Level of Math Required for Young’s University Physics

[enc12341]

I am a high school student who is planning to start Young and Freedman’s University Physics out of personal interest. However, I am not sure what level of math is required for the book.

I haven’t learned Calculus yet, so I’m planning to study Strang’s Calculus alongside Young’s University Physics. I am the planning to do the chapter about Differential Equations in James Nearing’s Mathematical Methods Of Physics.

I’m not sure, however, if I need anymore math for Uni Physics. The 2 areas I’m particularly concerned about are linear algebra and partial differential equations. Strang only has I think 1 chapter about vectors and matrices, and it only has 10 pages about linear algebra, specifically linear algebra in 3 dimensions. And also, do I need to study partial differential equations for Young’s University Physics? If so, what linear algebra and pde books would you recommend for me to learn these topics?

Thank you in advance.

 

[Doc Al]

For Young and Freedman, you won't need anything but the rudiments of calculus. No partial differential equations! (Or any differential equations at all, except the simplest.) Studying calculus in parallel will be good enough -- the physics applications will reinforce what you're learning in calculus.

 

[enc12341]

Oh okay, so I just need to complete Strang’s Calculus, then I will be fine?

How rudimentary, though, is “rudimentary”? Is it just single variable calculus, or is stuff like multi variable calculus and vector calculus still required; stuff that is covered in Strang?

Thanks for the response by the way.

 

[Doc Al]

Oh okay, so I just need to complete Strang’s Calculus, then I will be fine?

For sure. If you complete Strang you'll be more than prepared for Young & Freedman. (You don't even need to complete it.)

 

[enc12341]

Okay thank you so much!

 

[MidgetDwarf]

If i can offer a suggestion about the Calculus book you are using. I really do not like Strang's books at all. They are too wordy, hard to reference, and the order of topics can be a bit weird. I really dislike his Linear Algebra book the most; however, the problem sets are good.

If you want a gentle introduction to calculus, then I would pick Stewart: Calculus. It is more clear cut in the explanations...

A better suggestion:

Thomas: Calculus With Analytical Geometry 3rd edition.

Well written and explained. I think he offers the best explanation on revolution of solids. Shows you how to apply the calculus to physical problems. Also good explanation on the Theorem of Pappus. Most classes skip this theorem.

If you are looking for a free Ebook, then Keisler: Calculus. It does the nonstandard infenetisimal approach. It's really neat.

I would strongly avoid Strang.

 

[e-pie]

I've read both, University Physics and Resnick Halliday. You may want read them both because where Uni lacks detail/discussion, Resnick/Halliday fills and vice-versa. A similar book is there by George Gammow, nobel winning physicist.

About the Mechanics portion you need basic idea about function and differentiation, Thermodynamics and Electrostatics/Magnetism will require knowledge of integration.

You may want to read some binomial theorem, using Talyor series expansion, trigonometric identities. This would help solving the end chapter problems, especially the starred ones.

For wave theory/end portion of light(where the del(x) m del(v)>h bar/2) mind that University Physics uses it as an introduction to Quantum Mechanics. You will see lots of unknown operators,you may want to skip it.

Special theory of relativity, you just need the maturity to understand simultaneity etc.

You don't need rigorous maths(if you want, you may, it would be a great help for next level). Just pick some Calculus book(my recommendation Thomas) study preliminaries,AP, GP,HP,series, trigonometry,binomial,function, limit, differentiation, integration(upto byparts will do). Operational knowledge for maths will also do. You don't need the exact definition of limit, all that epsilon, delta etc. etc.

 

[enc12341]

Thank you so much guys, I'm now working on Thomas' Calculus, I'm starting differentiation. I'm writing this though, because you wrote "For wave theory/end portion of light(where the del(x) m del(v)>h bar/2) mind that University Physics uses it as an introduction to Quantum Mechanics. You will see lots of unknown operators,you may want to skip it." How do I learn the operators needed for wave theory? Any books/ resources suggested?

 

[e-pie]

Most of it is self contained in the book. But the maturity level needed to understand that is a bit higher. You need to know partial derivatives, trial solution to differential equations, exponential solution. You can find the math in Thomas alone. But it would be a little rigorous discussion.

Any books/ resources suggested?

Books on Quantum Mechanics discusses those in detail. This is way higher level. So for now you can read the Uni,skip where higher level math/Physics is required and return to it after you learn the math. Or you can skip the detailed discussion read the University Physics whole, except that part, read Kleppner Kolenkow's Mechanics then Griffiths Electrodynamics, then Quantum Mechanics. This is almost 3 years work in under grad physics. Assuming you want to study physics in undergraduate level.

So for now I would advice you to use the Thomas and University Physics religiously.

Thanks.

 

[MidgetDwarf]

If you want something to learn Ordinary Differential Equations, in a pain-free way. Then look at Ross: Differential Equations. Older editions would be good: Here is the one I own.

https://www.amazon.com/gp/product/B000NXNWT0/?tag=pfamazon01-20

Look into this book, after you have finished the Calculus 2 material.

 

[verty]

I've read both, University Physics and Resnick Halliday. You may want read them both because where Uni lacks detail/discussion, Resnick/Halliday fills and vice-versa.

Sorry, I have to jump in here to say that University Physics needs a university approach, in the sense that there is a lot to learn and not so much time to learn it. So you want to progress through it at a regular pace while getting the benefit as well. I think this is why e-pie said to read both for more insight. But I don't think you need both because the problems in UP are quite comprehensive and if you do enough problems so that you have that sense, upon seeing a question, to know more or less what to do to solve it, then perhaps you can read another book for insight but I think you will have a lot already. And I think it could also be distracting to do that.

I like the idea to learn the math first but I would not learn integration yet until you need it. I think the real challenge is just the size of the book and keeping up a head of steam so you always feel eager to continue learning.

 

[e-pie]

Size of the book is a factor. I had little less than 2 years to learn it. And I completed it around August of the second year. Of course I did not solve each problem, but I solved most of the starred, calculus based problems. I learned the math as part of regular school course so it never posed a problem.

problems in UP are quite comprehensive

Problems in University Physics are great! And both books have more or less the same type of problems. Doing them from anyone would suffice.
Resnick Halliday has a more everyday-science type problems.