24,907

The Homework Library (HL) is a database of solved problems.

HL materials are not original and are therefore made available for the sole purpose of studying and learning.
**Misuse of HL materials is strictly forbidden.**

The HL was created for students who need immediate help, and in many cases you can find step-by-step
explanations on how to solve a problem or examples of proper writing, including the use of citations,
references, bibliographies, and formatting.

If you donâ€™t find what you are looking for within our HL database, please reach out to one of our tutors
and schedule a tutoring session.

1. (a) (i) State the Cauchy-Riemann equations. (ii) Verify...

1. (a) (i) State the Cauchy-Riemann equations. (ii) Verify them for the function f : C C defined by 4v/2. (10) (b) (i) State the definition of a bounded set in C. (ii) State the definition of a compact set in C. (10) (c) Find the radius of convergence of the following series: 3 zn 3n + ...

Question: When evaluating integrals of real functions of th...

Question: When evaluating integrals of real functions of the type f(x) cos (ax) from 0 to infinity, why we cannot simply do contour integration by using the function f(z) cos (ax)? Provide some examples to evaluate some real integrals of this type (show all the works)?

Complex Analysis 1 What is a residue? Why do we care? 2 Fo...

Complex Analysis 1 What is a residue? Why do we care? 2 For what functions can we use residues to calculate their integral on the real line?(Notice this is an example of how the study of the complex plane gives profound insight into calculations with purely real numbers.) 3 What is a Fourier tr...

Complex Variables Practice Problems 1. 9 marks| Let f(x ig...

Complex Variables Practice Problems 1. 9 marks| Let f(x ig =corcoshy-isinrsinhy. - By choosing and parameterising an appropriate (potentially only piecewise-smooth) curve, determine the function = Explain why the result does not depend on your choice of curve. 2. 19 marks Using the Cauchy in...

(a) Evaluate the contour integral (oriented counter clock-wi...

(a) Evaluate the contour integral (oriented counter clock-wise): 210z³-9z Log + 4) dz |z|=3 (z-1)(z+4+5i) - (b) Determine the domain of analyticity of f(z) = Log(z + 4 - i) and explain why? & f '(z) dz = 0 2/=2 (c Find the value of Log (z) dz, where the integral is along a con...

1. (10pts) Show that u(z,y) = e-3r cos 3y is harmonic and fi...

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) F...

True/False justify with a few sentences. If false, give a c...

True/False justify with a few sentences. If false, give a counterexample and justify why it is a counterexample with a few sentences. 1. If 4(X,Y) is a harmonic function and v(x,Y) is its harmonic conjugate, then 42-v2 is also harmonic. 2. If C is the unit circle traversed clockwise, and f(z) i...

Use the field and subject filters to browse through Homework Library solutions that pertain to your areas of interest. We are adding new content to the library on a daily basis, so check back from time to time. If you'd like us to post solutions in a subject we don't yet have content for, let us know - we'd like to hear from you!

The solutions will include information such as the original question and sometimes a preview of the solution itself. When you are ready to purchase a solution just click on it and it will be yours.

There is no time limit. Once you purchase a solution you'll have access to it for as long as your registration on the site remains valid. If you can log into your account, you can view any purchased solutions.