What Math Books Are Needed for Self-Taught Physics?

[Puglife]

I am self taught, and would like to know more about physics, and engineering, the biggest issue I have been having is that for most physics courses, and textbooks I read, I do not understand the math behind. My highest math education was calc ab ap in high school.

I was wondering if you all could tell me specifically what math courses I need to learn in order to have the math basis for most forms of engineering and or physics.

I would also like to know if their is a textbook series out their, that would go through each course, like in volumes, that I could read through the entire series, and by the end of it, know the math I require. ( I would prefer this so as to avoid massive repetition most non volume textbooks have).

Also, if their are any other resources that you all could give me, that I could learn everything I needed to know from that one resource, such as a multi-part book series, or just a list of textbooks in order i need to follow, then that would be absolutely amazing!

A video playlist would be nice instead, as long as I get the same amount of content.

Thank you guys so much!

 

[The Bill]

If you understand the calculus you learned in high school, you shouldn't have any problem with a standard two or three part first year physics textbook. MAybe you've been aiming too high?

Try something like Halliday & Resnick's Physics (the 4th edition can be had for next to nothing used, and is a perfectly fine text for your purposes) or Shankar's two part Fundamentals of Physics. Shankar's text has a nice advantage in that complete videos of the course he teaches are available online.

If you can't handle the math in an introductory text like that, then you need to reinforce your calculus. Judith Gersting's Technical Calculus with Analytic Geometry is an excellent choice for this. Also, if you didn't get to keep your AP calculus textbook, Gersting would make a good reference as you continue your education. Plus, it's published by Dover now, so it only costs about $20 new, and much less used.

In parallel with that, you should learn linear algebra and matrix arithmetic thoroughly. It is used everywhere in mathematics, physics, and engineering. I wish I could punish whoever let me take differential equations in college without taking linear algebra first. The best part is that linear algebra is fun, and only requires basic high-school level algebra as a prerequisite. Linear algebra is also a great way to start building intuition about higher dimensional spaces. I recommend David C. Lay's Linear Algebra And Its Applications, 3rd edition. It's an excellent text, and is available very cheaply used.

Also, go to your nearest university library, make friends with the librarians, and get to know the mathematics and physics shelves. Having books on all the topics you need right at hand while taking a few hours to study at the library is a great help.

 

[Puglife]

If you understand the calculus you learned in high school, you shouldn't have any problem with a standard two or three part first year physics textbook. MAybe you've been aiming too high?

Try something like Halliday & Resnick's Physics (the 4th edition can be had for next to nothing used, and is a perfectly fine text for your purposes) or Shankar's two part Fundamentals of Physics. Shankar's text has a nice advantage in that complete videos of the course he teaches are available online.

If you can't handle the math in an introductory text like that, then you need to reinforce your calculus. Judith Gersting's Technical Calculus with Analytic Geometry is an excellent choice for this. Also, if you didn't get to keep your AP calculus textbook, Gersting would make a good reference as you continue your education. Plus, it's published by Dover now, so it only costs about $20 new, and much less used.

In parallel with that, you should learn linear algebra and matrix arithmetic thoroughly. It is used everywhere in mathematics, physics, and engineering. I wish I could punish whoever let me take differential equations in college without taking linear algebra first. The best part is that linear algebra is fun, and only requires basic high-school level algebra as a prerequisite. Linear algebra is also a great way to start building intuition about higher dimensional spaces. I recommend David C. Lay's Linear Algebra And Its Applications, 3rd edition. It's an excellent text, and is available very cheaply used.

Also, go to your nearest university library, make friends with the librarians, and get to know the mathematics and physics shelves. Having books on all the topics you need right at hand while taking a few hours to study at the library is a great help.

