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    Studying What to do in a gap year to prepare for a Physics + Math degree

    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...
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    Studying What to do in a gap year to prepare for a Physics + Math degree

    Overall, the Thomas calculus text book 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...
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    Programs Should I become a physicist or a mathematician?

    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.
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    Resources for self-studying PDEs

    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...
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    Studying Focus on in-depth understanding of the Maths behind Physics

    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.
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    Book of general physics (which covers the subjects of physics as a whole) with complete exercises?

    Joos' Theoretical Physics probably has the breadth and level you want but relatively few exercises.
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    Other Getting back into physics

    My method of recovering undergraduate physics knowledge, reading the text books 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 text book, which alone...
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    Physics major and programming

    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.
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    Other Will I be looked down on? (CS degree from Western Governor's University)

    What employment prospects did you have in mind after school?
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    Physics Beginning Physics Studies at Age 39: Is it Nuts?

    With about five months to the decision deadline I might suggest starting to work through a calculus textbook to filter this idea. If you can handle studying it, firming up the requisite math skills, seeking help as necessary, and find yourself hungry for more then you can take that as a sign to...
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    Studying Watching video lectures along with solving problems in a book?

    For upper division physics in general you'll want to first go through introductory physics with calculus and a math methods book at least on the level of Boas' Mathematical Methods in the Physical Sciences, a book to which Griffiths refers in Introduction to Electrodynamics.
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    Question about the efficiency of using an array or individual variables

    For memory efficiency: struct boolmap { char x:1; char y:1; char z:1; };
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    Boundary conditions in dielectric problems

    A bit late, but I found this thread searching for a similar problem: If the two dielectric media in contact with the sphere polarize differently they would have different surface polarization charge densities just outside the sphere. The charge on the sphere would get rearranged accordingly.
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    Order of Courses

    That'll do it. Reviewing the chapter on integration techniques (radical and trig/hyp substitution, partial fraction decomposition, etc) in your calculus text book and doing at least half of the exercises could remedy the problem.
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    Order of Courses

    I would expect AP Calculus to suffice to prepare you for differential equations and vector calculus in your freshman year. If you hadn't done AP Calculus I'd consider it a mistake for you to sign up for those classes and for the university to allow you to do so. If you have gone through AP...
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    Physics Study Marathon -- Book Suggestions Please

    If you've had introductory calculus get yourself a mathematical methods book like Boas' and start paving the contents into your brain.
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    Calculus Recommended book for advanced calculus

    For your listed concerns I can recommend the following: 1. Introduction to Analysis by Maxwell Rosenlicht ( I had this one on hand while working through a first year calculus text book so I can read some of the proofs omitted by the latter...
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    Calculus What is a good book to review basic calculus?

    This page has a strong recommendation.
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    I Derivation of Divergence in Cartesian Coordinates

    OK. The ##F_x(x_0, y, z)## term must subsume ##(y-y_0)\frac{\partial F_x}{\partial y}\Big\arrowvert_{x_0, y_0, z_0}## and ##(z-z_0)\frac{\partial F_x}{\partial z}\Big\arrowvert_{x_0, y_0, z_0}##. Thanks.
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    I Derivation of Divergence in Cartesian Coordinates

    If, in composing the Taylor expansion, you evaluate all the zero-order terms and partials at the point ##(x_0, y_0, z_0)## then would not the integrals have only constants over which to integrate, leaving only those constants multiplied by the area? But the expansions I copied above show the...
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    I Derivation of Divergence in Cartesian Coordinates

    In section 1-5 of the third edition of Foundations of Electromagnetic Theory by Reitz, Milford and Christy, the authors give a coordinate-system-independent definition of the divergence of a vector field: $$\nabla\cdot\mathbf{F} = \lim_{V\rightarrow 0}\frac{1}{V}\int_S\mathbf{F\cdot n}da$$...