Important Questions
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MA8353 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
Important Topics
UNIT -1
1.solving the partial equations { eg : solve (D^2 -2DD)z=x^3 y +e^2x-y}
UNIT-2
1.Half range cosine ,sine
2.3 table sums in Fourier harmonic
UNIT-3
1.String (displacement sums)
UNIT-4
1.Self reciprocal under Fourier transform
2.Parseval’s identity.
UNIT-5
1.Inverse Z transform
2.Convolution theorem
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SYLLABUS
uNIT I PARTIAL DIFFERENTIAL EQUATIONS MA8353 Syllabus Transforms and 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 MA8353 Syllabus Transforms and Partial Differential Equations
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.
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 III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS MA8353 Syllabus Transforms and Partial Differential Equations
UNIT IV FOURIER TRANSFORMS MA8353 Transforms and Partial Differential Equations Syllabus
Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.
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.
UNIT V Z – TRANSFORMS AND DIFFERENCE EQUATIONS MA8353 Transforms and Partial Differential Equations Syllabus
