## Video Lecture: Examples of Metric Spaces (Lecture 2)

Here’s a video discussing a few simple examples of metric spaces.

## Video Lecture: Definition of Metric Spaces (Lecture 1)

Here’s a video discussing the definition of metric spaces, and the inspiration behind it. Rarely

## Integral Equations: Self Contained Coursework

Coursework to learn/quickly revise Integral Equations for Mathematics/Physics and Engineering Students.
Also useful for CSIR-NET and GATE Mathematical Sciences Aspirants.

## Examples and Counterexamples: Real Line with Discrete Metric/Topology

Examples and Counterexamples: Real Line with Discrete Metric/Topology. Did you try the challenges at the end? Leave your thoughts in the comments below!

## Example and Counterexamples: Cyclic groups

Here are some important definitions, facts and examples of cyclic groups.

## CSIR-NET General Aptitude: Free Lecture by Christy Varghese

Free lecture on Unacademy discussing the previous year question paper of December 2019 CSIR-NET Exam. Timing: Tomorrow, 26th February, Morning 8:30 AM If you like to be an Unacademy plus member, subscribe now with the referral code “CC10” to access all the plus courses in Unacademy at 10% discount.

## Illustrating Simple Variation Problem

Calculus of variations is a subject where you study the extrema (maximum or minimum) of a function of functions. We know that, to find the extrema (maximum or minimum) of a “functional” of the form we first identify and substitute in Euler Equation (Or sometimes called Euler-Lagrange Equation) to obtain a Ordinary Differential Equation, solving…

## Selected Solutions (IEL6 Quiz)

Question 1 Question: Let be the solution of the integral equation . Then A couple of solutions to this problem are discussed in Unit Quiz 1 (Question 2, only difference is that options 3 and 4 are about value of phi at x=1), even using methods mentioned in Unit 2. Question 2 For the linear…

## Iterated Kernels and Fredholm Theorems (IEL6)

Method of Successive Approximation Solution Method 2 (Neumann Series Solution, Solution by Iterated Kernels) For Fredholm IE For the equation , Put g(s) = f(s) or any appropriate function of s. Find iteratively. where and solution will be of the form For Volterra IE where and solution will be of the form Example Solve the…

## Selected Solutions (IEL5-Quiz)

Question 2 Let ϕ be the solution of the integral equation . Then ϕ(0)=20exp(-1) – 8 ϕ(0)=20e-8 ϕ(0)=22 – 8e ϕ(0)=22 – 8exp(-1) Solution 1 Let . Substituting in the equation, Hence, Concluding, ϕ(0)=20exp(-1) – 8. Solution 2 For a Fredholm integral equation of 2nd Kind, using , where Here, . Hence Hence the solution…