APPLICATION MATHS FOR EEE
- 1. By : T.ANIL KUMAR(14A81A0237)& S HEMANTH DURGA REDDY(14A81A0236) SRI VASAVI ENGINEERING COLLEGE TADEPALLIGUDEM B.Tech 3rd year EEE
- 2. WHAT IS MATHS ? In Ramanujan’s point of view maths is defined as “A pattern connected with Calculus, Geometry, Trignomentry and etc., combined together to form a solution
- 3. CREATIVITY HOLDS TWO THINGS Engineering + Maths = Everything Enginnering – Maths = Nothing
- 4. DIFFERENT METHODS IN MATHS Laplace transforms Calculus Z- transforms Complex numbers Probability Fourier series Limits Trigonometry etc....
- 6. THE FRENCH NEWTON PIERRE-SIMON LAPLACE Transformation in mathematics deals with the conversion of one function to another function that may not be in the same domain. Laplace transform is a powerful transformation tool, which literally transforms the original differential equation into an elementary algebraic expression. This transform is named after the mathematician and renowned astronomer Pierre Simon Laplace who lived in France.
- 7. DEFINITION The Laplace transform is a linear operator that switched a function f(t) to F(s). Specifically: where: { ( )}f tL =F(s) t domain s domain
- 8. PROCESS OF APPLYING L.T First stage :To represent a system in the time domain. Second stage :To transform apply equivalence of that system in the Laplace domain making reduction of calculation and obtaining a solution in the Laplace domain. Third stage: To transform the solution in the Laplace domain back to a solution in the original time domain applying the Laplace inverse
- 9. REPRESENTATION OF ELECTRICAL ELEMENTS Element In Time Domain In Laplace Domain Resistance R R Inductance L(t) L(s) Capacitance C(t) 1/C(s)
- 10. AS TRANSFER FUNCTION Definition --> a transfer function is an expression that relates the output to the input n the s-domain differential equation r(t) y(t) transfer function r(s) y(s) 5. Transfer functions
- 11. APPLICATIONS OF LAPLACE TRANSFORMS Electrical circuits Control Systems Signals & Systems
- 12. FOURIER SERIES Introduced by JOSEPH FOURIER DEF:-A way to represent a (wave-like) function as the sum of simple sine waves.
- 13. Fourier series make use of the orthogonality relationships of the sine and cosine functions. FOURIER SERIES can be generally written as, Where, ……… (1.1) ……… (1.2) ……… (1.3)
- 14. The individual terms in Fourier Series are known as HARMONICS. Few Examples
- 15. APPLICATIONS Used in Harmonic Analysis Transient Analysis Conversion of Response from Time Domain to Frequency Domain Power Electronics
- 16. Electrical Engineering (A.C. Circuits): Resistors, inductors, capacitors, power engineering, analysis of electric magnetic fields and their interactions with materials and structures.
- 17. CONCLUSION Machines Rule The World We Rule The Machines Without Calculations There Are No Machines