Transforms and differential equations Subject from the Semester III B.E Electrical and Instrumentation Of Anna University syllabus. In this article, we aim to provide the unit-wise topics in a detailed manner.
We added the required textbooks and references from the faculty. It will assist you in making preparation strategies for the examination. Having a grip on every topic of the unit you can able to finish the syllabus before everyone else. Hope this information is useful. If you have any queries about the syllabus of MA3353 – Transforms And Differential Equations. Comment below on this article.
If you want to know more about the B.E Electrical and Instrumentation syllabus connected to an affiliated institution’s four-year undergraduate degree program. We provide you with a detailed Year-wise, semester-wise, and Subject-wise syllabus in the following link B.E Electrical and Instrumentation Syllabus Regulation 2021 Anna University.
Aim Of Concept:
- To acquaint the students with Differential Equations which are significantly used in engineering problems.
- To introduce the basic concepts of PDE for solving standard partial differential equations.
- To introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems.
- To make the students appreciate the purpose of using transforms to create a new domain in which it is easier to handle the problem that is being investigated.
- To introduce effective mathematical tools for the solutions of partial differential equations that model several physical processes and to develop Z transform techniques for discrete-time systems
MA3353 – Transforms And Differential Equations Syllabus
Unit I: Ordinary Differential Equations
Higher order linear differential equations with constant coefficients – Method of variation of parameters – Homogenous equation of Euler’s and Legendre’s type – System of simultaneous linear first order differential equations with constant coefficients – Method of undetermined coefficients.
Unit II: Partial Differential Equations
Formation of partial differential equations –Solutions of standard types of first-order partial differential equations – First-order partial differential equations reducible to standard types- Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.
Unit III: Fourier Series
Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series and cosine series – Root mean square values – Parseval’s identity –Harmonic analysis.
Unit IV: Laplace Transforms
Existence conditions – Transforms of elementary functions – Transform of unit step function and unit impulse function – Basic properties – Shifting theorems -Transforms of derivatives and integrals – Initial and final value theorems – Inverse transforms – Convolution theorem – Transform of periodic functions – Application to solution of linear second order ordinary differential equations with constant coefficients.
Unit V: Z – Transforms And Difference Equations
Z-transforms – Elementary properties – Convergence of Z-transforms – Initial and final value theorems – Inverse Z-transform using partial fraction and convolution theorem – Formation of difference equations – Solution of difference equations using Z-transforms.
Text Books:
1. Grewal B.S., “Higher Engineering Mathematics”, 44th edition, Khanna Publishers, New Delhi, 2018.
2. Kreyszig E, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, New Delhi, India, 2016.
References:
- Andrews. L.C and Shivamoggi. B, “Integral Transforms for Engineers” SPIE Press, 1999.
- Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 10th Edition, Laxmi Publications Pvt. Ltd, 2015.
- James. G., “Advanced Modern Engineering Mathematics”, 4th edition, Pearson Education, New Delhi, 2016.
- Narayanan. S., ManicavachagomPillay.T.K and Ramanaiah. G “Advanced Mathematics for Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.
- Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi, 2018.
- Wylie. R.C. and Barrett. L.C., “Advanced Engineering Mathematics” Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.
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