Where in your job do you use advanced math?

There are certainly careers for mathematicians outside of teaching: you have statisticians, actuaries, people brought in for contracting jobs involving optimization, operations research, etc. Calculus certainly comes up in all of these, and has so many other real-world applications. But even most people who get degrees in mathematics don't end up becoming "mathematicians". The reality is that in the tech world, new hires usually get picked due not so much for their knowledge, but for their ABILITY. So it's not that places like engineering companies need people to integrate tan^2(x) dx; they much more so like the fact that you CAN understand calculus and DID successfully pass so many classes that goes over the heads of 99.999% of other people, because that says a lot about your technical abilities. Various engineering companies for example want somebody who can quickly learn something strange and technical, think logically and methodologically, communicate very technical details to others in a correct and precise way, etc. So while your friend might not be applying everything technique he learned in Differential Equations II class, he still (I should hope) sharpened his engineering mind by learning HOW to go through all of that. And he most certainly wouldn't have been able to get a degree in EE if he couldn't pass basic calculus. This sort of thing happens with other school subjects too. I don't need to know the date of the Battle of Hastings to do my job, but I'm still glad I had History classes, because it's important in life to be able to recognize trends that have happened before, what people have tried to do and why certain things won't work, understand where other cultures are coming from, distinguish propaganda from facts, etc. Likewise, mathematics teaches you how to solve problems via analogies, use logic, and think of solutions.

Of course, if you are going to be a teacher you may use this math, or a professor. But other than the obvious, when you are just starting out in a career the math may not seem to be in play but, especially in engineering, the career will develop and you will be thankful for the math courses. In the science field, particularly biomedical and robotics engineering, the math courses come into play because you must have objects perfectly custom-fitted to each being.

Well last year in my internship, we had to use one concept in calculus and many things we learned from pre-calculus, such as arc length in a circle, and all the trigonometric functions. We had to come up with a design that maximized the concentration of the sun to make a portable solar concentration system for solar cells. For our second design, we attempted to use spring metal (can't remember the exact name of the material, but it's the springy material in sun visors to make it shapable). We had to come up with a good number for our "umbrella" design, and after coming up with the parabola equation the umbrella would be modeled after, we used the equation for calculating arc length to determine how much spring metal we'd need. We also used the calculus concept of determining the surface area of the parabola rotated around a center axis to determine how much reflective material we'd need to cover it. Later on, as my internship ended, I had to come up with a design that would maximize the performance, eliminating all the variables that caused problems (corners, upward reflectivity, ease of assembly, etc.). The design I came up with dealt with areas of a 2D surface, arc length of a circle, law of sines, law of cosines, and basic arts and crafts. My supervisor came up with the mathematics involving tan^2(x) for the maximum ideal condition. After all the tweaking, our solar concentrator design turned out to be extremely successful in the first couple tests. Unfortunately, we couldn't get the final tests on the product that we needed since our internship ended only three days later, and we had to type up the 30-page proposal... Admittedly, though, you won't see a ton of things you learn in calculus, or at the very least, some technology will already do it better for you. Why use vector calculus to determine what a ship's monitor can do for you in seconds? Why calculute the flux through a 4D (yeah, FOUR DIMENSIONAL. I still don't see the relationship to real life) object when we have tools that can measure it? Further, why should you learn how to calculate the flux to a 10D object? Or use polar/cylindrical/ spherical methods of integration to find the volume of a sphere, cylinder, or a shape involving all of them, when you can use simple water displacement to find it? I hope you can get other examples as well. I want to know when I'm going to use any of the stuff I'm learning in college.