Here’s a video discussing a few simple examples of metric spaces.
Tag: Free Materials
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…
