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

ma6351-transforms-and-partial-differential-equations-semester-iii-aero-be-anna-universityMA6351 Transforms and Partial Differential Equations -Semester III-AERO-BE-Anna University AERO SEM III Syllabus, AERO 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., 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-GrawHill 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.