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Unit - 1 Laplace Transformation

Unit 1Laplace Transformation

1.1 Laplace Transformation and its properties

1.2 Periodic function

1.3 Unit step function

1.4 Impulse function

1.5 Inverse Laplace Transformation and Convolution Theorem

1.6 Applications of Laplace transforms in solving certain initial value problems simultaneous differential equations

Unit - 2 Numerical Method

Unit 2Numerical Method

2.1 Finite difference

2.2 Symbolic relations

2.3 Interpolation Newton Gregory forward and backward formula

2.4 Extrapolation

2.5 Lagranges formula

2.6 Inverse Interpolation by Lagranges formula

2.7 Numerical Differentiation and Numerical Integration

2.8 Newton Cotes Quadrature formula

2.9 Trapezoidal rule

2.10 Simpsons 13 rule and Simpsons 38 rule

Unit - 3 Z-Transform & Inverse Z-Transform

Unit 3ZTransform Inverse ZTransform

3.1 ZTransform Properties

3.2 Inverse ZTransform Properties

3.3 Initial and Final value theorems

3.4 Convolution theorem Difference equations

3.5 Solution of difference equations using ZTransformation

Unit - 4 Fourier Series & Fourier Transform

Unit 4Fourier Series Fourier Transform

4.1 Expansion of Algebraic Exponential Trigonometric functions in Fourier series

4.2 Change of interval

4.3 Even and odd function

4.4 Half range sine and cosine series

4.5 Complex form of Fourier series

4.6 Fourier Transformation

4.7 Inverse Fourier Transformation

4.8 Fourier sine cosine transforms

4.9 Convolution theorem for Fourier transforms with simple illustrations

Unit - 5 Partial Differential Equations

Unit 5Partial Differential Equations

5.1 Formation of partial differential equations

5.2 Linear partial differential equations of first order Lagrange’s linear equation

5.3 Nonlinear equations of first order

5.4 Charpit’s method

5.5 Solution of one dimensional Wave equation Heat equation by the method of separation of variables and its applications

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