I am on the other side of the professional life from you who is thinking about what to study. At high school, in german Gymnasium, I finished mathematics with nearly the best rate possible. I also was and have always been a physics enthusiast. Nevertheless I decided to go for mechanical engineering in the late 70, which was a mistake. Many of my fellow students have spend their time to then working on a car or motorcycle, what I never did.
Now I had decided to do dedicate my time to naval modeling as a vehicle to organize my life, to have a positive motivation and to dig into the fields I was going to touch. I am working on my sailboat model from scratch since more than a decade. About 2 years ago I decided to apply the design by modeling technology to design, model and optimize the design of my own method to implement a sheet control system. So soon I decided to organize my partial knowledge of the fields involved in my modeling objective. Electronics, even having been an application engineer of one of the largest US semiconductor companies, analog electronics was alien to me. I went to the university here in Munich and was warmly welcomed and got access to all the material, even their intranet. Soon I realized without updating my mathematical skills it would not even be worth to dig into the electronics courses. Linear algebra and Analysis proved to be the starting challenges i would have to dedicate my efforts to. Another field relevant for my objective is physics, as my sailboat would have the physical environment to be most relevant to model the operation of the sheet control system. Here I found out the same without mathematics and without Linear Algebra and Analysis to start with, worthless to dig into the topic. But also electronics demands physics.
As part of the investigation I did I found the Moocs offerings from german, english (USA) and spanish a language I am a native speaker of. Soon I found out that I was able to choose the professor whose teaching style best fit to me. But if you look at the offering from the MIT, from edX, Coursera to name a few I glanced into related courses and was fascinated. So my decision to engage into my building o a sailboat model had brought me to a fantastic source of learning. But for all those courses, and calculus of single and multi variables adds to the Linear Algebra and Analysis. But I have come to the conclusion that without getting mathematical skills to a level where I could understand and think mathematically I would just be like an analfabet or legasthenic person. So I named myself a mathematical analfabet and/or legasthenic. Mathematics is really the only "language" in which you need to be able to think and speak, to really deal with any study this days. Prof Keith Devlin offers a great Mooc course about
"Introduction to Mathematical Thinking" in which he also speaks about what is the difference between high school mathematics and that you face in colleges. In 1978 i decided that I was not able to learn to speak, think and work with the language mathematics and that was the reason I decided to go for mechanical engineering. Sadly mathematics in the study for becoming a mechanical engineering career is even farther away from what Keith Devlin calls mathematical thinking and even from the way I did mathematics at high school. Just many years later I understood the justification for it. Engineers have to recognize to what basic mathematics equation a problem can be modified to to fit and then apply the "cook book" solution! I did solve all the the exams questions, but understanding them and did not modify it to fit a style where a cook book solution could be applied. So even having all solutions right I barely passed the exams as many of the in between steps were not touched.
Why I am giving this extensive response? Because if you love physics and you are able to learn and apply mathematical thinking this is the right course to follow. Nearls any course this day requires you to apply mathematics. So the challenge is kind of the same in any science or engineering field, while in physics and mathematics you have one extreme of the goal of learning the language mathematics, while in engineering you are more on the range of learning to do and apply mathematics. But to excel this days I believe you have to learn mathematical thinking. Now mid of 2015 I believe you can study upfront to gain the skills in mathematics to then have a much easier run when you register at a university. I can only tell you that having found out for me that I have found Moocs from professors whose style fit to me I enjoy mathematics. So I have decided to refresh my mathematical skills learning Calculus for single and multi variables by using the course for calculus from the MIT in their OpenCourseWare offering, same applies for Linear Algebra and to study Analysis from the Mooc offering of a german university who builds its course based on the Analysis Course of Terence Tao, Analysis with honours and where his 2 books can be legally downloaded from his personal website.