Definitions and properties

What you will 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


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.

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Definition and LT of standard functions
First Shifting Theorem and Multiplication by t
On Definition and LT of standard functions
Division by t property
Change of a Scale Property
Division by t and change of scale property
Laplace Transform of Derrivatives
Laplace Transforms of Derivatives