UNIT 1:
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Formation of partial differential equations
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Solutions of standard types of first order partial differential equations
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Solutions of standard types of first order partial differential equations
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Solutions of standard types of first order partial differential equations
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Lagrange’s linear equation
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Lagrange’s linear equation
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Linear partial differential equations of second order with constant coefficients(Homogeneous Problems)
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Linear partial differential equations of second order with constant coefficients(Homogeneous Problems)
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Applications
UNIT 2:
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Dirichlet’s conditions
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General Fourier series
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Odd and even functions
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Odd and even functions
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Half range sine series
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Half range cosine series
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Root mean square value
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Parseval’s identity
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Harmonic Analysis.
UNIT 3:
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Classification of PDE
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Solutions of one dimensional wave equation
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Solutions of one dimensional wave equation
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One dimensional equation of heat conduction
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One dimensional equation of heat conduction
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One dimensional equation of heat conduction
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Steady state solution of two-dimensional equation of heat conduction(Insulated edges excluded)
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Steady state solution of two-dimensional equation of heat conduction
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Steady state solution of two-dimensional equation of heat conduction
UNIT 4:
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Parseval’s identity
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Convolution theorem
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Statement of Fourier integral theorem
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Fourier transform pair
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Fourier transform pair
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Sine and Cosine transforms
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Sine and Cosine transforms
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Transforms of simple functions-Rectangular pulse , Triangular pulse
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Properties
UNIT 5:
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Z-transforms
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Elementary properties
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Initial and final value theorem
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Inverse Z-transform using partial fraction
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Convolution theorem
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Formation of difference equations
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Formation of difference equations
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Solution of difference equations using Z-transform
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Solution of difference equations using Z-transform
