# JNTUA B.TECH R 20 2-1 Syllabus For Complex variables, transforms & partial differential equations PDF 2022

February 11, 2022 2022-02-11 17:55## JNTUA B.TECH R 20 2-1 Syllabus For Complex variables, transforms & partial differential equations PDF 2022

# JNTUA B.TECH R 20 2-1 Syllabus For Complex variables, transforms & partial differential equations PDF 2022

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You will be able to find information about Complex variables, transforms & partial differential equations 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, transforms & partial differential equations after reading this blog. Complex variables, transforms & partial differential equations has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Complex variables, transforms & partial differential equations 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, transforms & partial differential equations are mentioned below in detail. If you are having a hard time understanding Complex variables, transforms & partial differential equations 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, transforms & partial differential equations 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 transformations (ez,, kz) Mobius transformations (bilinear) and their properties.

### Complex variables, transforms & partial differential equations 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, transforms & partial differential equations on Cynohub APP

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### Complex variables, transforms & partial differential equations 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 of transform –solving Initial value problems to ordinary differential equations with constant coefficients using Laplace transforms.

### Complex variables, transforms & partial differential equations 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 ofFourier series.

### Complex variables, transforms & partial differential equations Unit Five

#### Partial Differential Equations & Applications

Solution of second order PDEs by Method of separation of variables –Solutions of one dimensional wave equation, one dimensional heat equation under initial and boundary conditions. Steady state two dimensional heat equations (Laplace equations).

### Complex variables, transforms & partial differential equations Course Objectives

This course aims at providing the student to acquire the knowledge on the calculus of functions of complex variables. The aim is to analyze the solutions of partial differential equations.

### Complex variables, transforms & partial differential equations 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.•Evaluate the fourier series expansion of periodicfunctions.•Formulate/solve/classify the solutions of partial differential equations and also find the solution of one-dimensional wave equation and heat equation.

### Complex variables, transforms & partial differential equations Text Books

1.Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.

2.Advanced Engineering Mathematics, by Erwin Kreyszig, Wiley India

### Complex variables, transforms & partial differential equations Reference Books

1.Higher Engineering Mathematics, by B.V.Ramana, Mc Graw Hill publishers.

2.Advanced Engineering Mathematics, by Alan Jeffrey, Elsevier.

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Information about JNTUA B.Tech R 20 Complex variables, transforms & partial differential equations 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.