I feel ok about maybe 75% of my upcoming Calculus test. I haven't even done any math yet today, but I did kick the ass of the last definitions. It is literally a whole front and back of a sheet of notebook paper's worth of stuff to know. WORD. FOR. WORD. 😳
This is it. (You've probably already seen part of it, but repeating helps me.) (Feel free to skip this post if you don't care, but my freaking hand is SO TIRED of writing and I'm running low on paper; unfortunately, that is what sticks it in my brain.)
• Five Things Osborn Wants me to Know About Calculus:
1) Calculus is a way of measuring change, including change in time and and space.
2) Calculus can help address counterintuitive notions in physics and economics.
3) Calculus is effective in "managing infinity."
4) Calculus problems tend to lead to algebra and / or basic math problems.
5) Calculus is a set of procedures which convert any function or combination of functions into a derivative, which describes the relationship between the variable at a particular point.
- The two fundamental idea of Calculus are:
1) The derivative. This is a way of measuring instantaneous change.
2) The integral. This is a sum of numerous pieces.
- A tangent is a straight line that touches a curve at a specific point.
- A derivative, as it relates to the tangent, is the slope of a line that is tangent to a curve.
- The three main purposes of Differential Calculus are: 1) precision, 2) approximation, 3) maximum and minimum.
- Differential Calculus is the arithmetic of infinitely small differences of variable quantities.
- Integral Calculus is the deduction of magnitudes from the ratio of small changes of other magnitudes.
Examples I also have to know:
1) "Speed of Car." Differential Calculus deals with finding speed of a car based on position. Integral Calculus deals with determining the distance traveled when only the speed was known.
2) "Road." Differential Calculus is concerned with changes in elevation of the road, slope / steepness, and with guessing or determining what happened between measurements. Integral Calculus is concerned not with the road itself, but with the area under it and how the area changes.
3) "Vase." Differential Calculus is about the rate at which a liquid is poured into the vase. Integral Calculus is about how high the level of the liquid rises at a point, and how high this level will get over a time interval.
So yeah. I did it. I just went back and checked myself before posting and I had an "a" where there was supposed to be a "the" one time. I'd say that's not bad. I feel accomplished. I think I am gonna take a dinner break and then see if my brain is awake enough for some actual math. Woo! LOL