Laplace transform and its application

its ppt for the laplace transform which part of Advance maths engineering. its contains the main points and one example solved in it and have the application related the chemical engineering

1. Year: 2016-17 Subject : Advanced Engineering Maths(2130002) Topic : Laplace Transform & its Application Name of the Students: Gujarat Technological University L.D. College of Engineering Agnihotri Aparna 160283105001 Agnihotri Shivam 160283105002 Kansara Sagar 160283105004 Makvana Yogesh 160283105005 Padhiyar Shambhu 160283105006 Patil Dipak 160283105008 Patil Mayur 160283105009 Rohit Chetan 160283105010 Sindhav Jaydrath 160283105011 Vasava Yogesh 160283105012

2. Topics Definition of Laplace Transform Linearity of the Laplace Transform Laplace Transform of some Elementary Functions First Shifting Theorem Inverse Laplace Transform Laplace Transform of Derivatives & Integral Differentiation & Integration of Laplace Transform Evaluation of Integrals By Laplace Transform Convolution Theorem Application to Differential Equations Laplace Transform of Periodic Functions Unit Step Function Second Shifting Theorem Application in Chemical Engineering

3. Definition of Laplace Transform Let f(t) be a given function of t defined for all then the Laplace Transform of f(t) denoted by L{f(t)} or or F(s) or is defined as provided the integral exists, where s is a parameter real or complex.

4. Linearity of the Laplace Transform If L{f(t)}= and then for any constants a and b

5. Laplace Transform of some Elementary Functions

6. First Shifting Theorem

7. Inverse Laplace Transform

8. Laplace Transform of Derivatives & Integral

9. Differentiation & Integration of Laplace Transform

10. Evaluation of Integrals By Laplace Transform

11. Convolution Theorem

12. Application to Differential Equations

13. Laplace Transform of Periodic Functions

14. Unit Step Function

15. Second Shifting Theorem

16. Application In Chemical Engineering A fast numerical technique for the solution of P.D.E. describing time-dependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques .

17. Continue… Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems A pplication to mass-transfer in single and multi-stream laminar parallel-plate flow systems

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