Calc ab does not go into a lot of the math required, it is only like a 3rd of calculus, we only went over simple integrals, derivatives, and limits. A lot of my textbooks talk and reference aeriea, as well as complex exponentials. I have taken trough physics mechanics, and need a higher level, but, for example, when learning maxwell equations, they us a integral symbol that is similar to an integtal, but as a circle in the middle of it. I am not sure what this means, because calc ab is only a small section of calc. Do I just need to learn calc bc, and then linear algebra, then differential equstions? Because the issue isn't the textbooks are too high level, because they are the next level after what I have done.

 

[The Bill]

Okay. You need to learn vector calculus and basic complex algebra, leading into basic complex analysis.

Gersting does not cover vector calculus, so that's out.

H.M. Schey's book Div, Grad, Curl, and All That gets to closed line integrals (the integral with a circle) on page 75 or so, and covers a lot of other material you need to understand Maxwell's equations, also.

I'm not sure in which class I first learned Euler's formula and the properties of complex exponentials. It could have been calculus II, when we learned Taylor series, or it might have been in my first differential equations class. I can't think of a good book to recommend here, but there are lots of excellent videos which explain what you need to know.

I recommend you go to YouTube and watch David Metzler's video series "The Killer App for Complex Numbers" staring with (1).

But yes, calculus through basic vector analysis, linear algebra, and differential equations with Fourier series would be a good base before learning how to work with Maxwell's equations.

 

[Puglife]

Okay. You need to learn vector calculus and basic complex algebra, leading into basic complex analysis.

Gersting does not cover vector calculus, so that's out.

H.M. Schey's book Div, Grad, Curl, and All That gets to closed line integrals (the integral with a circle) on page 75 or so, and covers a lot of other material you need to understand Maxwell's equations, also.

I'm not sure in which class I first learned Euler's formula and the properties of complex exponentials. It could have been calculus II, when we learned Taylor series, or it might have been in my first differential equations class. I can't think of a good book to recommend here, but there are lots of excellent videos which explain what you need to know.

I recommend you go to YouTube and watch David Metzler's video series "The Killer App for Complex Numbers" staring with (1).

But yes, calculus through basic vector analysis, linear algebra, and differential equations with Fourier series would be a good base before learning how to work with Maxwell's equations.

ok, i will check out the video. I found a great book series on calc 1 2 and 3, so should i read that, and then a linear algebra textbook series, and then differential equations?

 

[jtbell]

I'm not sure in which class I first learned Euler's formula and the properties of complex exponentials.

I think I learned about complex exponentials in my physics courses. I don't remember if my freshman intro physics course (Halliday/Resnick) used them, but they were definitely in the intro modern physics course that followed. I think most intro modern textbooks specifically discuss the basic properties of complex numbers and complex exponentials, as a lead-in to QM wave functions. I taught such a course for many years, and we always spent a day in class on complex variables.

 

[The Bill]

ok, i will check out the video. I found a great book series on calc 1 2 and 3, so should i read that, and then a linear algebra textbook series, and then differential equations?

That would be a good plan. You only need one book for the linear algebra you need. Lay's text I mentioned above is an excellent value, and the third edition is a book I keep extra copies of to give to exceptionally motivated students.

 

[Puglife]

Thank you, I have one last question, which calc book is better,
http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/Calculus.pdf
or all three of these
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

?

Also, thank you all very much for all of your help, it is very kind of you all to spend your time to help me out.

 

[smodak]

For vector analysis, buy an old edition of Spiegel's vector analysis (schaum). inexpensive and fantastic.
https://www.amazon.com/dp/B000N991AI/?tag=pfamazon01-20

You should also plan to start reading slowly through a good mathematical methods book, e.g. the one written by Hassani
https://www.amazon.com/dp/0387989587/?tag=pfamazon01-20

Another book I find helpful in this regard is Joos. Although it may be a bit too much for you, it is inexpensive and nice to have as a second book.
https://www.amazon.com/dp/0486652270/?tag=pfamazon01-20

Shankar's book, however, may be most suitable for your purpose.
https://www.amazon.com/dp/0306450364/?tag=pfamazon01-20