1-10 conceptual question .111 T-Mobile 2:42 AM @ 46% i.O. + Back 1. Explain how
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1-10 conceptual question .111 T-Mobile 2:42 AM @ 46% i.O. + Back 1. Explain how the Laplace transformation relate to functions of differential equations What is the benefit? transformation of the derivatives? 2. Why do we do the Laplace transform? 3. What's the pattern for the Laplace 4. When do you use a power series to 5. Why does the power series work when 6. What is a recurrence relationship? solve a differential equation? used to solve a differential equation? 7. When are the initial conditions applied in Laplace transform as compared to Power series? 8. When would a power series not be able to give an accurate solution to a differential equation? 9. List the steps for an inverse Laplace transformation? What is the importance of partial fractions in this process? 10. Explain how you derive the Laplace transform using the expression -st Dashboard Calendar To Do Notifications InboxExplanation / Answer
ANS 2. The purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. However, the Laplace Transform gives one more than that: it also does provide qualitative information on the solution of the ODEs (the prime example is the famous final value theorem).
Additionally, the moment generating function of a random variable is related to the Laplace transform of its density (replacing -t by s) and can be useful when considering the densities of sums because the Laplace transform of a convolution is the product of their Laplace transforms.
laplace transformatio is also a very powerful tool for network analysis. any linear circuit consisting of linear circuit elements can be solved by the knowledge of laplce trtansformation.
laplace transforms methods offers the following advantages over the classical methods.
(i.) it gives complete solution.
(ii.) initial conditions are automatically considered into the transformed equations.
(iii.) much less time is involved in solving differential equations.
(iv.) it gives systematic and routine solutions for differential equations.
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