My Applied Mathematics course covers these subjects:
-Calculus of Variations
-Laplace Transform
-Fourier Analysis
-Special Functions
-Integral Equations
And as an introduction to the subject it has several things from calculus like maxima/minima of functions of several variables, some differential(also partial differential equations) equations, Jacobians, Lagrange multipliers, Leibniz rule and partial differential equations(primarily the variable separable method).
While some of you might find these subjects easy, bear in mind that i study physics and because i want to become a theoretical physicist i am attending this course which is from the mathematics department of my university. As i am only a second year undergraduate student, i feel like i am in some deep mathematics, so i will be needing some help(from a book). Any suggestion(s) for a book on the prerequisites(introductory topics that i mentioned) are appreciated.
P.S. Any suggestion for the actual topics of the course are also appreciated!
I have dug up some book titles that i found useful, so i am writing my own answer. Namely:
-Mathematical methods for physics and engineering by Riley, Hobson, Bence. -Many books or chapters from books of the author Vladimir Arnold.
-Strang's Calculus
-Hildebrand's Methods of Applied Mathematics
-Churchill's Fourier Series and Boundary Value Problems
The first covers a lot of subjects and is a pretty big book although it relies on the computational part.
The books of the second point all rely on computation and on intuition with graphs to illustrate what something means in mathematical language but also in physics. It is a bit difficult for a beginner but very useful. Its a unique and the best approach in my opinion.
The third book might cover a lot of single algebra, but it multivariable calculus part(roughly half of the book) is a gem of intuition(like the explanation of the Jacobian--not simply stating that it is used for change of variables)
Hildebrand's books covers integral equations and calculus of variations among others. It seems to be a pretty good book.
Churchill's book covers Partial differential equations, Fourier analysis, Laplace transforms, Bessel functions, Legendre polynomials etc. It is a popular book so i guess it might be good.