# MA401BS: Laplace Transforms, Numerical Methods and Complex Variables EIE Syllabus for B.Tech 2nd Year 2nd Sem R18 Regulation JNTUH

Laplace Transforms, Numerical Methods and Complex Variables detailed syllabus for Electronics & Instrumentation Engineering (EIE), 2nd Year 2nd Sem R18 regulation has been taken from the JNTUH official website and presented for the B.Tech students affiliated to JNTUH course structure. For Course Code, Subject Names, Theory Lectures, Tutorial, Practical/Drawing, Credits, and other information do visit full semester subjects post given below. We make sure the result links and syllabus uploaded here is latest and up to date, also the syllabus PDF files can also be downloaded from the universities official website.

For Electronics & Instrumentation Engineering (EIE) 2nd Year 2nd Sem R18 Regulation Scheme, do visit EIE 2nd Year 2nd Sem R18 Scheme. The detailed syllabus for laplace transforms, numerical methods and complex variables is as follows.

## Laplace Transforms, Numerical Methods and Complex Variables Subject Syllabus for EIE 2nd Year 2nd Sem R18 Regulation

#### Pre-requisites:

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#### Course Objectives:

To learn

• 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.

#### 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
• Analyse 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

#### UNIT – I

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#### UNIT – II

Numerical Methods-I 10 L
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

#### UNIT – III

Numerical Methods-II 08 L
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.

#### UNIT – IV

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#### UNIT – V

Complex Variables (Integration) 10 L
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)

#### TEXT 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.

#### REFERENCES:

For the complete Syllabus, results, class timetable, and many other features kindly download the iStudy App
It is a lightweight, easy to use, no images, and no pdf platform to make students’s lives easier.
.

For detailed syllabus of all the other subjects of B.Tech 2nd Year Electronics & Instrumentation Engineering (EIE), visit Electronics & Instrumentation Engineering (EIE) 2nd Year Syllabus Subjects.

For results of Electronics & Instrumentation Engineering (EIE) 2nd Year 2nd Sem R18 Regulation, visit EIE 2nd Year 2nd Sem R18 Regulation results direct link.

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