MA8251 Notes Engineering Mathematics 2 Unit 5

MA8251 Notes Engineering Mathematics 2 Unit 5 LAPLACE TRANSFORMATION Regulation 2017 For Anna University Free download. ENGINEERING MATHEMATICS 2 MA8251 Unit 5 LAPLACE TRANSFORMATION Notes Pdf Free download.

Content Engineering Mathematics 2 ma8251 Unit 5 LAPLACE TRANSFORMATION

LAPLACE TRANSFORMATION

1. Laplace transformation-Conditions and existence

Definitions 1. Transformation

A “Transformation” is an operation which converts a mathematical expression to a different but equivalent form

2. Laplace Transformation

Let a function f(t) be continuous and defined for positive values of ‘t’. The Laplace transformation of f(t) associates a function s defined by the equation (ma8251 notes engineering mathematics 2 unit 5)

2. Transforms of Elementary functions-Basic Properties

2.1 Problems Based On Transforms Of Elementary Functions- Basic Properties

3. Transforms Of Derivatives And Integrals Of Functions

3.1 Transform of integrals

3.2 Derivatives of transform

3.3 Problems Based On Derivatives Of Transform (ma8251 notes engineering mathematics 2 unit 5)

4 Transforms Of Unit Step Function And Impulse Function

4.1 Problems Based On Unit Step Function (Or) Heaviside’s Unit Step Function

Define the unit step function. Solution: The unit step function, also called Heaviside’s unit function (ma8251 notes engineering mathematics 2 unit 5)

5 Transform Of Periodic Functions Definition:

(Periodic) A function f(x) is said to be “periodic” if and only if f(x+p) = f(x) is true for some value of p and every value of x. The smallest positive value of p for which this equation is true for every value of x will be called the period of the function.

6 Inverse Laplace Transform

a.If L[f(t)] = F(s), then L–1[F(s)] = f(t) where L–1 is called the inverse Laplace transform operator. b.If F1(s) and F2(s) are L.T. of f(t) and g(t) respectively then

7. Convolution theorem (ma8251 notes engineering mathematics 2 unit 5)

8. Initial and final value theorems

8.1 Initial value theorem

8.2 Final value theorem

9. Solution of linear ODE of Second Order with constant coefficients (ma8251 notes engineering mathematics 2 unit 5)

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