The theory of functions of a complex variable plays an increasingly important part in the applications of mathematics to physical problems.

This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

Section 1.1 (Page 4): 3,4, 5(a),6(b),7(c)8-16,18,22-23. Turn in: 22,23 Section 1.2 (Page 12): 3-5, 7(a)-(d), 8-11,13-14. Turn in: 7,13 Section 1.3 (Page 22): 2,5,6, 7 ...

Complex variables are used throughout this part of the paper, and the problem is reduced to the determination of four canonical functions of a complex variable, these functions being the solutions of ...

Some Julia Sets Julia sets are defined by iterating a function (of a complex variable). Pick a point in the complex plane (i.e., a complex number; these can be represented as a point z= (x,y) in the ...

The course will cover the fundamental concepts and methods in complex analysis. The basic objects of study in the course will be complex differentiable functions in domains, and the far-reaching ...

This paper is concerned with the determination of tight lower and upper bounds on the expectation of a convex function of a random variable. The classic bounds are those of Jensen and ...

WHAT is the theory of functions about? This question may be heard now and again from a mathematical student; and if, by way of a pattial reply, it be said that the elements of the theory of ...