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Advanced Math For Physics: A Complete Self-Study Course

Profound Physics

What if there was a way to learn both physics as well as advanced mathematics all at the same time?

What if there was a resource that combined both to give you the perfect starting point for learning any physics topic you want?


Mathematics is the language in which physics is described - ANYONE wanting to learn classical mechanics, electromagnetism, relativity or any other physics topic needs to master the math first.

Perhaps you'd actually like to go beyond a surface-level understanding of physics and truly learn it.

However, there is just one very common issue...

Most math is taught in an abstract and unpractical way that doesn't emphasize its applications to physics enough - leaving you wondering "what am I ever going to use this knowledge for?"

Personally, I understand the struggle of learning advanced physics way too well - everything is so filled with high-level math concepts, it's nearly impossible to NOT get overwhelmed.

At least this is how it felt like when I was a beginner.

But the thing is... all I really lacked was just the right resource that would've taught me exactly what I needed to know.

This is what a good resource will do for you; it will have you take a step back and distill everything into what you actually need to learn.

The surprising fact is that mastering physics is very simple - at least that's what it feels like when you find the right resource.

Well, this is exactly why this course exists; to give you a complete resource for learning exactly what you need for understanding advanced physics.

And better yet, without any unnecessary fluff so that you'll be able to directly apply the math you learn to real-world physical phenomena.


My goal with this course is actually very simple.

It is to teach you the mathematical tools underlying all of physics in a way that leaves you to wonder "wow, that was actually easier than I thought!".

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 mechanics, cosmology, particle physics and so on.

That's why I've built this course in a way that enables you to learn these topics even if you're not good at math to begin with - this is a very beginner-friendly course with a very low barrier to entry.

However, the things you learn in this course are not just basic cookie-cutter physics and math. After this course, you'll specifically be able to:

  • Understand real physics from scratch, beyond popular science
  • Learn the necessary math needed to tackle any advanced physics subject you want to
  • Have the tools to work through advanced physics textbooks
  • Gain an edge in your physics classes if you're a student


I've structured the course into three main parts, currently consisting of 16 lessons (with more to be added soon) and tons of examples:

  • Part 1: Physics With Calculus - this part introduces you to the very basic concepts of calculus and calculus-based physics so that you have a strong foundation to learn more advanced topics later in the course. We cover topics like coordinate systems, bases, vectors, single-variable calculus and how all of these apply to physics.
  • Part 2: Vector Calculus - this part will build on top of the concepts you learned in Part 1, first covering multivariable calculus and partial derivatives. After this, we dive deep into vector calculus, covering many advanced topics like parametric curves and surfaces, line integrals, surface integrals as well as Stokes' theorem, the divergence theorem and the Helmholtz decomposition theorem.
  • Part 3: Calculus of Variations - in this part, we learn calculus of variations, one of the most ubiquitous areas of math you’ll encounter especially in Lagrangian mechanics, quantum field theory and general relativity. We will cover many math topics like functionals, variations, the Euler-Lagrange equation, the Beltrami identity, constraints and Lagrange multipliers as well as lots of applications in the fields of optics, mechanics and differential geometry to name a few.

I'm a huge fan of explaining ideas through visualizations. That's why in each lesson, there are many many diagrams, pictures and even animations (such as this one here, which shows you visually how the Laplacian describes the time evolution of a temperature profile - one of the many topics discussed inside the lessons).

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

  • Workbooks with lots of practice problems for you to do. These include the Physics With Calculus Workbook, the Vector Calculus Workbook and the Calculus of Variations Workbook.
  • Solution manuals that include step-by-step solutions to every problem in the workbooks
  • The Vector Calculus For Physics -cheatsheet (a downloadable eBook) that includes all the important stuff like formulas and key ideas from Part 2
  • Easy access to all course content through a mobile app along with a desktop dashboard as well
  • Lifetime access to all currently existing as well as future content

You can download a sample lesson here, in PDF form. This isn't the most rigorous or longest lesson of the course, but shows you a good example of the style of explanations you can expect to find inside.


In addition to everything from above, you'll get access to my "Mathematics of General Relativity: A Complete Course", which I am currently working on and adding new lessons to.

This is a full course that aims to teach you everything you need to know to understand one of the most famous theories in modern physics: Einstein's general relativity.

Note that the Mathematics of General Relativity -course is not ready yet and includes only two lessons so far, but there will be more in the near-future.

This course will teach you two key subjects in math, which are both highly advanced:

  • Tensor Calculus: This forms the basis for all the math that general relativity uses. We'll cover topics including tensor index notation, coordinate transformations, Jacobian matrices, covectors, one-forms, metric tensors, Christoffel symbols as well as detailed tutorials on tensor manipulation and working with tensor equations in general.
  • Differential Geometry: This is where we apply the tools of tensor calculus to understand differential geometry - the area of math that general relativity uses to describe gravity. The plan for this part of the course is not fully ready yet, and it will take a while before all of the content is added here.

There will also be a full workbook that will include solved practice problems for each lesson.

This course is exactly the resource I wish I had along my own physics journey - and you can have it today!

Sign me up!

In case you have any questions about the course, feel free to contact me at

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Advanced Math For Physics: A Complete Self-Study Course

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