Purchase Solution

Two examples using Fourier transforms

Not what you're looking for?

Ask Custom Question

1. Find the Fourier sine series of f(x)=1, 0<x<L/2. Use this to prove that 1-1/3+1/5-1/7+...=Pi/4

2. Solve df/dt=d^2 f/dx^2 - f subject to the initial condition f(0,x)=1 if |x|<L/2 or f(0,x)=0 if |x|>L/2

Please see the attachment to view the questions with correct mathematical notation (and also phrased slightly differently)

Purchase this Solution

Solution Summary

Working with Fourier transforms and Fourier series is an extremely important technique in applied mathematics. This solution contains two questions; the first is a simple example of finding a Fourier series, then using this series to find the exact value of an infinite sum (a remarkable and beautiful application of Fourier series). The second shows how inverse Fourier transforms can be used to find solutions of PDEs. The solution is a 2 page Word document with equations written using Mathtype. Each step is explained.

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Multiplying Complex Numbers

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

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.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.