I have been slowly chipping away at new chapters that I have been wanting to upload but I have finally finished writing my favourite section by far, Section 2.5 — Beyond Classical Mechanics: The Action in Relativistic and Quantum Theories.

This section goes beyond classical mechanics and delves into the role of the Lagrangian formalism in relativistic and quantum theories. It illustrates how our ideas of classical mechanics explored in previous sections (2.1 – 2.4), namely the Lagrangian framework and the action principle, extend far beyond their origins and help build the framework of relativistic electrodynamics, general relativity, and quantum field theories. It also includes a discussion of the path integral formulation of quantum mechanics, which builds a fundamental bridge between classical and quantum physics. Overall, this section gives a glimpse into how theoretical physicists approach modern physics and think about theories from first principles.

Wow — it’s been a year since I added any major sections onto this site, but I have been working on a few topics in classical mechanics (sections 2.4 and 2.5) on my spare time. My second year of medical school is starting tomorrow and I really wanted to upload these sections before things get hectic again.

I have finally uploaded section 2.4 — Applying the Euler-Lagrange Equation in classical mechanics. This is a busy section filled with many examples of how to properly use the Euler-Lagrange equations. The examples get progressively more difficult, building up to my favourite example of deriving the equations of motion of a charged particle in an electromagnetic field (i.e., the Lorentz force law). This last example gives a glimpse into the types of heavy calculations that go into theoretical physics.

I have also worked on another section focused on the role of the Lagrangian formalism beyond classical mechanics. This is a personal favourite of mine and it should be up shortly — stay tuned!

With the days of the summer coming to an end, I am going on a writing frenzy to finish up all the sections of Lagrangian mechanics before I begin my first year of medical school. I have just finished writing section 2.3 — The Bridge to Newtonian Mechanics.

This section is relatively short but dense with important concepts and vocabulary. It introduces the idea of a generalized force and generalized momentum. It also shows how the conservation of momentum and energy make their way into the Lagrangian formalism. You even get a sneak peak of Hamiltonian mechanics towards the end! Overall, this section serves as a bridge between the Newtonian, Lagrangian, and Hamiltonian formalisms.

I have also added a resources section on the menu bar. This resources section contains a large collection of textbook references as well as videos and lectures made by others that have been immensely helpful for my own studies, and will hopefully be useful for you as well. I also included a discussion of physicists that have inspired me and left a positive impact on my life. I highlighted some of their amazing writings, lectures, and videos for your reference.