MA6351 Transforms and Partial Differential Equations - Syllabus-Semester III-MECH-BE-Anna University

NotesKhan MA6351 Transforms and Partial Differential Equations - Syllabus-Semester III-MECH-BE-Anna University MECH SEM III Syllabus, MECH SYLLABUS

 

MA6351             TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS                    L T  P  C

3 1  0  4

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.

 

 

OUTCOMES

 

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

 

• 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., Second reprint, New Delhi,  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, New Delhi, 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",  Sixth  Edition,  Tata

McGraw Hill Education Pvt Ltd, New Delhi, 2012.

6. Datta.K.B., "Mathematical Methods of Science and Engineering", Cengage Learning India Pvt

Ltd,  Delhi, 2013.