Calculus is one of the basic understandings needed to complete higher physics and engineering because the math behind calculus is the basis for the understanding of the theory. Finding a direct relation and explaining if a laplace transform or a Fourier series is what you need to study is quite a bit more difficult, but once you understand those areas you begin to apply them in new ways.
A codec is a COmpression-DECompression standard, its going to be a combination of both math and for lossy formats like MP3 or JPG a study of human senses. How much background noise or low level audio can be discarded before you can hear a difference, how much color and detail information can be discarded before you see a difference? Or, it could be better said its a question of how much can be discarded to make for an acceptable compromise of storage/speed to reduce cost or improve playtime?
Life is analog, the sun comes up and the light progressively gets brighter as the angle relative to the surface improves, water flows in a river as influenced by gravity. Now we could quantify such activities and represent the quantifications with numbers. We could then specify how we look at those numbers and further refine it into how many numbers we want to look at.
Take a person talking for example. Going back to bell we've had the ability to talk, creating air pressure variations that moved a diaphram with a coil of wire and transmit this on copper wires over distance to another diaphram with a coil of wire and magnet and have a reasonable copy of the sound transmitted. Today this could be captured by a small chip constantly examining the audio coming from the device sampling the air pressure variations and making each of those variations a number. Each number could then be processed into pulses of light sent over a thin piece of glass for miles and sent to a satellite thousands of miles in the sky and converted back again to an analog air pressure variation that would be the sound you hear on the receiving end of a telephone.
The same goes for a PSP. It has a small computer and software inside with numbers describing everything. Now it goes through many a process to convert those numbers into light/sound that you can use. Otherwise it would be about as exciting as watching the green symbols changing in the movie the Matrix, digital is a means to an end but it isn't really the end itself.
At 17 you can explore much of this in many different ways. Maybe you want to be a game designer and like to think creatively about using color and role-playing to make new challenging levels of games. Maybe you're fascinated with the math of kinematics and could go into developing a new software game engine or video chip design. Maybe analog circuits are of interest and you want to be involved in helping reduce the power consumption so the device runs cooler and uses less battery power. Hundreds of possibilities exist.
Just as there are hundreds of ways calculus is used, even if indirectly. Some brilliant people have taken the transistor valve and shrunk it to the size and cost that makes my computer possible, but a lot more people were involved in making hundreds of other items that make just my computer possible much less our conversation. Its mind boggling to consider that we've come this far from hunting-gathering, but an appreciation of such a thing is important to respecting the beauty of what we've created and the progress we (as a society) make through time.
Appreciate the beauty, but also find a outlet to use it if you desire to and don't be concerned with all the details that go into what makes your goals possible. I think the plain old light bulb overhead is a impressive invention I can purchase for a few cents, but I don't think much past the switch besides how it can provide light so I can do work. And a complex device like a PSP has a lot more to it than that!
