calculus

a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1].
i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral.

ii) Evaluate the integral ∫0,1+i z^2dz

iii) What is the relationship between the integrals in (i) and (ii)? Give reasons for your answer.

b) Use Green's Theorem to evaluate the integral
∮C (5 + 10xy + y^2)dx + (6xy + 5y^2)dy
where C is the rectangle with vertices (0, 0), (0, a), (b,a) and (b, 0) traversed counterclockwise.

c) Consider the contour γR(t) = Re^it, t ∈ [0, pi]. Show that
∫γR dz/(z^2 + 4) -> 0, as R -> infinity.

1. 👍 0
2. 👎 0
3. 👁 142
1. so, where do you get stuck? Surely your text discusses this topic.

1. 👍 0
2. 👎 0
posted by Steve
2. just wanted solutions and maybe working out as my previous year exams papers don't come with solutions. So I cant compare to see if I got it correct or not.

1. 👍 0
2. 👎 0
posted by jack

Similar Questions

1. 3 grade english ms sue

vowels: r-controlled riddle read a clud and write the list word. when you have written all seven word, the answer will appear in the boxes. THIRD,EARLY, WORLD, CERTAIN, DIRTY, HERSELF, EARTH, WORD, PERFECT, VERB, NERVE, WORM,

asked by dw on March 8, 2012
2. language

When you are interviewed, be relaxed and friendly. Write a thank-you note to the potential employer when the interview is over. The most effictive combination of sentences 10 and 11 would include which of the following groups of

asked by none on May 11, 2010
3. Math

When doing translation you have to write for example A(1,1) then when you write it you write A'(2,2) how would you write it to the fourth. Would you tally or do Roman numerals

asked by Neha on December 10, 2012
4. Math

Write 15% as a decimal 1.5 0.15•• 0.015 0.0015 Write 5.6 as a percent 56% 5.6% 560%•• 0.56% Write 0.5% as a fraction 1/2•• 1/20 1/200 1/500 Write 3 3/5 as a percent 360% 335%•• 36.0% 33.5%

asked by Estephania on January 15, 2016
5. Programming

Write a program (pseudocode) that would calculate and display the results for the multiplication table for values ranging from 1 to 100. This what I have so far: Declare X, Y, Z As Integer Write “10 x 10 Multiplication Table”

asked by Amanda on March 11, 2012
6. writing skills

Sentences 10 and 11:When you are interviewed, be relaxed and friendly. Write a thank-you note to the potential employer when the interview is over. The most effective combination of sentences 10 and 11 would include which of the

asked by ASIA on July 2, 2016
7. Maths

suppose function f,g,h and l are defined as follow:f(x)=4xsquared-5x+1,g(x)=-1/2x-3,h(x)=squared root(2-x)squared+1/2x,l(x)=square root2-x-3. .write down Df and solve inequality f(x)

asked by Joel on June 6, 2011
8. writing skills

6. Which of the following skills is most important in learning how to write? [A. Knowing how to plan before you write] B. Knowing proper grammar before you write C. Knowing proper punctuation before you write D. Knowing how to use

asked by jake on August 23, 2012
9. American Literature

I have to write a report on Mark Twain. I'm not suppose to write his biography. I'm supose to write about his works, achievements, impact on his readers, society, american literature, etc. I haven't been able to find too much,

asked by Jennifer on April 20, 2010
10. english

I have to write a paragraph which sustains an ironic tone. I have two thesis that I want to write about. (1)Being organized shows a lack of creativity. (2) Reading is a waste of time. I want to write about the first one. Please

asked by Maria on November 21, 2010
11. chemistry

when writing chemical equations, for example, next to oxygen I have to write (g) for gas and next to other different chemicals I have to write (aq) for aqueous. What do I write next to H2O?

asked by julie on January 8, 2008

More Similar Questions