This post explains the basic method of converting an integral equation into a corresponding differential equation.
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If you’re a 16-year-old student preparing for any exam, you must know one thing – your brain needs special treatment. We have the power to understand so many things about our memory’s structure, which is why it’s our duty to find the best training strategies for the brain and prepare it for intensive testing. The…
In this article, I will teach you about Square Integrable Functions, Norms and the solution of Integral Equations by the trial method. Don’t forget to refer: Definitions and Types of Integral Equations Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the…
It is so fun and enjoyable to travel through rail routes. Most people love to travel by rails instead of preferring to travel by car. Traveling by rail is a good experience along with watching the beauty of nature and different sceneries when you travel long distances. Many people believe that it is safe to…
In this article, I will explain what Integral Equations are, how they are structured and what are certain types of Integral Equations. What is an Integral Equation? An integral equation is an equation in which an unknown function appears under one or more integration signs. Any integral calculus statement like — $ y= \int_a^b \phi(x)…
Every student or graduate knows how hard the first experience of passing exams is. Preliminary preparation starves the nervous system and the physical condition of the human body, however, the exam itself is always a stressful situation, which requires a candidate a great manifestation of mental and physical abilities. Therefore, just the knowledge of a…
This is a continuation of the series of summer projects sponsored by department of science and technology, government of India. In this project work, I have worked to collect and expand what Ramanujan did with Nested Radicals and summarized all important facts into the one article. In the article, there are formulas, formulas and only…
I just discovered Barry Martin’s Hopalong Orbits Visualizer — an excellent abstract visualization, which is rendered in 3D using Hopalong Attractor algorithm, WebGL and Mrdoob’s three.js project. Here is a demo video: Hop to the source website using your desktop browser (with WebGL and Javascript support) and enjoy the magic. Hopalong Attractor Algorithm Hopalong Attractor…
In this study note, I have discussed and explained about real sequences — a very important topic in Real Analysis and Calculus. I will cover the topic, definitions and examples under the following headings: Real Sequence: A sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function…
What Happens If We Drop a Ball Through a Tunnel in the Earth? Imagine creating a tunnel straight through the Earth and dropping a ball or any other object into it. How would gravity affect the ball, and would it emerge on the other side? If so, how long would it take? Tunnel through the…
The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The prime generating equation by Euler is a very specific binomial equation on prime numbers and yields more primes than any…
Ensembles in Chemical Sciences and Statistical Physics are a collection of a number of macroscopically identical but essentially independent systems. The System, here, is defined by the collection of a large number of particles and the term macroscopically identical means that each of the systems constituting an ensemble satisfies the same macroscopic conditions, like Volume,…
