# Laplace transform

By Prof. Indrava Roy   |   IMSC
Learners enrolled: 2529
Laplace transform is a fundamental tool in integral calculus. It is used to solve various types of differential equations, difference equations, integral equations etc., which arise naturally in engineering and basic sciences. Laplace transform techniques are therefore very useful for applications in science and technology.

INTENDED AUDIENCE
2nd year BE/BSc onwards

PREREQUISITES Differential and integral calculus
Summary
 Course Status : Completed Course Type : Elective Duration : 4 weeks Category : Mathematics Credit Points : 1 Level : Undergraduate Start Date : 25 Jul 2022 End Date : 19 Aug 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 25 Sep 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1:Introduction and basic definitions, with brief review of limits and Riemann integration, with special emphasis on improper Riemann integrals
Week 2:Functions of exponential order and existence theorem for Laplace transforms- with lots of examples and some non-examples; Properties of Laplace transforms with applications in computing them for various functions
Week 3: Inverse Laplace transforms, criteria for uniqueness, computation of inverse Laplace transform via various examples
Week 4:Applications of Laplace transform techniques for solving integrals, differential equations, difference equations, integral equations and integro-differential equations

### Books and references

1. Chapter 6 of “Advanced Engineering Mathematics”, E. Kreyzig, 10th Edition, Wiley
2. Chapters 1-3 of “Introduction to Laplace Transforms and Fourier Series”, Philip Dyke, Springer

### Prof. Indrava Roy

IMSC
Indrava Roy is an Assistant Professor of Mathematics at the Institute of Mathematical Sciences, Chennai

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 25 September 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 3 assignments out of the total 4 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

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- NPTEL team