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!
Best Answer
I recommend checking out Gilbert Strang's book Introduction to Applied Math.
Strang has great intuition and I think he explains things in a very clear, simple, and yet deep way.