 # JNTUA B.TECH R 20 2-4 Syllabus For Complex variables and transforms PDF 2022

### Get Complete Lecture Notes for Complex variables and transforms on Cynohub APP  You will be able to find information about Complex variables and transforms along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Complex variables and transforms after reading this blog. Complex variables and transforms has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Complex variables and transforms can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

All of the Topic and subtopics related to Complex variables and transforms are mentioned below in detail. If you are having a hard time understanding Complex variables and transforms or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.

### Complex variables and transforms Unit One

#### Complex Variable –Differentiation:

Introduction to functions of complex variable-concept of Limit & continuity-Differentiation, Cauchy-Riemann equations, analytic functions (exponential, trigonometric, logarithm), harmonic functions, finding harmonic conjugate-construction of analytic function by Milne Thomson method-Conformal mappings-standard and special transformations (sin z, ez, cos z, z2) Mobius transformations (bilinear) and their properties.

### Complex variables and transforms Unit Two

#### Complex Variable –Integration:

Line integral-Contour integration, Cauchy’s integral theorem, Cauchy Integral formula, Liouville’s theorem(without proof) and Maximum-Modulus theorem (without proof);power series expansions: Taylor’s series, zeros of analytic functions, singularities, Laurent’s series; Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral involving sine and cosine, Evaluation of certain improper integrals (around unit circle, semi circle with f(z) not having poles on real axis).

### Get Complete Lecture Notes for Complex variables and transforms on Cynohub APP  ### Complex variables and transforms Unit Three

#### Laplace Transforms

Definition-Laplace transform of standard functions-existence of Laplace Transform –Inverse transform –First shifting Theorem, Transforms of derivatives and integrals –Unit step function –Second shifting theorem –Dirac’s delta function –Convolution theorem –Laplace transform of Periodic function. Differentiation and integration oftransform –solving Initial value problems to ordinary differential equations with constant coefficients using Laplace transforms.

### Complex variables and transforms Unit Four

#### Fourier series

Determination of Fourier coefficients (Euler’s) –Dirichlet conditions for the existence of Fourier series –functions having discontinuity-Fourier series of Even and odd functions –Fourier series in an arbitrary interval –Half-range Fourier sine and cosine expansions-typical wave forms -Parseval’s formula-Complex form of Fourier series.

### Complex variables and transforms Unit Five

#### Fourier transforms & Z Transforms:

Fourier integral theorem (without proof) –Fourier sine and cosine integrals-complex form of Fourier integral. Fourier transform –Fourier sine and cosine transforms –Properties –Inverse transforms –convolution theorem .Z-transform –Inverse z-transform –Properties –Damping rule –Shifting rule –Initial and final value theorems. Convolution theorem –Solution of difference equations by z-transforms.

### Complex variables and transforms Course Objectives

This course aims at providing the student to acquire the knowledge on the calculus of functions of complex variables. The student develops the idea of using continuous/discrete transforms.

### Complex variables and transforms Course Outcomes

Understand the analyticity of complex functions and conformal mappings.Apply cauchy’s integral formula and cauchy’s integral theorem to evaluate improper integrals along contours.Understand the usage of laplace transforms, fourier transforms and z transforms.Evaluate the fourier series expansion of periodic functions.Understand the use of fourier transforms and apply z transforms to solve difference equations.

### Complex variables and transforms Text Books

1.Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.2.Advanced Engineering Mathematics, by Erwin Kreyszig, Wiley India

### Complex variables and transforms Reference Books

1.Higher Engineering Mathematics, by B.V.Ramana, Mc Graw Hill publishers.2.Advanced Engineering Mathematics, by Alan Jeffrey, Elsevier.

### Scoring Marks in Complex variables and transforms

Information about JNTUA B.Tech R 20 Complex variables and transforms was provided in detail in this article. To know more about the syllabus of other Engineering Subjects of JNTUH check out the official CynoHub application. Click below to download the CynoHub application.

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