MA8353 – NOTES & QP
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MA8353 – SYLLABUS
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 — 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
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) — Initial and final value theorems — Convolution theorem — Formation of difference equations — Solution of difference equations using Z — transform.