No |
Units |
Titles |
Sub Titles |
Chapters |

1 |
Unit 1 |
Partial differential equations |
Formation - Solutions of first order equations - Standard types and Equations reducible to standard types - Singular solutions - Lagrange's Linear equation - Integral surface passing through a given curve - Classification of Partial Differential Equations - Solution of linear equations of higher order with constant coefficients - Linear non-homogeneous PDE |
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2 |
Unit 2 |
Fourier series |
Dirichlet's conditions - General Fourier series - Odd and even functions - Half-range Sine and Cosine series - Complex form of Fourier series - Parseval's identity - Harmonic Analysis |
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3 |
Unit 3 |
Applications of partial differential equations |
Method of separation of Variables - Solutions of one dimensional wave equation and onedimensional
heat equation - Steady state solution of two-dimensional heat equation - Fourier series solutions in Cartesian coordinates |
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4 |
Unit 4 |
Fourier transform |
Fourier integral theorem - Fourier transform pair-Sine and Cosine transforms - Properties - Transform of elementary functions - Convolution theorem - Parseval's identity |
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5 |
Unit 5 |
Z-transform and difference equations |
Z-transform - Elementary properties - Inverse Z-transform - Convolution theorem - Initial and Final value theorems - Formation of difference equation - Solution of difference equation using Z-transform |
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