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# MA6351-TRANSFORMS-AND PARTIAL DIFFERENTIAL EQUATIONS-SYLLABUS-REGULATION-2013

MA6351 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS SYLLABUS REGULATION 2013

MA6351 Â  Â  Â  Â TRANSFORMSÂ  ANDÂ  PARTIALÂ  DIFFERENTIAL EQUATIONS Â  Â  Â L TÂ  P C Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Â 3 1 0Â  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 IÂ Â Â Â Â Â Â Â Â Â Â Â  PARTIALÂ  DIFFERENTIALÂ  EQUATIONS Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

Formation of partial differential equations â€“ Singular integrals — Solutions of standard types of first order partial differential equations – Lagrangeâ€™s linear equation — Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types.

UNIT IIÂ Â Â Â Â Â Â Â Â Â Â  FOURIERÂ  SERIES Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

Dirichletâ€™s conditions â€“ General Fourier series â€“ Odd and even functions â€“ Half range sine series â€“ Half range cosine series â€“ Complex form of Fourier series â€“ Parsevalâ€™s identity â€“ Harmonic analysis.

UNIT IIIÂ Â Â Â Â Â Â Â Â Â  APPLICATIONSÂ  OF PARTIALÂ  DIFFERENTIALÂ  EQUATIONS Â  Â  Â  Â 9+3

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

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UNIT IVÂ Â Â Â Â Â Â Â Â  FOURIERÂ  TRANSFORMS Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

StatementÂ Â  ofÂ Â  FourierÂ Â  integralÂ Â  theoremÂ Â Â Â Â Â  â€“Â Â  FourierÂ Â  transformÂ Â  pairÂ Â  â€“Â Â  FourierÂ Â  sineÂ Â  and cosine transforms â€“ Properties â€“ Transforms of simple functions â€“ Convolution theorem â€“ Parsevalâ€™s identity.

UNIT VÂ Â Â Â Â Â Â Â Â Â  Z – TRANSFORMSÂ  ANDÂ  DIFFERENCEÂ  EQUATIONS Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  9+3

Z- transforms – Elementary properties â€“ Inverse Z – transform (using partial fraction and residues) â€“ Convolution theorem – Formation ofÂ  difference equations â€“ Solution of differenceÂ  equationsÂ  usingÂ  Z- transform.

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

OUTCOMES:

• The understandingÂ  ofÂ  theÂ  mathematicalÂ  principlesÂ  onÂ  transformsÂ  andÂ  partialÂ  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.

1. Grewal B.S., “Higher EngineeringÂ Â  Mathematics”, 42ndÂ Â Â Â  Edition, Khanna Publishers, Delhi, 2012.
1. Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for

Engineering Students”Â  Vol. II & III,Â  S.ViswanathanÂ  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 McGraw Hill Publishing CompanyÂ  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 WylieÂ  CÂ  andÂ  Barrett.L.C,Â  “AdvancedÂ  EngineeringÂ  Mathematics”Â  TataÂ Â Â  McGrawÂ  Hill Education Pvt Ltd, Sixth Edition, New Delhi, 2012.
6. Datta K.B., “Mathematical Methods of Science and Engineering”, Cengage Learning India Pvt Ltd,Â  Delhi, 2013.