VTU Notes | 18EC31 | ENGINEERING MATHEMATICS III

VTU Module-1 | Laplace Transform

Module-1

4.9
2018 Scheme | ECE Department

Created by VtuNotes.in
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5 Modules

18EC31 | ENGINEERING MATHEMATICS III | Module-1 VTU Notes

Summary:

"Laplace Transform: Definition and Laplace Transforms of Elementary Functions"

The Laplace Transform is a mathematical technique used to convert a time-domain function into a frequency-domain representation. It is defined as the integral of a given function multiplied by the exponential of a complex number s. Laplace transforms of elementary functions, such as constants, exponentials, and trigonometric functions, provide fundamental tools for solving differential equations and analyzing dynamic systems.

"Laplace Transforms of Periodic Functions"

When dealing with periodic functions, the Laplace Transform allows us to express them in a more convenient form for analysis. By applying the Laplace Transform to periodic functions, we can obtain their frequency-domain representations, making it easier to analyze their behavior and properties over time.

"Unit-Step Function – Problems"

The unit-step function, often denoted as u(t), is a fundamental piecewise function in engineering and mathematics. It represents a step change from zero to one at t = 0. Problems involving the unit-step function typically require us to analyze and solve differential equations or perform system analysis with discontinuous inputs. Understanding the Laplace Transform of the unit-step function is crucial for solving such problems efficiently.

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