MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS |syllabus

MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS 

OBJECTIVES:
 To introduce Fourier series analysis which is central to many applications in engineering apart
from its use in solving boundary value problems.
 To acquaint the student with Fourier transform techniques used in wide variety of situations.
 To introduce the 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.

UNIT I      PARTIAL DIFFERENTIAL EQUATIONS         (9+3)
Formation of partial differential equations – Singular integrals -- Solutions of standard types of first
order partial differential equations - Lagrange’s linear equation -- Linear partial differential equations of
second and higher order with constant coefficients of both homogeneous and non-homogeneous
types.

UNIT II      FOURIER SERIES                      (9+3)

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series –
Half range cosine series – Complex form of Fourier series – Parseval’s identity – Harmonic analysis.

UNIT III     APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS  (9+3)

Classification of PDE – Method of separation of variables - Solutions of one dimensional wave
equation – One dimensional equation of heat conduction – Steady state solution of two dimensional
equation of heat conduction (excluding insulated edges).

UNIT IV      FOURIER TRANSFORMS     (9+3)

Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and
cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s
identity.

UNIT V       Z - TRANSFORMS AND DIFFERENCE EQUATIONS  (9+3)

Z- transforms - Elementary properties – Inverse Z - transform (using partial fraction and residues) –
Convolution theorem - Formation of difference equations – Solution of difference equations using
Z - transform.

                                                                                                      TOTAL (L:45+T:15): 60 PERIODS
OUTCOMES:

 The understanding of the mathematical principles on transforms and partial differential
equations would provide them the ability to formulate and solve some of the physical problems
of engineering.

TEXT BOOKS:

1. Veerarajan. T., "Transforms and Partial Differential Equations", Tata McGraw Hill Education Pvt.
Ltd., New Delhi, Second reprint, 2012.
2. Grewal. B.S., "Higher Engineering Mathematics", 42nd Edition, Khanna Publishers, Delhi, 2012.
3. Narayanan.S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for
Engineering Students" Vol. II & III, S.Viswanathan Publishers Pvt. Ltd.1998.

REFERENCES:

1. Bali.N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 7th Edition, Laxmi
Publications Pvt Ltd, 2007.
2. Ramana.B.V., "Higher Engineering Mathematics", Tata Mc Graw Hill Publishing Company Limited,
NewDelhi, 2008.
3. Glyn James, "Advanced Modern Engineering Mathematics", 3rd Edition, Pearson Education, 2007.
4. Erwin Kreyszig, "Advanced Engineering Mathematics", 8th Edition, Wiley India, 2007.
5. Ray Wylie. C and Barrett.L.C, "Advanced Engineering Mathematics" Tata Mc Graw Hill Education
Pvt Ltd, Sixth Edition, New Delhi, 2012.
6. Datta.K.B., "Mathematical Methods of Science and Engineering", Cengage Learning India Pvt Ltd,
Delhi, 2013.


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