# An Introduction…

Introduction and intentions of this blog.

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# An Introduction…

# A PROBLEM IN THERMODYNAMICS AND STATISTICAL MECHANICS: ANALYTICAL AND NUMERICAL STUDY OF AN EINSTEIN SOLID-Analytical Solution

# Basics of Tensor Calculus & General Relativity|A Digression into Special Relativity

# Basics of Tensor Calculus and General Relativity: An Introduction to Manifolds and Coordinates

# Derivation of the Euler-Lagrange Equation for a Function of Several Dependent Variables

# Astrophysics Series: Derivation of the Total Energy of a Binary Orbit

# A Problem in Thermodynamics and Statistical Mechanics: Analytical and Numerical Study of an Einstein Solid

# A “Proof” of the Sturm-Liouville Theorem/Problem

Introduction and intentions of this blog.

IMAGE CREDIT/OBTAINED FROM: https://mappingignorance.org/2015/12/17/einstein-and-quantum-solids/ Quite some time ago, I had posted a numerical study of an Einstein solid and I now present the analytical study of an Einstein solid. As this was one problem in one of my problem sets while studying thermodynamics and statistical mechanics, one may find this exact problem in the following text: […]

So far in this series I have given the definitions of vectors, scalars, tensors, and manifolds. As a result, much of this series has been mostly mathematics and not necessarily physics. To that end, the purpose of this post is to develop the salient points of special relativity. Namely, the intention of this post is […]

SOURCE FOR CONTENT: General Relativity: An Introduction for Physicists, Hobson, M.P., Efsttathiou, G., and Lasenby, A.N., 2006. Cambridge University Press. D-Dimensional Hypersphere and Gamma Function: Introduction to Thermal Physics, Schroeder D.V. 2000. Addison-Wesley-Longmann. IMAGE CREDIT: NASA/JPL. The intended purpose of the post is to introduce the concept of manifolds in the context of physics (mathematicians beware!). Furthermore, […]

IMAGE CREDIT: NASA/JPL SOURCE FOR CONTENT: Classical Dynamics of Particles and Systems. Thornton and Marion. 5th Edition. Consider a functional where . By the method used in a previous section of the aforementioned text, we may write Additionally, we will find it useful to define Further we may also define an integral functional by way of […]

SOURCE FOR CONTENT: An Introduction to Modern Astrophysics, Carroll & Ostlie, Cambridge University Press. Ch.2 Celestial Mechanics Here is my solution to one of the problems in the aforementioned text. I derive the total energy of a binary system making use of center-of-mass coordinates. In order to conceptualize it I have used the binary Alpha Centauri […]

Every physics major at some point in their undergraduate career takes a course in thermodynamics and statistical mechanics. One of my problem sets included a problem that considers an Einstein solid with 50 oscillators and 100 units of energy and then increases the number of oscillators to 5000. I will be presenting my solution to […]

IMAGE CREDIT: NASA/JPL: This shows Jupiter’s Great Red Spot; a storm that has been occurring for over 300 years now. Quite recently, however, observations show that the Spot appears to be shrinking in size. About a week ago, I was looking through my notebooks and came across an unfinished problem posed by one of my […]