Purchase Solution

Integration using residues

Not what you're looking for?

Ask Custom Question

I want to find the Cauchy value by using residues. (See attached file for full problem description)

Attachments
Purchase this Solution
Solution Summary

The integration using residues applications are determined.

Solution Preview

Please see the attached file.

Consider

∫ ___dz__ = ∫ f(z) dz
C (z+1)^2 + 1 C

Where C is the contour consisting of the semi circle CR of radius R together with the part of the real axis from -R to R as shown below

The integrand has two simple poles -i-1, i-1 of which i-1 only lies inside the circle C
Therefore ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

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

Graphs and Functions

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

Exponential Expressions

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

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

  • Residues Theorem and Integration

    517462 Residues Theorem and Integration of the function 1/(1+x^2) Using the Residues Theorem, calculate the following: Integral limits between negative infinity and positive infinity [dx/(1+x^2)].

  • Solution to the steady state load-deflection equation.

    One is obviously k=0 and the others are the roots of the equation: The roots can be obtained using: Hence: An on the complex plane the poles and the integration contours are: The values of the residues at

  • Residues / Integrals - Complex Analysis : integral from 0 to pi/2 of ( d theta/ ( a + sin^2 theta) ) = pi/2[a(a+1)]^1/2 if a > 0.

    Residue Theory Many real integrals can be evaluated using integration within the complex plane using the astonishing result that: That is, integrating f(z) around a closed loop in the complex plane results in a value which is

  • Integration using residues

    79960 Integration using residues applications Application of Residue theorem. See attached file for full problem description. Please see the attached file.

  • Inverse Fourier Transform

    This means that the direction of integration is clockwise, and opposite to the normal way for contour integration. this leads to a negative sign before the sum of the residues. 2.

  • Solve: Communications Systems

    We will apply the complex integration residue theorem by which, h(n) = Summation[residues of h(z)z^(n-1) enclosed in the unit circle = Summation[residues of z^n*(z+2)/[{z+(1/2^0.5)}*{z-(1/2^0.5)}] enclosed in the unit circle) h(z) has poles at z

  • Calculus

    Using contour integration and calculus of residues, find the sum Summation (going from 0 to infinity) 1/n^2 +a^2 4. Let Sinz = z-z^3/3! +z^5/5!-----------+ (-1)^2n+1(z)^2n+1/(2n+1)!

  • Amino acids produced using fixed proportions of nucleotide residues

    see attachment 'Identifying amino acids produced using fixed proportions of nucleotide residues' Identifying amino acids produced using fixed proportions of nucleotide residues Sol: The ratio of proline, serine, leucine and phenylalanine would be

  • Fourier Transforms and Convolution Theorem

    Thanks for using BrainMass.

View More Related Solutions