Physics Extreme Project: learning physics/math in spare time

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The discussion centers on a structured approach to self-study in physics and mathematics, initiated by a desire to strengthen foundational knowledge after realizing gaps in classical physics understanding. The proposed study plan begins with calculus, linear algebra, and differential equations, followed by classical mechanics and electrodynamics. The individual aims to cover these subjects comprehensively within 2-3 months, using specific textbooks for each topic. However, responses suggest that this timeline is overly ambitious, recommending a slower pace to ensure thorough comprehension. The suggested order of study emphasizes mastering calculus first, then moving to differential equations and linear algebra, followed by physics topics starting with classical mechanics and progressing to electromagnetism, statistical mechanics, and quantum mechanics. The importance of a solid mathematical foundation before tackling advanced physics is highlighted, along with the need for better organization in the study plan.
Dr_Pill
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I added the 'extreme' part to generate a cool acronym: P.E.P.

I want to review/learn as much as I can from physics & mathematics, in my spare time(!).

I started out with quantum mechanics & solid state physics, yet I discovered that my notions of classical physics are poor.

So I turned to classical mechanics & electrodynamics, then it became obvious to me that my basic math skills were also underachieving.
So I must add calculus, linear algebra and differential equations as well.
Of course I once studied this material, but it's so far away.Plus, my brains are rusty, not in shape.

I'm trying to get a nice logical order of subjects.

Phase 1:
Calculus =>Linear Algebra => Differential Equations
combined with
Classical Mechanics followed by Electrodynamics.

Is that a good start?

For Calculus, I use Stewart, Linear Algebra : Lay
Differential Equations: Boyce
Classical Mechanics: Classical Dynamics Particles/Systems
Elektrodynamics: Griffiths

I'm planning to review these subjects as profoundly as possible in as much as 2-3 months.
After that, I throw in Thermodynamics/Statistical Mechanics/Quantum Mechanics/Solid State Physics.
Possibly Abstract Algebra as well.
Problem is: I'm terrible at organizing, so advice/suggestions are more than welcome. :)
 
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Dr_Pill said:
I added the 'extreme' part to generate a cool acronym: P.E.P.

I want to review/learn as much as I can from physics & mathematics, in my spare time(!).

I started out with quantum mechanics & solid state physics, yet I discovered that my notions of classical physics are poor.

So I turned to classical mechanics & electrodynamics, then it became obvious to me that my basic math skills were also underachieving.
So I must add calculus, linear algebra and differential equations as well.
Of course I once studied this material, but it's so far away.Plus, my brains are rusty, not in shape.

I'm trying to get a nice logical order of subjects.

Phase 1:
Calculus =>Linear Algebra => Differential Equations
combined with
Classical Mechanics followed by Electrodynamics.

Is that a good start?

For Calculus, I use Stewart, Linear Algebra : Lay
Differential Equations: Boyce
Classical Mechanics: Classical Dynamics Particles/Systems
Elektrodynamics: Griffiths

I'm planning to review these subjects as profoundly as possible in as much as 2-3 months.
After that, I throw in Thermodynamics/Statistical Mechanics/Quantum Mechanics/Solid State Physics.
Possibly Abstract Algebra as well.
Problem is: I'm terrible at organizing, so advice/suggestions are more than welcome. :)

I think that's a little ambitious! That is a huge body of material to study in such a short time, especially in your "spare" time.

I think you should take things on a bit slower. I would definitely review the calculus and differential equations, and that is enough to get you going with some real classical mechanics. Then you can do some vector calculus and move on to some E&M. Then do some Linear Algebra and move on to Quantum mechanics etc...
 
Have you already studied physics at the level of a typical calculus-based introductory course that uses something like Halliday/Resnick/Walker or the dozen or so similar textbooks? If not, then you might want to start there while you're catching up on calculus etc. You don't actually need a whole lot of calculus for books at that level.
 
jtbell said:
Have you already studied physics at the level of a typical calculus-based introductory course that uses something like Halliday/Resnick/Walker or the dozen or so similar textbooks? If not, then you might want to start there while you're catching up on calculus etc. You don't actually need a whole lot of calculus for books at that level.

Yes, I did three standard physics courses, that covered the whole Serway with Modern Physics + Giancoli.

Want to broaden my knowledge, from basic physics to intermediate.
 
Dr_Pill said:
I added the 'extreme' part to generate a cool acronym: P.E.P.

I want to review/learn as much as I can from physics & mathematics, in my spare time(!).

I started out with quantum mechanics & solid state physics, yet I discovered that my notions of classical physics are poor.

So I turned to classical mechanics & electrodynamics, then it became obvious to me that my basic math skills were also underachieving.
So I must add calculus, linear algebra and differential equations as well.
Of course I once studied this material, but it's so far away.Plus, my brains are rusty, not in shape.

I'm trying to get a nice logical order of subjects.

Phase 1:
Calculus =>Linear Algebra => Differential Equations
combined with
Classical Mechanics followed by Electrodynamics.

Is that a good start?

For Calculus, I use Stewart, Linear Algebra : Lay
Differential Equations: Boyce
Classical Mechanics: Classical Dynamics Particles/Systems
Elektrodynamics: Griffiths

I'm planning to review these subjects as profoundly as possible in as much as 2-3 months.
After that, I throw in Thermodynamics/Statistical Mechanics/Quantum Mechanics/Solid State Physics.
Possibly Abstract Algebra as well.
Problem is: I'm terrible at organizing, so advice/suggestions are more than welcome. :)

The "2-3 months" part is far too ambitious. Even with a good algebra backing, going through Stewart's Calculus book would take 2-3 months if you're rushing. At my University, that book is divided into three courses and is taught over the time period of about 15 months. I don't know how much spare time you have, but you'll probably have to extend your plan.

I would say do your math in the order of:
1. Calculus
2. Diff Eqns
3. Linear Algebra
4. Any/all math

For physics:
1. Classical Mechanics
2. E&M
3. Statistical Mechanics
4. Quantum Mechanics
5. Any/all physics

I threw Stat mech in because it's one of the four "pillars" of physics and is quite useful in all other areas.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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