[Algebra] [Calculus] [Classical Mechanics] [Discrete Mathematics] [Geometry]

[Number Theory] [Python] [Quantum Mechanics] [Research] [Statistical Mechanics] [Statistics] [Thermal Physics]

Algebra

• 08 Jun 24: Third Fundamental Form and How to Find it
• 18 Feb 24: Tensors and its transformations

Calculus

• 06 Jun 24: Integration by Laplace Transform
• 16 Oct 23: More on Multivariable Calculus

Classical Mechanics

• 26 Jul 24: Problem of Two Fixed Centers (Part III)
• 22 Jul 24: Classifying and Finding New Possible Orbits (Part I)
• 17 Jul 24: A Proof of the Existence of the Figure-8 Orbit using Actions and the Shape Sphere
• 16 Jul 24: Sundman's Power Series Solution to the Three Body Problem (Part II)
• 12 Jul 24: Sundman's Power Series Solution to the Three Body Problem (Part I)
• 09 Jul 24: Problem of Two Fixed Centers (Part II)
• 04 Jul 24: Understanding and Visualizing the Shape Sphere
• 28 Jun 24: Problem of Two Fixed Centers (Part I)
• 27 Jun 24: Ellipses and the Two-Body Problem
• 25 Jun 24: Symplectic Integrators
• 24 Jun 24: Plotting and Visualizing the Three-Body Problem
• 08 Apr 24: Why is Momentum Conserved?
• 20 Feb 24: Overview of the Two-body Problem
• 15 Aug 23: Two Particles Collision
• 29 Jul 23: Two Interesting Questions related to Free Fall
• 13 Jan 23: Perturbations - A view on Classical Mechanics and Quantum Mechanics
• 25 Dec 22: Conservations in Physics - Noether's Theorem
• 25 Dec 22: Two Laws Related to Planetary Revolution

Discrete Mathematics

• 18 Jun 24: An example of Discrete Fourier Transform using FFT Algorithm
• 13 Jun 24: Image Processing using Python and Convolution Theorem

Geometry

• 27 Jun 24: Ellipses and the Two-Body Problem
• 08 Jun 24: Third Fundamental Form and How to Find it
• 04 Jun 24: Theorema Egregium --- The reason why all maps are wrong
• 31 Mar 24: Julia Sets and the Mandelbrot Set

Number Theory

• 11 Jun 24: Solving a system of Congruences
• 10 Jun 24: Wilson's Theorem
• 09 Jun 24: Infinite Descent and Vieta's Formulas
• 07 Jun 24: An Application of the LTE lemma and Fermat's Little Theorem
• 06 Jun 24: Euler's Totient function, Reduced Totient function and Carmichael Number

Python

• 19 Jun 24: Linear Regression using OLS and SGD Methods in Python
• 13 Jun 24: Image Processing using Python and Convolution Theorem

Quantum Mechanics

• 08 Jun 24: An Easy and Brief Introduction to Bose Gas and Fermi Gas
• 13 Jan 23: Perturbations - A view on Classical Mechanics and Quantum Mechanics

Research

• 26 Jul 24: Problem of Two Fixed Centers (Part III)
• 22 Jul 24: Classifying and Finding New Possible Orbits (Part I)
• 17 Jul 24: A Proof of the Existence of the Figure-8 Orbit using Actions and the Shape Sphere
• 16 Jul 24: Sundman's Power Series Solution to the Three Body Problem (Part II)
• 12 Jul 24: Sundman's Power Series Solution to the Three Body Problem (Part I)
• 09 Jul 24: Problem of Two Fixed Centers (Part II)
• 04 Jul 24: Understanding and Visualizing the Shape Sphere
• 28 Jun 24: Problem of Two Fixed Centers (Part I)
• 27 Jun 24: Ellipses and the Two-Body Problem
• 25 Jun 24: Symplectic Integrators
• 24 Jun 24: Plotting and Visualizing the Three-Body Problem
• 19 Mar 24: Group Research in fluid behaviours
• 20 Feb 24: Overview of the Two-body Problem

Statistical Mechanics

• 08 Jun 24: An Easy and Brief Introduction to Bose Gas and Fermi Gas

Statistics

• 19 Jun 24: Linear Regression using OLS and SGD Methods in Python

Thermal Physics

• 12 Jun 24: Thermodynamic Potentials and Maxwell Relations