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501+62(063) 20+3043 , 2014 ISBN 978-617-7041-76-0 , 2014 . , 24-25 2014 . 3 ̲ Բ-Ͳ Bolor-Erdene Turmunkh USING LAPLACE TRANSFORMS FOR ELECTRICAL CIRCUITS

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THE RESEARCHES OF COMPOSITE AND SPATIAL GRID

CABLE-STAYED CONSTRUCTIONS FOR CIVIL ENGINEERING................56 Jinadu Abdulbaqui, Tinyakov D.V., Koloskov V.Yu.

INVESTIGATION OF THE INFLUENCE OF GEOMETRICAL

PARAMETERS ON THE TAKE-OFF MASS OF UNMANNED

AIRCRAFT WING

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AERODYNAMIC ANALYSIS OF WING FOR ZERO FUEL

PASSENGER AIRCRAFT (ZFPA)

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ANALYSIS OF THE PROBLEM OF MISAPPROPRIATION

OF PUBLIC FUNDS BY OFFICIALS AND ITS IMPACT

ON THE EXISTENCE OF A LEGAL STATE

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EXAMPLE 2 Comparisons with the Usual Method Solve the initial value problem Solution. From (1) and (6) we see that the subsidiary equation is

   

( ) Advantages of the Laplace Method

a) Solving a nonhomogeneous ODE does not require first solving the homogeneous ODE. See Example 3

b) Initial values are automatically taken care of See Examples 3 and 4.

c) Complicated inputs can be handled very efficiently, as we show in the next sections.

2. Electrical Circuits We examine a number of basic circuits, solve the problem analytically using the Laplace transform, and then check our result empirically against an actual circuit.

EXAMPLE 3 Responses of an RC-Circuit to a Single Rectangular Wave Find the current in the -circuit in Fig. 2 if a single rectangular wave with voltage is applied. The circuit is assumed to be quiescent before the wave is applied.

   

References:

1. Erwin Kreyszig, Advanced engineering mathematics, 9th editor, Ohio State University, 2006.

2. Erwin Kreyszig, Instructors manual of advanced engineering mathematics, 9th editor, Ohio State University, 2006.

3. Marcel B. Finan, Laplace Transforms: Theory, Problems, and Solutions, Arkansas Tech University, 2009.

4. Joel L. Schiff, The Laplace Transform: Theory and Applications, Springer.

5. John Polking, Albert Boggess, David Arnold, Differential Equations with Boundary Value Problems, 2nd Edition, Pearson Prentice Hall, 2006.

6. William Tyrrell Thomson, Laplace Transformation, 2nd Edition, Prentice-Hall, 1960.

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2. Compton A. H., The Spectrum of Scattered X Rays, Phis. Rev. 22, 409 (1923).

3. Compton A. H., A Quantum Theory of the Scattering of X Rays by Light Elements, Phis.

Rev. 21, 483 (1923).

5. Klemperer O., On the Annihilation Radiation of the Positron, Proc. Camber. Phil. Soc. 30, 347 (1934).

7. . ., , . 1, , 575 (1974).

8. ., , 528 (1974).

   

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