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HomeADV-MATHEMATICS

Posts in category: ADV-MATHEMATICS

fluid dynamics
March 26, 2024
by rsroybaruah

An Introductory Guide to Fluid Dynamics for Beginners

Fluid dynamics is a branch of science that is concerned with the study of the motion of fluids or that of bodies in contact with fluids. Fluids are classified as liquids and gases. Liquids are compressible under the action of heavy forces whereas ga ...

continuum mechanics
March 19, 2024
by rsroybaruah

Discovering the Secrets of Continuum Mechanics: A Journey into the World of Deformable Bodies

Welcome to the fascinating realm of continuum mechanics, where the study of deformable bodies and continuous media unveils the intricate dynamics of materials under various forces and conditions. In this blog post, we'll embark on a journey to explo ...

mass energy
September 8, 2023
by rsroybaruah

Equivalence of Mass Energy: E=mc^2, Einstein’s Famous Equation

Introduction to Mass Energy Equivalence Albert Einstein’s equation E=mc2E=mc^2E=mc2 is one of the most famous equations in physics, symbolizing the deep connection between mass and energy. This elegant formula encapsulates a groundbreaking idea: ...

variation of mass
September 8, 2023
by rsroybaruah

The Variation of Mass with Velocity: Special Theory of Relativity

Introduction to the Concept of Variation of Mass Albert Einstein's Special Theory of Relativity introduced several groundbreaking ideas that reshaped our understanding of physics. Among these, the concept of the variation of mass with velocity st ...

group
September 8, 2023
by rsroybaruah

Lorentz Transformation: Lorentz Transformation forms a Group

Introduction: The Elegance of Symmetry in Physics In the vast and intricate world of physics, symmetry plays a crucial role. One of the most profound examples of symmetry is found in the Lorentz transformation. When we say the Lorentz transformat ...

lagrangian
September 6, 2023
by rsroybaruah

Lagrangian and Lagrange’s Equation from Hamilton’s Principle in Classical Mechanics

Introduction to Classical Mechanics Classical mechanics is a cornerstone of physics, describing how objects move and interact with forces. It encompasses various formulations, each providing unique insights and tools for solving mechanical proble ...

geodesics
September 3, 2023
by rsroybaruah

Geodesics: Shortest Path Between Two Points in a Curved Space

When we think about the shortest path between two points, we often envision a straight line on a flat surface. However, in the realm of curved spaces, the concept of the shortest path takes on a new form known as a "geodesic." Understanding geodesic ...

special cases
September 3, 2023
by rsroybaruah

Special Cases of Euler’s Equation: Calculus of Variation

Welcome, fellow math enthusiasts, to an intriguing journey through the world of the calculus of variations! Today, we will explore the special cases of Euler's Equation, a cornerstone in this field. Whether you are a seasoned mathematician or a curi ...

euler-lagrange equation
September 2, 2023
by rsroybaruah

Euler-Lagrange Equation in Calculus of Variations

Euler's equation, also known as the Euler-Lagrange equation, is a fundamental concept in the calculus of variations, a branch of mathematics that deals with finding the extremum (minimum or maximum) of a functional. In this context, a functional is ...

addition law of velocities
September 1, 2023
by rsroybaruah

The Relativistic Addition Law of Velocities or Velocity Addition Theorem

Introduction to the Addition Law of Velocities In our everyday experiences, velocities simply add up. If you're walking at 5 km/h on a train moving at 60 km/h, your speed relative to the ground is just 65 km/h. This intuitive rule, however, break ...

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