence

    A Fourier Series and Convergence are investigated. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.

  • Finding Values Using Dirichlet's theorem

    series are periodic , we know the Fourier series converges to.

  • Partial Sums of Fourier Series

    This solution shows how to calculate the partial sums of a Fourier series of a given periodic function. The solution is provided within an attached pdf. file.

  • Fourier Series Expansions : Periodic Functions, Graphing and Finding Terms

    58188 Fourier Series Expansions : Periodic Functions, Graphing and Finding Terms Find the first four terms of the Fourier series expansion of the function f(x) = (1 - (x^2/pi^2))per on the interval (-pi, pi).

View More Related Solutions