All the Math You Need for Physics: The Ultimate Guide (Step-by-Step)

[@keithwald5349]

Don't miss these two gems on PDEs and Green's functions: 1. Elements of Greens Functions and Propagation by Gabriel Barton 2. Mathematical Methods for Physics by H.W. Wyld They both contain great stuff with systematic treatments of inhomogeneous problems. And both include the beautiful calculation of radiation by moving sources, from the retarded solutions of the wave equation to the calculation of the Lienard-Wiechert potentials to the evaluation of the fields for several important cases.

[@TheMathSorcerer]

Thank you!!!!!

[@lucforand8527]

Don't most students do algebra and trigonometry in High School? This was definitely the case when I went to high school in Canada. In fact, I even took Calculus in Nova Scotia and was given credit for it at University (following passing a University administered test). The credit was for what you call Calculus 1, 2 and 3; a terminology I am not at all familiar with. At my university it was essentially divided into differentiation and integration and covered over two semesters. I ended up taking 2nd year Calculus or what was called Mathematical Analysis. This was my first heavy math course full of proofs and theorems. We used the book by Apostol. During my physics degree I used the following math books: 'Mathematical Analsysis', Div, Grad, Curl and all That' (required and taught during my 2nd year EM courses), 'Linear Algebra', 'Elementary Differential Equaitons and Boundary Value Problems', 'Mathematical Methods for Physicists', 'Differential Geometry of Curves and Surfaces', 'Computer Methods for Mathematical Computations', 'Statistics (professor's binder book), 'Undergraduate Topology'. My highschool calculus course was based on Schaum's Outline Series: Theory and Problems of Differential and Integral Calculus (2nd Ed.).

[@douglasstrother6584]

"To use mathematics effectively in applications, you need not just knowledge but *skill* . Skill can only be obtained through practice.", from Mary Boas in "To The Student" of her "Mathematical Methods in the Physical Sciences". This is true for both applied (computational-oriented) and pure (theorem-proof oriented) courses. I always had to work through the derivations, examples and do all of the homework to "get it".

[@budgarner3522]

Why working out problems AND examples is critical.

[@douglasstrother6584]

@@budgarner3522 In a recent MS video, he mentions that Paul Halmos did homework problems when studying something new!

[@PaladinLeeroy42069]

Real

[@troyjulianacevedo3068]

Waited for this video 30 years 😂

[@TheMathSorcerer]

hehehehehe

[@troyjulianacevedo3068]

@@TheMathSorcerer figured I’d comment instead of email. I’m 45 now. Lots of education, but took a different path. At this stage in my life, it doesn’t bring me happiness. Since I was 13, I’ve wanted to be a physicist. Sadly, my self esteem and confidence is greatly lacking. The intimidation factor appears to best my drive. Any suggestions or recommendations? For me, I consider this a bucket list item. They say, when you pass, all of your dreams and goals that were never fulfilled are there to see you on. To remind you that it was our responsibility to see them into existence… As always, thank you for the inspiring content.

[@hijackbyejack5458]

@@troyjulianacevedo3068I’ve seen his content enough to know that his reply will likely be “just get started” 🙂

[@lucforand8527]

I should mention that I also had in my possession and continually made reference to the CRC Standard Mathematical Tables (23rd Ed.) and later on the CRC Handbook of Chemistry and Physics (60th Ed.). Of course, today much of this information can be found by an internet search, but it can be useful to have lots of good information all in one place.

[@Neo-Reloaded]

Great video! Apart from what you mentioned, I'd like to add a few comments. In physics, people also study Hilbert spaces, especially in quantum physics, though not in a very formal way. Group theory is also crucial across all of physics because many phenomena involve symmetries. Topology is important too, with topics like topological insulators and topological quantum theories making use of it. Finally, differential geometry plays a key role in general relativity.

[@TheMathSorcerer]

Thanks for adding these important concepts!

[@arphaksad01]

Math classes will depend on physics you are studying. MS level is different than phd. Also theoretical vs experimental. If you are studying particle or pure theoretical physics than get as much math as possible. But if you are working in classical mechanics or more in engineering than don’t need as much high level math

[@ahina_phoenix]

Thank you so much. As a Physics major, I needed this badly!!

