A BRIEF VIEW ABOUT COMPLEX ANALYSIS IN MATHEMATICS

MATHEMATICS

Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are generally supposed to have a domain that contains a nonempty open subset of the complex plane. Complex Analysis, is divided into four blocks, which are further subdivided into fourteen units. This book provides a basic understanding of the subject and helps to grasp its fundamentals. In a nutshell, it explains various aspects, such as complex numbers, geometric representation of a complex number, the spherical representation and stereographic projection, complex analytic function, complex differentiation, the Cauchy-Riemann equations, orthogonal trajectories and harmonic functions, Milne-Thomson method, power series, radius of convergence, Complex analysis is full of amazingly beautiful theorems that have no analogue in standard calculus. For instance, if you know the value of a real-valued function on some circle in the plane, that is not enough to determine its value at any point in the interior. Yet, for complex differentiable functions, this is sufficient, thanks to the delightful.

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