MA 9211 Mathematics III syllabus download

MA 9211       MATHEMATICS-III                                              L T  P  C

          3 1  0   4

AIM

To facilitate the understanding of the principles and to cultivate the art of formulating physical

problems in the language of mathematics.

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 in which the functions used are not periodic 
•  To introduce the effective mathematical tools for the solutions of partial differential equations that model physical processes 
•  To develop Z-  transform techniques which will perform the same task for discrete time systems as Laplace Transform, a valuable aid in analysis of continuous time systems      

UNIT I    FOURIER SERIES                                                         9+3

Dirichlet’s conditions  – General Fourier series – Odd and even functions  – Half-range Sine

and Cosine series – Complex form of Fourier series – Parseval’s identity – Harmonic Analysis.

UNIT II   FOURIER TRANSFORM                                  9+3

Fourier integral theorem – Fourier transform pair-Sine and Cosine transforms – Properties –

Transform of elementary functions – Convolution theorem – Parseval’s identity.

                                                                                                                                                     

UNIT III   PARTIAL DIFFERENTIAL EQUATIONS                                                       9+3

Formation – Solutions of first order equations – Standard types and Equations reducible to

standard types – Singular solutions – Lagrange’s Linear equation –  Integral surface passing

through a given curve – Solution of linear equations of higher order with constant coefficients.

                                                 

UNIT IV   APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS               9+3

Method of separation of Variables – Solutions of one dimensional wave equation and onedimensional heat equation – Steady state solution of two-dimensional heat equation – Fourier

series solutions in Cartesian coordinates.

UNIT V   Z – TRANSFORM AND DIFFERENCE EQUATIONS                           9+3

Z-transform – Elementary properties – Inverse Z-transform – Convolution theorem – Initial and

Final value theorems  –  Formation of difference equation  –  Solution of difference equation

using Z-transform.

                                                                                             L: 45, T: 15, TOTAL: 60 PERIODS                        

TEXT BOOK 

1.  Grewal, B.S. “Higher Engineering Mathematics”, Khanna Publications (2007)

REFERENCES             

1. Glyn James, “Advanced Modern Engineering Mathematics, Pearson Education (2007)

2. Ramana, B.V. “Higher Engineering Mathematics” Tata McGraw Hill (2007).

3. Bali, N.P. and Manish Goyal, “A Text Book of Engineering 7th Edition (2007) Lakshmi Publications (P) Limited, New Delhi.

 

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