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):
Mathematicos 