Contour Integral, Where am I going wrong?

In summary, the person is seeking help with a math problem from their book, but despite going over it multiple times, they cannot find their mistake. They are looking for suggestions and the correct answer is supposed to be 2Pi/9.
  • #1
BigFlorida
41
1
Misplaced in a math technical section before being moved by mentor
So, my book (Mathematical Methods in the Physical Sciences 3rd ed by Boas) proposed a problem that I have really been struggling with:
IMG_20160117_112504263_HDR.jpg
IMG_20160117_112510854_HDR.jpg


I know it is probably just an algebra mistake, but I have gone over it multiple times and cannot seem to find my mistake. Any ideas? The answer is supposed to be 2Pi/9.
Thank you in advance for any help.
 
Physics news on Phys.org
  • #2
BigFlorida said:
So, my book (Mathematical Methods in the Physical Sciences 3rd ed by Boas) proposed a problem that I have really been struggling with:
View attachment 94420 View attachment 94421

I know it is probably just an algebra mistake, but I have gone over it multiple times and cannot seem to find my mistake. Any ideas? The answer is supposed to be 2Pi/9.
Thank you in advance for any help.

The image is too small and blurry to make out properly, so I will not even try. Why don't you do what others here do, and type it out?
 
  • Like
Likes vela and fresh_42

1. What is a contour integral?

A contour integral, also known as a path integral, is an extension of a regular integral in calculus to complex functions. It involves integrating a function along a path or contour on a complex plane.

2. How is a contour integral different from a regular integral?

A contour integral involves integrating a function along a path on a complex plane, while a regular integral involves integrating a function over an interval on a real number line. Additionally, a contour integral involves the use of complex numbers, while a regular integral uses only real numbers.

3. What is the significance of contour integrals?

Contour integrals are important in complex analysis and have many applications in physics, engineering, and other fields. They are used to solve difficult integrals, evaluate complex functions, and study the behavior of functions on a complex plane.

4. How do I know if I am doing a contour integral correctly?

To ensure that you are doing a contour integral correctly, you should follow the steps of the Cauchy's integral formula and use the Cauchy-Riemann equations to check for differentiability. It is also important to choose the correct contour and understand the properties of the function being integrated.

5. What are some common mistakes when working with contour integrals?

Some common mistakes when working with contour integrals include choosing the wrong contour, not understanding the function being integrated, and not following the proper steps of the Cauchy's integral formula. It is also important to be careful with the orientation of the contour and to use the correct branch of the function if it is multivalued.

Similar threads

Using Contour Integration with no singularity
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Contour Integration: Branch cuts
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
How Does the Sinc Function Integral Relate to Quantum Collision Theory?
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
Contour integration with a branch cut
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
Fresnel Integrals, Contour Integration
    • Calculus and Beyond Homework Help
Replies
4
Views
2K
Contour integration by parametisation
    • Calculus and Beyond Homework Help
Replies
1
Views
884
Contour integral along the imaginary axis
    • Calculus and Beyond Homework Help
Replies
6
Views
5K
Find, using complex contour integrals, the function f(x)....
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Determining Cauchy principal value of divergent integrals
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Complex analysis integral
    • Calculus and Beyond Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top