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Hi, you all,
I open this thread to ask for any recommendation concerning integration as well as ODE/PDE solving techniques for physics. I love mathematics, and I usually read material on pure mathematics (most notably abstract algebra and a bit of topology) but here I'm more interested in the learning and practicing methods to solve ODEs, PDEs and general integrals, or at the very least, being able to reduce them to known equations whose numerical solution is well established (Hermite polynomials, Bessel functions, etc.).
I'm finishing my third year in physics with the intention of going towards theoretical physics, and even though I know basically everyone solves these problems numerically, I would like to dig in the equations and integrals that led to functions like Riemann zeta, the Legendre polynomials, the Airy functions, etc. I'm not as interested in learning their story as to practice how to reduce problems to these "solved" problems, since my purpose is to understand where these constants that appear in many equations of physics come from. Any recommendation will be appreciated. Oh, and by the way: I understand that it might be the case that integration techniques and ODE/PDE solving techniques might be treated in separate books.
I open this thread to ask for any recommendation concerning integration as well as ODE/PDE solving techniques for physics. I love mathematics, and I usually read material on pure mathematics (most notably abstract algebra and a bit of topology) but here I'm more interested in the learning and practicing methods to solve ODEs, PDEs and general integrals, or at the very least, being able to reduce them to known equations whose numerical solution is well established (Hermite polynomials, Bessel functions, etc.).
I'm finishing my third year in physics with the intention of going towards theoretical physics, and even though I know basically everyone solves these problems numerically, I would like to dig in the equations and integrals that led to functions like Riemann zeta, the Legendre polynomials, the Airy functions, etc. I'm not as interested in learning their story as to practice how to reduce problems to these "solved" problems, since my purpose is to understand where these constants that appear in many equations of physics come from. Any recommendation will be appreciated. Oh, and by the way: I understand that it might be the case that integration techniques and ODE/PDE solving techniques might be treated in separate books.
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wow I'll check out Churchill. Thanks!