QuestionQuestion

Transcribed TextTranscribed Text

1. (10pts) Show that u(z,y) = e-3r cos 3y is harmonic and find a harmonic conjugate. 2. (10pts) Find a biholomorphic map between the unit disk A and the region = 3. (20pts) Let a € C be a constant. (a) Find the inverse Laplace transform of F(8)= 3+28 using the Bromwich integral. (b) Find the inverse Laplace transform of 1 s+a using the Bromwich integral. (c) Find the inverse Laplace transform of 1 F(s) (s+a)² using the Bromwich integral. (d) Decompose the rational function 1 s+2s²+s into principal parts and use this together with (b) and (c) to find the inverse Laplace transform. 4. (20pts) Show that do dx = where O and 1 if>>0 sgn = -1 if < < 0. (Hint: First do the case a > 0 and 8>0.) 5. (20pts) Compute .° where a € (-1,1). 1 6. (20pts) Show that the equation Z4 + z+1 = 0 has one solution in each quadrant. Prove that all solutions lie inside the open disk [zec1121<21 2

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    50% discount

    Hours
    Minutes
    Seconds
    $35.00 $17.50
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Complex Analysis Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats