Recent content by Zexuo

Jackson.

The first eight chapters of Boas encompass the math requirements in the syllabus entirely. You can definitely cover that much in eight months if you already know single variable calculus. However, I doubt that you could cover the other material in that time, even at the level of Halliday and...

I've found different presentations of the same material helpful on occasion. For instance, I recall feeling like Boas's PDE chapter skipped an important detail early on, so I worked through the PDE chapter in Boyce/DiPrima first. I then picked up where I left off with Boas without my earlier...

If I read you correctly, you don't deal directly with the probabilities here, but with the counts. p(E_i) = count(E_i) / SUM[count(E_i)]

You can express h1 - h2 in terms of L and theta. Part b will have a term for the spring energy at maximum compression on the final side.

My job title never stopped me from doing this at any office with a whiteboard. The number of people at work who appreciate this may surprise you.

$$\nabla\cdot\mathbf{F} = \lim_{V\rightarrow 0}\frac{1}{V}\oint_S\mathbf{F\cdot n}da$$ $$\nabla\times\mathbf{F} = \lim_{V\rightarrow 0}\frac{1}{V}\oint_S\mathbf{n\times F}da$$ No coordinate system needed... until you want to solve a problem.

With a restricted timeline you might want to switch to Boas for linear algebra and multivariable calculus. She covers those topics in the early chapters. Since you plan to major in math as well you'll take a complete linear algebra course at some point but Boas gives you enough to proceed with...

Overall, the Thomas calculus textbook will likely mirror the beginning calculus course better. Read it through and do all the odd or even numbered exercises. If you have the time do all of them. Same with physics text. If you already know Python, learn to use the numpy, scipy, matplotlib, and...

I would echo Choppy's comments. I would add that, if the physics department has a "math methods" course, you may prefer to take the courses in the math department covering the topics in that course, even if you end up pursuing physics. Ask your advisor about that option.

Assuming you've diagnosed the problem correctly, you already have a handle on the derivation of the Laplacian in Cartesian, cylindrical, and spherical coordinates, separation of variables in PDEs, Fourier series, and solving PDEs with rectangular symmetry. Vis à vis PDEs, Legendre and Bessel...

I consider a mathematical method understood once I've followed the proof for it step by step, noting the techniques involved. I find it helpful in holding the method in mind or, failing that, deriving it from more basic principles when needed.

Joos' Theoretical Physics probably has the breadth and level you want but relatively few exercises.

My method of recovering undergraduate physics knowledge, reading the textbooks from the foundational courses and solving all the problems, may not fit your desired timeline. Then again, I had much more time away from it than you do and needed to start from my calculus textbook, which alone took...

If you feel comfortable with Python, learn numpy, scipy and matplotlib as jedishrfu mentioned above. You might find sympy handy and you don't need to delve very deeply into pandas and scikit-learn before putting them to use with lab data.