I am currently a 3rd year undergraduate electronic engineering student. I have completed a course in dynamics, calculus I, calculus II and calculus III.
I am very interested in mathematics and physics, however there is some clarification that I need regarding these matters as I am confused as to why we study functions, calculus and physics.
I know that mathematics is required in order to describe physics, but in many cases we require a function that describes the phenomena at hand. The major question I have is, how do we know what these functions are? I know that we make use of differential equations in order to obtain a function that represents the desired system, but this is not always the case.
For the sake of clarity I will provide a few examples that I have in mind:
(a) Take for instance Maxwell's equations, in order to apply Faraday's law we need the function describing the electric field, for Gauss' law we need a function for the magnetic flux density &/or electric displacement field etc.
(b) For Green's theorem, if we wanted to determine the flux of a vector force field within a given region we would first need the vector function of this force field.
(c) In the subject of sequences and series, how do we determine an explicit formula for the pattern describing these discrete systems, if there exists any at all and why would we need this?
In real life how do we find these functions on our own? In a calculus and physics class, we are given these functions and are required to compute the quantities at question using the appropriate theorems/formulas.
The thought of these subjects requiring us to poses a function, which we in real life do not know is causing me discomfort as I am uneasy with the idea that we first need to obtain a mathematical object, which is non trivial - we can't see a magnetic field nor can we see the function that governs it - in order to make use of these beautiful theorems. This is discouraging me from wanting to pursue further studies in the field of mathematics and physics. Where's the machine which generates these function that I need? :(