[@douglasstrother6584]

I used "Elementary Differential Equations and Boundary Value Problems" (3rd ed.) by Boyce & DiPrima in a DE course offered by the Math Department; and "Mathematical Methods in the Physical Sciences" (2nd ed.) by Boas for the Mathematical Methods course offered by the Physics Department. They both have very applied approaches to the subject. "Partial Differential Equations in Physics" by Arnold Sommerfeld is based on his lectures on Theoretical Physics. It, like other volumes in the series, illustrates the thought-processes of a truly great mind; he was one of the strong bridges between Classical and Quantum Mechanics.

[@TheMathSorcerer]

Excellent books! I have the Boyce & DiPrima book but not the Boas one, yet. Thanks for this comment:) Fun stuff!!

[@rahulsubramanian6545]

Thanks for the video Math Sorcerer.

[@MOXTHEGAMER]

Been looking for this video for a LONG TIME because I want to improve my maths. Thank you.

[@arphaksad01]

My math classes when I studied physics Calc 1,2, Diff Eqs, mathematical physics 1,2(Mary Boas). Optional Complex Analysis. At grad school Butkov, Mathematical Physics 1/2. That was a while back

[@neomagneto84]

Great recommendations and I like the "get after it" mentality as well 💪

[@lucforand8527]

One of the difficult things about Physics is that you often need to learn the math in your physics courses at the same time as you might be taking it in a math course. In other words, part of learning physics is learning the math. For example, you will almost definitely learn about tensors in a physics course, long before you ever see it in a math course. This is just something you have to be aware of. Physics is based on math, so you have to learn the math one way or another; either formally in a math course or during your physics courses.

[@leonstabile]

I think a good sugestion is ''books on theoretical physics'', covering Advanced Linear Algebra, Group Theory/Representation Theory(Particle physics loves these topics), topology(Condensed Matter), differential geometry and manifolds(General Relativity). Some Mathematical Physics books tries to cover these topics, but personaly I like some ''more mathematical books'' than ''physicists books''.

[@TheMathSorcerer]

Thank you!!!!

[@douglasstrother6584]

"Integral Equations" by Francesco G. Tricomi, is a fun read. (It's a short Dover book.) Considering their many physical applications, Integral Equations don't get enough exposure.

[@Paraok3]

We need maths for computer science and Artificial Intelligence next😊

[@MrMegatherium]

I think what this channel provides is a set of teachings, which need to be understood and ultimately applied.

[@BhavukKakkar]

Thank you so much!!

[@labcat647]

You say every engineer needs the Stewart calculus book… but we physicist know you meant us. Good list… and note, because physics majors take so many math classes, it doesn’t take much to get a double major in math.

[@labcat647]

I also used Mathematical Methods For Physicists by Arfken.

[@CategoryTheorist]

@@labcat647have you seen math methods by Boas? How do you think these two math methods books compare?

[@labcat647]

@@CategoryTheorist I have not seen the Boas book, so can't compare. The Arfken book is quite rigorous. I highly recommend it if you are studying upper level undergraduate physics.

[@edwardgraham-j8l]

Some great books on your list ... the later editions are more expensive but the earlier editions have great value as well.

[@budgarner3522]

Great stack of math books for physics and engineering. Matrix algebra is really important, too. That first book is a great selection to start. All the basic skills to make success with the rest of the math selections.

[@qualiqueancrum9135]

All the Math You Need for Statistics: The Ultimate Guide (Step-by-Step) should be next The Math Sorcerer.

[@2384539]

Bro is getting high on math. (sniffing books)

[@lastzulu180]

thank you sir

[@lucforand8527]

All physicists need to take a course in Probability and Statistics, unfortunately, too many do not have enough of this subject. They will know how to combine uncertainties at a basic level but this isn't enough for those who are going to be an experimental physicists. This isn't just the case for physicists, many people working with data (chemists, biologists, geologists, geneticists, etc.) just don't have a strong enough foundation in this area.

[@rahulsubramanian6545]

The Mathematical methods for Physics and Engineering by Cambridge University Press covers pretty much all of the math you would need for Physics.

[@bigdima6945]

Shocked it wasn’t included

[@RaidWahid]

It's not a fit book for beginners learning math, It is better to use that book as a reference book if you already know the math subjects covered in it.

[@rahulsubramanian6545]

@@RaidWahid if you've studied Science with mathematics in CBSE, this book should be a natural progression. If you don't know Calculus then it's better to learn using a pure math book first.

