MA8353-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

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MA8353-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

MA8353-TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus 2017 Regulation

MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS                 L T P C
                                                                                                                            4 0 0 4

OBJECTIVES :

  • To introduce the basic concepts of PDE for solving standard partial differential equations.
  • 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 series techniques in solving heat flow problems used
    in various situations.
  • 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 12

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 nonhomogeneous
types.

UNIT II FOURIER SERIES 12

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 12

Classification of PDE – Method of separation of variables – Fourier Series Solutions of one
dimensional wave equation – One dimensional equation of heat conduction – Steady state
solution of two dimensional equation of heat conduction.

UNIT IV FOURIER TRANSFORMS 12

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 12

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

TOTAL: 60 PERIODS

OUTCOMES :

Upon successful completion of the course, students should be able to:

  •  Understand how to solve the given standard partial differential equations.
  • Solve differential equations using Fourier series analysis which plays a vital role in
    engineering applications.
  • Appreciate the physical significance of Fourier series techniques in solving one and two
    dimensional heat flow problems and one dimensional wave equations.
  • Understand 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.
  • Use the effective mathematical tools for the solutions of partial differential equations by
    using Z transform techniques for discrete time systems.

 

TEXT BOOKS:

1. Grewal B.S., “Higher Engineering Mathematics”, 43rd Edition, Khanna Publishers, New
Delhi, 2014.
2. Narayanan S., Manicavachagom Pillay.T.K and Ramanaiah.G “Advanced Mathematics for
Engineering Students”, Vol. II & III, S.Viswanathan Publishers Pvt. Ltd, Chennai, 1998.

 

REFERENCES :

1. Andrews, L.C and Shivamoggi, B, “Integral Transforms for Engineers” SPIE Press, 1999.
2. Bali. N.P and Manish Goyal, “A Textbook of Engineering Mathematics”, 9th Edition, Laxmi
Publications Pvt. Ltd, 2014.
3. Erwin Kreyszig, “Advanced Engineering Mathematics “, 10th Edition, John Wiley, India,
2016.
4. James, G., “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education,
2007.
5. Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New
Delhi, 2016.
6. Wylie, R.C. and Barrett, L.C., “Advanced Engineering Mathematics “Tata McGraw Hill
Education Pvt. Ltd, 6th Edition, New Delhi, 2012

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