This book on Mathematics - IV covers the syllabus for the 2nd year 1st Semester course of B.E / B.Tech programmes offered by various major universities and autonomous colleges. It covers the following topics Functions of a Complex Variable, Complex Integration, Evaluation of Integrals, Fourier Series and Transforms and Applications of PDE.

Line integral, Cauchy’s integral theorem, Cauchy’s integral formula, and Generalized Cauchy’s integral formula, Power series: Taylor’s series- Laurent series, Singular points, isolated singular points, pole of order m – essential singularity, Residue, Cauchy Residue theorem (Without proof).

Types of real integrals:
a) Improper real integrals integer->infinity->(-infinity) f(x) dx
(b) Integer -> (c+2pi)->(c) f(cos-theta sin- heta) d heta
Bilinear transformation- fixed point- cross ratio- properties- invariance of circles.

Introduction, Periodic functions, Fourier series of periodic function, Dirichlet’s conditions, Even and odd functions, Change of interval, Half range sine and cosine series. Fourier integral theorem (without proof), Fourier sine and cosine integrals, sine and cosine, transforms, properties, inverse transforms, Finite Fourier transforms.