How someone who lived in 18th century is helping us fight the pandemic today? An introduction to Euler and Graph Theory, on how it is used to #fight CoVID-19 Pandemic.

#BeAProudMathematician

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Mathematicos

# Category: Applied Mathematics

## Euler and The Corona Pandemic

## Promo: Mathematics and CoViD-19

## About a few Geometric Shapes and Brachistochrone Problem

## Illustrating Simple Variation Problem

## Prerequisites: Properties of Resolvent Kernels

## A Simple Integral Equation

## Selected Solutions (IEL6 Quiz)

## Iterated Kernels and Fredholm Theorems (IEL6)

## Selected Solutions (IEL5-Quiz)

## Separable Kernels and Approximation Methods (IEL5)

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How someone who lived in 18th century is helping us fight the pandemic today? An introduction to Euler and Graph Theory, on how it is used to #fight CoVID-19 Pandemic.

#BeAProudMathematician

How does mathematics help in the fight against pandemic? Here’s a quick promo of our upcoming video on the same.

What is a Catenary Curve? In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. Catenary curves were for a long time misunderstood to be parabolas, and has a history behind this shape worth reading! (Continue reading on…

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…

This is a bunch of prerequisites to understand section 3.5 of Ram P. Kanwal. There are three properties listed here: is absolutely and uniformly convergent for all values of s and t in the circle It satisfies integrodifferential equations Some Extra Links Compilation of Series Convergence Tests (Wikipedia) Some important sequences and series (Blog) Generalisation…

Question Find x such that Points to Ponder Is the solution unique? Leave your thoughts in the comments below!

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…

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…

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…

Recollect: General Linear Integral Equation where h(s) and f(s) are known functions g(s) is the unknown function K(s,t) is called the kernel If f(s) = 0 and h(s) = 1, is called the eigenvalue. Classification Based on limits Fredholm: Limits are constant Volterra: Limits are functions of s Singular: Either one, or both the limits…