Lagrangian Mechanics & Field Theory: A Complete Course

Anyone who truly wants to understand general relativity, quantum field theory or any other area of modern physics first needs to master Lagrangian mechanics.

The issue with most resources teaching Lagrangian mechanics is that they don't truly teach you the why behind it.

But what if it didn't have to be that way? What if you could truly learn Lagrangian mechanics the right way?

LEARN LAGRANGIAN MECHANICS THE RIGHT WAY - EVEN IF YOU'RE A BEGINNER

The truth is that trying to understand physics at a deep level without understanding Lagrangian mechanics is like driving a car without a steering wheel – you’ll eventually run into a wall and not be able to move forward anymore.

The issue is that Lagrangian mechanics is often taught in a way that does not truly explain why it's needed and instead leaves you wondering “who cares about this?”

The true reason why Lagrangian mechanics is so incredibly powerful is that it gives you a general framework for describing literally any area of modern physics.

THIS is the reason why Lagrangian mechanics exists, but almost no one will teach you it this way... even though they should.

Whether you want to learn:

• Electrodynamics
• Special and general relativity
• Quantum field theory
• String theory

You absolutely need to have a deep understanding of Lagrangian mechanics to even get started on any of these topics.

For myself, learning Lagrangian mechanics was the biggest catalyst that enabled me to understand high-level physics and I believe it will be for you too.

Today, I can confidently say that learning Lagrangian mechanics was the single most important thing I ever did in terms of my physics education.

However, if there is one thing I wish I would've had back when I first began learning it, it would be a dedicated resource that introduces Lagrangian mechanics completely from scratch and gives you everything in one place.

This is exactly what this course will give you.

You'll learn Lagrangian mechanics in a completely unique way you've likely never seen before - as both a fundamental framework for advanced modern physics, but also as an incredibly powerful problem solving tool.

Lagrangian Mechanics & Field Theory: A Complete Course is a complete resource specifically designed to teach you everything you'd possibly need to know about Lagrangian mechanics and modern field theory - the fundamentals, prerequisites, theory, math and practical applications. It's all here.

WHAT THIS COURSE WILL DO FOR YOU

My goal with this course is actually very simple. It is to teach you Lagrangian mechanics and field theory exactly the way I would have needed as a beginner and what I believe you will as well.

Personally, I want to make this course as accessible as possible.

From my own experience, I've found that there is a huge barrier to entry on learning the "cool" subjects in physics - general relativity, quantum field theory, particle physics and so on.

That's why I've built this course in a way that enables you to learn these topics from the ground up through understanding the Lagrangian framework, both in the context of mechanics and field theory.

This is a very beginner-friendly course with a low barrier to entry, but you will certainly learn more than just basic beginner stuff.

After this course, you'll specifically be able to:

• Understand real physics and build a much deeper understanding than most people will ever have
• Have the tools to work through nearly any advanced modern physics textbook
• Gain an edge in your physics classes on Lagrangian mechanics or field theory if you're a student

And better yet, you'll save tons of time and money as this is the last resource on Lagrangian mechanics you'll ever need.

HERE'S EXACTLY WHAT YOU GET

The course is structured in easy-to-navigate parts that each cover a particular aspect of Lagrangian mechanics or field theory.

In total, the course includes 596 pages worth of completely unique lesson material. You'll find the exact lesson plan at the end of this section.

Along with the main course content, you will also get:

• Workbook that includes tons of practice problems you can do yourself
• Solution manual with answers and step-by-step solutions to every problem
• All content available in a downloadable & printable format, along with a mobile app that gives you easy access to all course content on your mobile device
• Course material also available in paperback and hardcover book formats (coming soon)
• Bonus Resources & Tutorials: These haven’t been fully planned yet but there will be bonus resources on at least orbital mechanics and Hamiltonian mechanics
• Lifetime access to all currently existing as well as future content

Here are some samples of the style of explanations you can expect to find inside the course:

THE COURSE LESSON PLAN

The course is structured in 9 main parts, covering a total of nearly 600 pages worth of material:

• Part 1: Basic Concepts & Newtonian Mechanics – the first part covers all the basic concepts you’ll need, including energy, momentum, equations of motion as well as the Newtonian framework of mechanics. We also look at the main issues with Newtonian mechanics, which works as motivation for introducing the Lagrangian formulation in the first place.

• Part 2: Lagrangian Mechanics Intuitively – in this part of the course, Lagrangian mechanics is introduced in a very intuitive manner. This part is meant to give you the big picture behind Lagrangian mechanics, which the latter parts of the course will then expand on in MUCH greater detail.

• Part 3: Calculus of Variations – calculus of variations is the area of math Lagrangian mechanics and a lot of other areas of physics like field theory are largely based on. In this part, you’ll learn the most important concepts in variational calculus and how to apply them in practice through various physics-focused examples. We will also discuss how variational calculus is used in Lagrangian mechanics – this gives you all the mathematical tools you’ll need to really understand Lagrangian mechanics deeply.

• Part 4: Lagrangian Mechanics In Action – in this part, we’ll dive deep into the main topics related to Lagrangian mechanics as well as how to apply it in practice. Among other things, we’ll discuss solving problems in Lagrangian mechanics (general strategies and lots of examples), generalized coordinates and momenta as well as constrained dynamics and Lagrange multipliers.

• Part 5: Generalized Forces & Virtual Work – the main goal of this part is to generalize various familiar concepts in mechanics like forces and work to the Lagrangian formulation. In particular, we’ll look at the concept of generalized forces and virtual work, how to incorporate friction, non-conservative forces and velocity-dependent forces into the Lagrangian formulation, the principle of virtual work as well as d’Alembert’s principle.

• Part 6: Symmetries & Conservation Laws – the link between symmetries and conservation laws is one of the most important discoveries about modern physics Lagrangian mechanics allows us to make. This part of the course is about exactly that – we’ll discuss symmetries of Lagrangians, cyclic coordinates, how conservation laws come about in Lagrangian mechanics and Noether’s theorem.

• Part 7: A Crash Course In Field Theory – pretty much all modern theories of physics are field theories. With all the tools of Lagrangian mechanics we’ve learnt throughout this course, we are now ready to begin studying field theory. Throughout this part, you’ll learn the general framework for constructing field theories and describing them, general rules for building relativistic theories, working with four-vectors and tensors as well as – of course – plenty of examples along the way.

• Part 8: Examples of Field Theories – this part is all about the applications of everything we’ve learnt about field theory so far. We’ll dive into various different field theories, their predictions as well as how the Lagrangian formulation naturally encodes all of this – including different properties of fields (and quantum particles), such as mass, charge, polarization and so on. One of the important topics we cover in this part is electromagnetism as a relativistic field theory and how fundamental properties of electricity and magnetism arise from its Lagrangian field theory description.

• Part 9: Particles, Fields & Interactions – Part 9 of the course is all about interactions – how particles interact with various fields and how different fields interact with each other. We dive deep into the theory and practical applications of constructing interacting field theories – everything from self-interacting field theories to gauge interactions (describing the full theory of photons) as well as an extensive discussion of the Higgs mechanism in particle physics!

This is exactly the resource I wish I had back when I first began learning Lagrangian mechanics – and you can have it today!

In case you have any questions about the course, feel free to contact me at ville@profoundphysics.com.