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1234
March 17, 2025
by rsroybaruah ADV-MATHEMATICS

Euler’s Equation of Motion in Fluid Dynamics

Fluid dynamics, a branch of fluid mechanics, deals with the motion of fluids and their interactions with solid boundaries. One of the fundamental equations governing fluid flow is Euler's equation of motion. Named after the Swiss mathematician and physic ...

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SWZ1
March 10, 2025
by rsroybaruah ADV-MATHEMATICS

Schwarzschild’s Exterior Solution for the Gravitational Field of an Isolated Particle

The concept of curved spacetime, introduced by Albert Einstein in his General Theory of Relativity (GR), revolutionized our understanding of gravity. One of the most important solutions to Einstein’s field equations is the Schwarzschild solution, which d ...

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einstein's field equation
March 3, 2025
by rsroybaruah ADV-MATHEMATICS

Einstein’s field equation in General Relativity for Beginners

Einstein’s field equation is the foundation of General Relativity—a theory that describes how gravity works. The equation: R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu} may look complicated, but let’s break it down step by step in ...

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PE
February 28, 2025
by rsroybaruah ADV-MATHEMATICS

Energy Momentum Tensor in the General Theory of Relativity

The energy-momentum tensor, also known as the stress-energy tensor, is a fundamental concept in the General Theory of Relativity (GTR). It describes the distribution and flow of energy and momentum in spacetime, acting as the source of the gravitational ...

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54
PE1
February 24, 2025
by rsroybaruah ADV-MATHEMATICS

Poisson’s Equation as an Approximation of Field Equations

Poisson’s equation is a fundamental equation in mathematical physics, appearing in electrostatics, gravitation, and fluid dynamics. In the context of General Relativity, it serves as an approximation of Einstein’s Field Equations under certain conditions ...

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a55
February 21, 2025
by rsroybaruah ADV-MATHEMATICS

Principle of Equivalence and Principle of Covariance

Albert Einstein’s theory of relativity revolutionized our understanding of space, time, and gravity. Two fundamental principles at the heart of this theory are the Principle of Equivalence and the Principle of Covariance. These principles provide the fou ...

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148
cosmological models
January 25, 2025
by rsroybaruah INSIGHTS

Cosmological Models in Mathematics: Exploring the Universe Through Equations

Understanding the universe has always fascinated humanity. Cosmological models bridge the gap between philosophy, physics, and mathematics, providing a structured framework for understanding how the universe behaves. Let’s dive deep into the mathematical ...

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2525
November 5, 2024
by rsroybaruah RESOURCES

Create a Professional CV Using LaTeX: A Complete Guide

Crafting a professional CV can be a challenging task. However, if you're looking to create a unique and structured resume, using LaTeX is a great option. In this guide, we'll walk you through how to create a visually appealing, customizable CV using LaTe ...

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379
T1
October 22, 2024
by rsroybaruah INSIGHTS

Applying Mathematics in Your Life: Making Everyday Tasks Easier

Mathematics is often viewed as a subject confined to classrooms or technical professions. However, applying mathematics is essential in day-to-day life. From managing finances to organizing tasks, math helps us make better decisions, solve problems, and ...

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2525
September 26, 2024
by rsroybaruah PROGRAMMING

Construction of Matrices: Mathematica Programs

Construction of Matrices 1. Identity Matrix: Construct an identity matrix of size 4. IdentityMatrixConstruction := IdentityMatrixIdentityMatrixConstruction Output: {{1, 0, 0, 0},  {0, 1, 0, 0},  {0, 0, 1, 0},  {0, 0, 0 ...

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