There are several books in the market that give a good overview about the mathematical methods that Physicists must learn in their undergraduate formation at University. Some of them are Boas "Mathematical Methods in the physical science", Cahill "Physical Mathematics", Hassani "Mathematical Physics" and of course Arfken ,Weber and Harris with "Mathematical Methods of Physics" This last one is my favorite. I must say that I have all of them but I have only gone very deep on the last two. Hassani is very terse, it covers much more than Arfken but is not an easy reading at all. That's why I recommend to every physics student Arfken, after a first chapter that touches and make contact with what one sees on the calculus courses this is infinite series, vectors, derivatives, integrals, Dirac's delta function, complex numbers and induction there follows a second chapter that reminds the reader about some of the topics that are covered in a Linear Algebra course which are matrices and determinants. The third chapter is basically a Calculus III review where all about curvilinear coordinates, transformations coordinates and the typical Integral theorems of Gauss, Stokes and Green identities are covered. Chapter four begins with new stuff for the student, with a full chapter on Tensors and Differential forms. Chapters 5 and 6 are again a Linear algebra course for vector spaces and the eigen value problem. Chapter 7 is about ordinary differential equations which usually are seen in a different a previous course just on ODEs. Chapter 8 is about Sturm Liouville theory which is new stuff for the undergraduate where you learn about self adjoint differential operators, chapter 9 deal with Partial Differential Equations (PDEs) where you learn about some of the methods to deal with this awesome subject like the separation of variable and you treat the Laplace, Poisson, Heat and Wave equations for example. Chapter 10 is about Green's functions which are the solutions to any differential equation as a response to the Dirac delta function. Chapter 11 and 12 are about complex analysis these are a MUST seen by the student for the methods of complex variable are used nearly everywhere in advanced Physics, chapter 13 introduces the Gamma Function it is HERE that I learned everything I know about the Gamma Function, its functional equation, its various representations, its zeros, poles and analytic continuation etc. Chapter 14 you have Bessel Functions, these functions are a bit terse to treat but are fundamental in Physics they not only satisfy recurrence relations but you have a whole Zoo of them, first kind second kind , modified, spherical etc. Their orthogonality is given and also various integral representations. Chapter 16 is about Angular Momentum which is vital introduction to what one sees on a Quantum Mechanics course for the solution of the Hydrogen Atom. Chapter 17 is about Group Theory, chapter 18 gives more special functions other than the Gamma and Bessel like the Chebyshev polynomials, Hermite functions, Laguerre functions and the Hypergeometric function, all off these functions pop up as different solutions of classic ODEs that appear in Physics. Chapter 19 is about Fourier Series which are a basic tool to treat PDEs, Chapter 20 is about Integral Transforms which are used as another method to solve ODEs and PDEs, The Laplace Transform for ODEs and typically The Fourier Transform for PDEs. Chapter 21 treats Integral Equations, Chapter 22 Calculus of Variations, here is presented the Euler-Lagrange equation fundamental for High energy physics and finally chapter 23 is about probability and Statistics which should be covered as usual in a separate course but these is a resume. All in all a great textbook to learn the mathematics a Physicists needs in order to acquire its undergraduate title, more important the exercises are doable and in case you are doing self study as me, you can find on the internet its solution manual with the answers to every single question and exercise, it is a delight for me, my favorite!