Where do I start in math for physics comprehension?

[mpatryluk]

I am looking to work my way through classical physics and into more complex modern physics topics.

I try to learn from a combination of internet resources and textbooks, but on the internet I find them often using terminology which is too mathematically advanced for me.

Some examples are:
-Hilbert space
-Lagrangian/Hamiltonian
-Fourier transforms

And when i try to research these topics online, I don't have the necessary context or experience to understand the vocabulary that explains them, i.e. terminology like "a structure on a set" or other vocabulary that is too vague for me to understand (because I don't have the experience to know which context the words should be taken in).

I've learned up to calculus/trig, and am starting work on linear algebra, but I'd like to know which topics I can study which will give me the math literacy I need to understand concepts like the above mentioned. Ideally resources that introduce me to the vocabulary without presuming prior knowledge.

Thanks!

 

[jedishrfu]

When I went to school, I had Calc 1,2,3, Advanced Calculus, linear algebra and Diff Eqns and that was sufficient to study Classical Mechanics from Marion or from Goldstein, E and M Theory and Quantum Mechanics. For self-study you probably need to study them in that order too as QM depends on some CM and EM concepts.

I also took Tensor Analysis and that helped with the notation.

 

[mpatryluk]

Thank you so much, I'll do it in that order then!

 

[jedishrfu]

For me, the Lagrangisn formulation in CM was the coolest thing I had ever encountered. Consider how you've studied Newtonian physics and used force diagrams and vector math to solve your problems which can get very involved to determine the motion of the system.

It never occurs to you that there is this underlying principle call Least Action that says things move is a way to expend the least amount of energy and from simply accounting for the energy of the system and taking its difference in T-V and doing some math determine the motion. It was very profound for me.

 

[CellCoree]

I understand your struggle with understanding mathematical concepts in physics. It can be overwhelming to try to learn both physics and advanced mathematics at the same time. However, the good news is that you have already started with the basics, such as calculus and trigonometry, which are essential for understanding physics.

To improve your math literacy for physics, I would suggest focusing on a few key topics that are commonly used in classical and modern physics. These include:

1. Vector calculus: This is an essential tool for understanding the concepts of motion, forces, and fields in physics. It includes topics such as vector operations, differentiation and integration of vector functions, and theorems like Gauss's and Stokes's theorems.

2. Differential equations: Physics is all about understanding how physical quantities change with time or space. Differential equations are used to describe these changes and are crucial for understanding concepts like motion, energy, and waves.

3. Linear algebra: This branch of mathematics deals with systems of linear equations and matrices, which are widely used in physics to solve problems involving multiple variables.

4. Complex numbers: In physics, many quantities are represented using complex numbers, such as in the case of electromagnetic waves. Understanding complex numbers and their properties will be beneficial in understanding these concepts.

I recommend starting with these topics and mastering them before moving on to more advanced concepts. There are many resources available online, such as Khan Academy and MIT OpenCourseWare, that offer introductory courses on these topics. It is also helpful to practice solving problems and applying these concepts to real-world situations.

In addition, don't hesitate to ask for help from your peers, teachers, or online forums if you come across any difficult concepts. With patience and dedication, you will be able to improve your math literacy and understand the mathematical concepts used in physics.