Basics of Laplace Transforms

Name: Basics of Laplace Transforms
Rating: 4.3 (2 reviews)

Definitions and properties

Created byChavan Ashwinkumar Raosaheb

Last updated 3/2023

English

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What you'll learn

Find the Laplace transforms of given function
Apply the properties of Laplace Transforms
Apply the techniques of Inverse Laplace transforms to find the function
Apply the Laplace transform to solve the first order differential equation

Course content

1 section • 5 lectures • 1h 49m total length

Definition and LT of standard functions29:03
Learn the definition and properties of the Laplace transform, including Dirichlet conditions and linearity, and derive standard transforms for constants, exponentials, polynomials, sines, cosines, and hyperbolic functions with examples.
First Shifting Theorem and Multiplication by t25:23
Apply the first shifting theorem to translate Laplace transforms with exponential terms, and use multiplication by t to relate t-variants to derivatives of phi(s).
On Definition and LT of standard functions
Division by t property22:57
explain division by t property of the laplace transform, where L{f(t)/t} equals integral from s to infinity of F(s), with examples of sine t / t and sine^2(2t)/t.
Change of a Scale Property16:05
Explain how the change of scale property in Laplace transforms converts f(t) multiplied by a to phi(s/a)/a, with examples including sine 2t and sine root t.
Division by t and change of scale property
Laplace Transform of Derrivatives15:40
Learn to compute the Laplace transform of derivatives, from first to nth order, using the differentiation property and initial conditions, with worked examples.
Laplace Transforms of Derivatives

Requirements

Basics trignometric relations, Differentiation, Integration

Description

The transform turns integral equations and differential equations into polynomial equations, which are comparatively much easier to solve. In this course, we have mainly focussed on the basic definitions and the Laplace transforms of some standard functions. Also, we have covered the properties in detail like shifting theorem, change of scale, multiplication by t, division by t, and Laplace transform of derivatives with supporting examples. Course 2 will be floated on the rest of the properties and the inverse Laplace transforms with its applications. This course will help the participant to get introduced to the basics of Laplace transforms in a very short period of time and the performance will be recorded through the quizzes available in the course. After every one or two lectures there is autograded activity which records your performance and create the grade report. Also, this course have downloadable content as e-material for the students to refer additionally. All solved examples are covered in the study material which are downloadable. This course is designed purposely in two sets so that it can be made available free of cost to the users. The basic objective of the course is students are able to find the Laplace transform of given function and apply it in allied areas.

Who this course is for:

Mathematical approach to Laplace Transform