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SYLLABUS

Unit - 1

1. 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 - 2

2. 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 - 3

3. 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 - 4

4. 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 - 5

5. 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.