[@RaidWahid]

​@@rahulsubramanian6545 Someone without calculus knowledge will definitely struggle in this book as it doesn't cover calculus in depth.

[@saifurrahmanfaysal8736]

1/Intermediate Algebra 2/ College Algebra 3/Algebra & Trigonometry 4/Calculus 5/Differential Equation & Boundary Value Problems 6/Probability & Statistics 7/Understandable Statictics 8/Linear Algebra 9/ Partial Differential Equation 10/Complex Analysis For Physics Student...

[@PeregrinePitty]

He never misses a chance to bust out the Kreyszig book.

[@Dr.PaulNjeruM369]

Greetings from Kenya!!! 🍻🍻🍻

[@Paraok3]

We need math for Quantitative Finance

[@7743san]

Can we please also get a video for computer science? Would love it!

[@A.Hisham86]

"Smell amazing!!"

[@lucforand8527]

Thickness isn't a measure of content. Have you ever used Landau and Lifshitz's Mechanics and Electrodynamics? The density of information is staggering!!

[@sbando2203]

No differential geometry? Pretty crucial in understanding general relativity

[@daudkaun3807]

That’s like 10,000 pages? You should make a video on how to go through a math book. It’s obviously not the same as reading a philosophy textbook nor a novel. It seems like, in recommending 10k pages of books to people, you seem to know how to maneuver them, whereas a 10k book of philosophy would take years to read properly.

[@luphumlovimbi738]

😮😮😮 the is calculus 4 wow 🤯 I never knew that By the way great content sir I really love it ❤🏆🎖️🥇

[@KymDerriman]

do you know any methods to help someone who constantly mixes things up like signs (positive vs negative) and doing derivatives when you should do integrals and vice versa and tons of variations of that?

[@realestalex2728]

I judge the character of a man by the way he treats his books, and smelling them is Grand Master Wizard tier.

[@TheMathSorcerer]

ROFL

[@Blabluuee]

How am i supposed to finish the calculus book or even 1 book of these books as high school learner

[@mrslave41]

10:56 “pde is hard”????

[@Lucky69K]

2:08 the lol part😂 Smells good

[@ahon720]

Thanks for the video! Could you make one on books about physics too? ^^ Thanks again😃

[@epicjoshy1485]

Just passed my physics I course! I’m waiting for my final grade to be posted but I know I’ll pass 🎉

[@thems2002]

Can you make a video on how can an average student be a mathematician. I am student in final year of college I had this dream of becoming a mathematician.i was in depression in 12th class and couldn't study well then anxiety ocd sufferer in college .I couldn't enjoy the my college well .I used to feel terrible In class as I wanted to do amazing not only passing exams and stuff . unfortunately I kept myself why and what are these teachers doing why can't I grow .OCD wasted my lot of time .can you guide me which books and sequence should I follow to be pro in maths so that I can contribute in this field . Sometimes i feel like a loser sometimes a victim etc

[@Abdullah-t4e6m]

Where are you from Mr sorcerer ? Are you from NRY Florida California or any state ?

[@smaharaj180]

Math for (the) life science(s)

[@omarahmed1760]

can you make a play list of videos like : I'm Going To Give You a SUPERPOWER In This Video - Use It Right Now To Find Your Big Dream Why Smart People Fail Why Your Life Feels Like A Complete Disaster And How To Fix It Act Now or Stay Stuck Forever

[@TheMathSorcerer]

Ya I have one, it's the "inspiration and advice" playlist.

[@omarahmed1760]

@@TheMathSorcerer thank you for that great advices

[@presidentrepublic2479]

I am from india and a book store near me has some MIR books. ( soviet era books) they are rotting there. If you are interested i can send you the video of their name and you can buy them. I dont want to make a profit . I just want to send them to a welcoming place

[@douglasstrother6584]

The MS loves books by MIR Publishing.

[@presidentrepublic2479]

@douglasstrother6584 good

[@kjmav10135]

Why do they only give you HALF the answers? Is there a resource where you can check your work on the other half? Why even bother with the even numbered questions if you can’t know for sure if you’ve got it right? So, it would make the book a few pages longer, but, yeesh. What’s the point?

[@dimitrijestankovic6199]

With all this books, you are rich men.

[@douglasstrother6584]

"Mathematics is difficult, even for mathematicians." ~ Reinhold Böhme, quoted in Appendix A of "Vector Calculus" (2nd Edition) by Marsden & Tromba.