Exam (elaborations)
MAT3705 Assignment 4 Semester 2 2023
- Course
- Institution
MAT3705 Assignment 4 Semester % TRUSTED workings with detailed Answers for A+ Grade.
[Show more]
Seller
Follow
StudyStore
Reviews received
Content preview
MAT3705ASSIGNMENT 4 2023
, MAT3705 - 2023
Assignment 04
Chapters 6 and 7
Due date: 24 August 2023
Please note:
No typed solutions will be accepted. Only handwritten assignments will be accepted. Please scan your
solutions and upload them as a single pdf on the mymodules page.
Please make sure that you submit the correct file on the MAT3705 mymodules page. No changes will be
allowed after the closing date. No e-mailed solutions will be accepted.
Your submission has to be your own work. Copying answers, using answers from the internet, buying
solutions, etc. are academic offences and detrimental to your own learning.
You have three weeks to submit your solutions.For this reason, loadshedding and technical difficulties will
not be considered valid excuses for failing to submit.
This assignment has 2 pages and 6 questions.Please make sure that you answer all questions.
Questions:
1. Let f (z) = cos (π/z).
(a) Write down the Laurent series of f about the point z = 0 and specify the region of validity.
(b) Describe why z = 0 is an isolated singularity of f .
(c) What type of isolated singularity is z = 0?
(d) Use the definition of a residue to calculate the residue of f at the point z = 0.
z+2
2. Let g(z) = .
(z 2 + 1)(z − i)
(a) Locate and classify all the isolated singularities of g and compute the residues at each of these singu-
larities. Provide motivations for your answers.
(b) Let C denote the positively oriented contour C = {z ∈ C : |z − i| = 3}. Use Cauchy’s Residue
R
Theorem to calculate C g(z) dz.
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyStore. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.71. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
80630 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now