Vector Calculus For Physics: A Complete Self-Study Course

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?

BUILD A DEEP UNDERSTANDING OF ANY TOPIC IN PHYSICS

One of the most important areas of mathematics that ANYONE wanting to learn classical mechanics, electromagnetism, relativity or any engineering discipline needs to master is vector calculus.

Vector calculus underlies almost all of advanced physics and not understanding it will just leave you frustrated trying to learn physics without actually progressing anywhere.

Vector calculus and advanced math are often taught in an abstract and unpractical way, leaving you wondering "what am I ever going to do with this knowledge?"

This is the exact issue this course aims to fix; to help you actually learn the math needed 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.

Interested yet?

HOW YOU'LL BENEFIT FROM THIS COURSE

In case it's not quite clear yet, here is exactly how you'll benefit from this course.

First of all, you'll be able to understand intuitively why particular areas of physics use the math they use and what the physical implications of these concepts are.

This is done using interesting visualizations, such as the animation below (which shows you how the Laplacian dictates the time evolution of a temperature profile), among other things.

You'll also learn how to apply advanced mathematical concepts in practice through various step-by-step examples.

Not only will you get to see worked-through examples, you'll also be able to solve various practice problems yourself in the workbook that's included with the course.

You'll get to build an understanding of physics and math that is not only practical, but also vastly deeper than what most people have.

The course lessons relentlessly focus on giving you the big picture and, while also giving you deep insights into why particular mathematical tools are used to describe any given physical phenomena.

The best part about this course is that anyone will be able to understand the topics covered with basic high school level math (if even that).

This is because each concept is carefully built up to from scratch and the physical as well as the practical motivation behind each new concept is explained (see below for the exact topics covered).

You'll be able to save TONS of time and effort as this course only focuses on the things that are actually necessary, rather than having you learn a bunch of useless fluff you're never going to use anywhere.

This course will take you from being a complete beginner to someone with a deeper understanding of vector calculus and physics in general than what most people will probably ever have.

"I've always wanted to understand physics and learn the math needed for it. I've tried learning these things on my own, but never really got anywhere until I discovered the Profound Physics website and this course, in particular.

Now I'm finally making progress and learning new things everyday as I'm going through this course. Each of the lessons clearly lays out what you truly need to know to understand physics. I've also learned to apply the concepts very well from the few practice problems I had time to work through so far!"

-Samantha

HERE'S EXACTLY WHAT YOU'RE GOING TO GET:

• 16 lessons (with more to be added soon)
• Worked-through examples of each concept (related to both math and physics)
• The Vector Calculus For Physics -workbook with tons of practice problems for you to do yourself
• Step-by-step solutions to all of the practice problems
• The Vector Calculus For Physics -cheat sheet (a downloadable eBook guide) with all of the important equations and concepts
• Database of various tools and resources (such as online calculators)
• Lifetime access to all course content

THE EXACT TOPICS YOU'LL LEARN FROM THIS COURSE ARE:

Part 0: Course Introduction & Resources

Here you'll be given some tips on how to go about taking the course as well as all the resources (calculators, Workbook, Cheat Sheet and so on).

Part 1: Essentials

In this part we'll carefully go over the very basics and how they relate to physics, so that you have a strong foundation to learn more advanced topics:

1. Coordinates, Vectors & Basis Vectors
2. Differential Calculus & Derivatives
3. Integral Calculus & The Fundamental Theorem of Calculus

Part 2: Vector Calculus

In this part, you'll first get introduced to the main concepts behind vector calculus, which include:

1. Scalar & Vector Fields
2. Multivariable Calculus & Partial Derivatives
3. Double & Triple Integrals
4. Gradient, Divergence, Curl & Laplacian

Then, you'll be walked step-by-step through the most important and advanced topics in vector calculus as well as physical motivation and applications for each concept:

1. Parametric Curves & Surfaces
2. Line Integrals & Surface Integrals
3. Stokes' Theorem & The Divergence Theorem
4. The Helmholtz Decomposition Theorem

Part 3: Vectors More Abstractly

In this section, we will discuss various advanced and arguably quite abstract topics relating to tensors and coordinate transformations.

Understanding the concepts in this section is essential for many topics in physics including advanced electrodynamics, special relativity and general relativity.

The exact topics that are covered here include:

1. Tensor Notation
2. Coordinate Transformations & Jacobian matrices
3. Integral Transformations & Jacobian Determinants
4. Covariant & Contravariant Vectors

In case you have any questions, feel free to contact me at villeh@profoundphysics.com.