 # JNTUH R18 B.Tech Laplace Transforms, Numerical Methods And Complex Variables 2022

You will be able to find information about Laplace Transforms, Numerical Methods And Complex Variables 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 Laplace Transforms, Numerical Methods And Complex Variables after reading this blog. Laplace Transforms, Numerical Methods And Complex Variables has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Laplace Transforms, Numerical Methods And Complex Variables 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 Laplace Transforms, Numerical Methods And Complex Variables are mentioned below in detail. If you are having a hard time understanding Laplace Transforms, Numerical Methods And Complex Variables 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.

## Laplace Transforms, Numerical Methods And Complex Variables Unit 1

Laplace Transforms: Laplace Transforms; Laplace Transform of standard functions; first shifting theorem; Laplace transforms of functions when they are multiplied and divided by‘t’. Laplace transforms of derivatives and integrals of function; Evaluation of integrals by Laplace transforms; Laplace transforms of Special functions; Laplace transform of periodic functions.

Inverse Laplace transform by different methods, convolution theorem (without Proof), solving ODEs by Laplace Transform method.

## Laplace Transforms, Numerical Methods And Complex Variables Unit 2

Numerical Methods – I: Solution of polynomial and transcendental equations – Bisection method, Iteration Method, Newton-Raphson method and Regula-Falsi method. Finite differences- forward differences- backward differences-central differences-symbolic relations and separation of symbols; Interpolation using Newton’s forward and backward difference formulae. Central difference interpolation: Gauss’s forward and backward formulae; Lagrange’s method of interpolation.

## Laplace Transforms, Numerical Methods And Complex Variables Unit 3

Numerical Methods – II: Numerical integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules. Ordinary differential equations: Taylor’s series; Picard’s method; Euler and modified Euler’s methods; Runge-Kutta method of fourth order.

## Laplace Transforms, Numerical Methods And Complex Variables Unit 4

Complex Variables (Differentiation): Limit, Continuity and Differentiation of Complex functions. Cauchy-Riemann equations (without proof), Milne- Thomson methods, analytic functions, harmonic functions, finding harmonic conjugate; elementary analytic functions (exponential, trigonometric, logarithm) and their properties.

## Laplace Transforms, Numerical Methods And Complex Variables Unit 5

Complex Variables (Integration): Line integrals, Cauchy’s theorem, Cauchy’s Integral formula, Liouville’s theorem, Maximum-Modulus theorem (All theorems without proof); zeros of analytic functions, singularities, Taylor’s series, Laurent’s series; Residues, Cauchy Residue theorem (without proof).

## Laplace Transforms, Numerical Methods And Complex Variables course objectives:

• Concept, properties of Laplace transforms
• Solving ordinary differential equations using Laplace transforms techniques.
• Various methods to the find roots of an equation.
• Concept of finite differences and to estimate the value for the given data using interpolation.
• Evaluation of integrals using numerical techniques
• Solving ordinary differential equations using numerical techniques.
• Differentiation and integration of complex valued functions.
• Evaluation of integrals using Cauchy’s integral formula and Cauchy’s residue theorem.
• Expansion of complex functions using Taylor’s and Laurent’s series.

## Laplace Transforms, Numerical Methods And Complex Variables course outcomes:

After learning the contents of this paper the student must be able to

• Use the Laplace transforms techniques for solving ODE’s
• Find the root of a given equation.
• Estimate the value for the given data using interpolation
• Find the numerical solutions for a given ODE’s
• Analyze the complex function with reference to their analyticity, integration using Cauchy’s integral and residue theorems
• Taylor’s and Laurent’s series expansions of complex function.

## Laplace Transforms, Numerical Methods And Complex Variables reference books:

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010.
2. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4th Edition, 2005.
3.     J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Mc-Graw Hill, 2004.
4. M. K. Jain, SRK Iyengar, R.K. Jain, Numerical methods for Scientific and Engineering Computations, New Age International publishers.
5. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons,2006.

## Scoring Marks in Laplace Transforms, Numerical Methods And Complex Variables

Information about JNTUH B.tech R20 Laplace Transforms, Numerical Methods And Complex Variables 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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