TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS (SEMESTER III)

ANNA UNIVERSITY :: CHENNAI 600 025
UNIVERSITY DEPARTMENTS
REGULATIONS – 2008
CURRICULUM FROM III TO VIII SEMESTERS AND ELECTIVES FOR
B.TECH. INFORMATION TECHNOLOGY

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TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
(Common to all branches)

UNIT I

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 identify – Harmonic Analysis.

UNIT II

FOURIER TRANSFORMS

Fourier integral theorem (without proof) – Fourier transform pair – Sine and Cosine transforms – Properties – Transforms of simple functions – Convolution theorem– Parseval’s identity.

UNIT III

PARTIAL DIFFERENTIAL EQUATIONS

Formation of partial differential equations – Lagrange’s linear equation – Solutions of standard types of first order partial differential equations - Linear partial differential equations of second and higher order with constant coefficients.

UNIT IV

APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS

Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two-dimensional equation of heat conduction(Insulated edges excluded) – Fourier series solutions in cartesian coordinates.

UNIT V

Z -TRANSFORMS AND DIFFERENCE EQUATIONS

Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z-transform.