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 ...

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 ...