I have a longer term goal to study and to understand Quantum Mechanics and Quantum Physics. Why? Because I don’t know much about them. My university training in physics covered classical, or Newtonian physics in a fair amount of detail. We touched on behavior of electrons in molecules and the link between physics and chemistry in Physical Chemistry. But modern physics. Not so much. I didn’t really need to understand that for a BS in Chemical Engineering.
My initial foray into learning QM quickly showed that my math skills had eroded to the point that I couldn’t get started. So, in January 2024 I began taking an undergraduate course in Calculus. My plan is to take several courses in Calculus before tackling QM. The first class in the math series is MTH 251. Differential calculus. When did I last study this? My senior year in high school!. That was quite awhile ago.
I spent the weeks leading up to the first class reviewing the textbook, and scanning the precalculus chapter. The concepts looked familiar. I even did a few of the problems. Feeling confident, I walked into the class room for the first class.
The instructor drew the following on the black board (it was actually a dry erase board. But I think of it as a blackboard.). “What is this function?”
I’m thinking. “How should I know”. So, I mentally guess “it’s a sine wave”
The instructor says. “It’s a sine wave.”
“I’m doing great”, I think. He then says. “Consider this to be a unit sine wave. What are the highest and lowest points it reaches on the y axis? (this is the vertical axis, in case you don’t know)”
I’m thinking. “It’s a unit sine wave. Unit means 1. So I’ll guess +1 and -1”.
The instructor labels the points on the y axis as +1 and -1. I’m kicking ass in here.
“Where does it cross the x axis”, he then asks.
“How TF should I know?” I’m thinking. He labels a few significant points on the wave. π/2. π 3π/2. 2π.
I’m lost. Where does this come from? Am I in the wrong class? I never remembered taking a precalculus class. When would I have learned this?
The remainder of this first class he also discussed cosines, exponential functions, log functions, and wrapped up by saying “This concludes our review of precalculus. Have the homework completed by Sunday and we will next begin studying limits”.
Let’s cut to the chase. I spent a couple hours reviewing this stuff online. I learned or relearned it well enough to move on from precalculus. In the next class, we already covered some of the stuff on limits and I’m having no difficulty.
But for a moment there, I felt like I was in the wrong place.