Integral Equations

Mainly developed for my students – do drop a word if you find it useful!

Textbook and Extra Resources

Textbook: Linear Integral Equations by Ram P Kanwal (PDF here).

Suggested: NPTEL Lectures, available for free on YouTube (link).

L1. Introduction

What are integral equations (IEs)? How to we identify an integral equation?

Quizzes included in the lesson.

Textbook Portions: Chapter 1, Section 1.1

L2. Linear IE

We will be studying a particular type of Integral Equations, called Linear Integral Equations. This lesson introduces the concept of Linear IE.

Textbook Portions: Chapter 1, Section 1.1

L3. Classification 1

We will categorise Linear IEs based on few of its characteristics. This helps us find narrow down our hunt for solution techniques.

Textbook Portions: Chapter 1, Section 1.1

L4. Classification 2

We will categorise kernels based on few of its characteristics. Kernels play a key role in solving IEs.

Textbook Portions: Chapter 1, Section 1.3, 1.4

L5. Methods Set 1

These methods apply to

  • Fredholm IE of 2nd Kind
  • Has Separable Kernel

Textbook Portions: Chapter 2

L6. Methods Set 2

Most of the solution techniques discussed here are for Fredholm IE.

Also discusses our first solution technique for Volterra IE.

Textbook Portions: Chapter 3,4


Notes to Learners

Most of the questions in L5, L6 quizzes are from CSIR NET. Including Boundary Value/Initial Value problems in differential equation that can be solved by converting it to IE, you will get questions from this topic for 15-20 Marks in NET every year.

This coursework is not complete yet – more information need to be added, like IVP/BVP to IE, solution using Laplace Transforms, using Hilbert Schmidt Theorem etc.


Integral Equations: Book Suggestions

Here are some book suggestions for IE (Click to buy):

https://m.media-amazon.com/images/I/41DE7ulwJVL._SL160_.jpg