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There are two courses specifically called math methods for scientists (grad level) that are offered in my school. I am doing a interdepartmental degree in microelectronics/solid state physics (Electrical Engineering/Materials Engineering/Physics) focused more on the physics side of it. I eventually do plan on getting a PhD in physics and would like to know the topics in these courses (I literally do not have the time to take these courses). I am going to list the topics below and would like to know any good textbooks/online resources that thoroughly go through these topics so I can go through it during my free time. I have a good background in linear algebra, calculus, Differential equations and a very good understanding of math that has to do with signal processing (fourier/z/laplace transforms/systems theory and a lot of background with complex numbers). I am taking multivariable calculus next term so if anything I list is covered in a typical multi class let me know please. Here are the topics from the course descriptions.
Bessel functions, and Legendre polynomials as involved in the solution of vibrating systems; tensors and vectors in the theory of elasticity; applications of vector analysis to electrodynamics; vector operations in curvilinear coordinates; numerical methods of interpolation and of integration of functions and differential equations.
Vector and Tensor Fields: transformation properties, algebraic and differential operators and identities, geometric interpretation of tensors, integral theorems. Dirac delta-function and Green's function technique for solving linear inhomogeneous equations. N-dimensional complex space: rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation, similarity transformations and diagonalization, Schmidt orthogonalization.
Sorry for the wall of text!
Bessel functions, and Legendre polynomials as involved in the solution of vibrating systems; tensors and vectors in the theory of elasticity; applications of vector analysis to electrodynamics; vector operations in curvilinear coordinates; numerical methods of interpolation and of integration of functions and differential equations.
Vector and Tensor Fields: transformation properties, algebraic and differential operators and identities, geometric interpretation of tensors, integral theorems. Dirac delta-function and Green's function technique for solving linear inhomogeneous equations. N-dimensional complex space: rotations, unitary and hermitian operators, matrix-dyadic-Dirac notation, similarity transformations and diagonalization, Schmidt orthogonalization.
Sorry for the wall of text!