QUESTION Let f(2)= 1 +3:+5 (2²+9) cos(4) (1.1) Find the zeros of cos(4). You may use what is known about the zeros of cos z. (1.2) Evaluate [ƒ(2)dz, where C : |2 - 1] = 1. Write your answer in the form a + ib. (1.3) Evaluate [ƒ(2)dz, where C : |2 - i| = 3. Write your answer in the form a + ib. (1.4) For the integral [ƒ(z)dz, where C : [2] = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.
QUESTION Let f(2)= 1 +3:+5 (2²+9) cos(4) (1.1) Find the zeros of cos(4). You may use what is known about the zeros of cos z. (1.2) Evaluate [ƒ(2)dz, where C : |2 - 1] = 1. Write your answer in the form a + ib. (1.3) Evaluate [ƒ(2)dz, where C : |2 - i| = 3. Write your answer in the form a + ib. (1.4) For the integral [ƒ(z)dz, where C : [2] = 4, draw the contour with the singularities. DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the theorems you will use. You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you have used the zeros of cos() to evaluate the contour integrals. You may use the fact that > 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:QUESTION 1
z²+3z +5
Let f(2)= (2²+9) cos()
(1.1) Find the zeros of cos(). You may use what is known about the zeros of cos z.
Jo
f(z)dz, where C:|z1|= 1. Write your answer in the form a + ib.
(1.2) Evaluate
•Jose
f(z)dz, where C: z-i = 3. Write your answer in the form a + ib.
(1.3) Evaluate
(1.4) For the integral [ƒ(2)dz, where C : |Z| = 4, draw the contour with the singularities.
DO NOT EVALUATE THE INTEGRAL, but explain what you would do and quote the
theorems you will use.
You may use one or all of the following theorems: Cauchy-Goursat Theorem, Cauchy's Integral
Formulae and the Deformation Corollaries. You must sketch C in each case. Explain how you
have used the zeros of cos() to evaluate the contour integrals.
You may use the fact that > 3.
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