# MA6351 Transforms and Partial Differential Equations Previous Year Question Papers

MA6351 Transforms and Partial Differential Equations Previous Year Question Papers

B.E – Common to All departments Second Year 3rd Semester MA6351 Transforms and Partial Differential Equations (TPDE) Previous Year Question Papers For The Regulations 2013, 2008, 2007.

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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
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
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
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
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
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.

## MA6351 Transforms and Partial Differential Equations (TPDE) Previous Year Question Papers for the Regulation 2008 & 2007

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