MA6351 Transforms and Partial Differential Equations Syllabus for Anna University

Anna University Syllabus

Anna University 3rd Semester Syllabus for EEE / ECE / CSE / IT / MECH , Anna university M3 Syllabus , Syllabus for mathematics 3 .

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MA6351        TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS           

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.

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