Transforms and Partial Differential Equations

Transforms and Partial Differential Equations - Engineering Subject

Transforms and Partial Differential Equations - MA3351 3rd semester civil, Mechanical Dept | 2021 Regulation | Anna University Engineering Subject Paper

Unit I: Partial Differential Equations

1. Formation of partial differential equations by elimination of arbitrary Constants - Solved Example Problems

2. Formation of partial differential equations by elimination of arbitrary functions - Solved Example Problems

3. Singular integrals grals - solution of standard types of first order partial differential equations - Solved Example Problems

4. Lagrange's Linear Equation - Solved Example Problems | Partial Differential Equations

5. Linear partial differential equations of second and higher order with constant coefficients of both homogeneous and non-homogeneous types - Solved Example Problems

6. Questions and Answers - Partial Differential Equations | Transforms and Partial Differential Equations

Unit II: Fourier Series

1. Fourier Series - Uses, Definition of Periodic Function, Continuity of a Function, Examples, Advantages, Solved Example Problems

2. Fourier Series: Definition, Euler's Formula, Convergence Theorem, Important Formulae - with Solved Example Problems

3. Odd and Even Functions - Definition, Example, Waveform, with Solved Example Problems | Fourier Series

4. Half-range series - Sine and Cosine series with Solved Example Problems | Fourier Series

5. Complex form of fourier series - Formula, Solved Example Problems

6. Parseval's relation (or) theorem (or) identity - Definition, Solved Example Problems | Fourier Series

7. Harmonic Analysis - Definition, Formula, Solved Example Problems | Fourier Series

8. Questions and Answers - Fourier Series | Transforms and Partial Differential Equations

Unit III: Applications of Partial Differential Equations

1. Classification of partial differential equations - Example with Solved Example Problems

2. Method of separation of variables - Solved Example Problems | Partial Differential Equations

3. Solutions of one dimensional wave equation - Solved Example Problems | Partial Differential Equations

4. One dimensional equation of heat conduction - Solved Example Problems

5. Steady state solution of two dimensional equation of heat conduction (Heat flow equations) (excluding insulated edges) - Solved Example Problems

6. Questions and Answers - Applications of Partial Differential Equations | Transforms and Partial Differential Equations

Unit IV: Fourier Transforms

1. Statement of Fourier Integral Theorem - Sine and Cosine | Solved Example Problems

2. Fourier Transform Pair - Definition, Properties, Proof Statement, Inversion formula, Parseval's identity, Convolution theorem, Solved Example Problems

3. Fourier sine & Cosine transforms - Definition, Statement, Proof, Solved Example Problems

4. Questions and Answers - Fourier Transforms | Transforms and Partial Differential Equations

Unit V: Z - Transforms and Difference Equations

1. z - transforms - Applications, Elementary properties, Definition, Solved Example Problems

2. Inverse z-transform - Definition, Solved Example Problems

3. Convolution Theorem - Definition, Statement, Proof, Solved Example Problems | Z - Transforms

4. Formation of difference equations - Definition, Statement, Solved Example Problems

5. Solution of difference equations using Z-transform - Formula with Solved Example Problems

6. Questions and Answers - Z - Transforms and Difference Equations | Transforms and Partial Differential Equations

Formula

1. Some important hints, results & formulae - Transforms and Partial Differential Equations

Question Paper

1. Model Question Paper - Transforms and Partial Differential Equations