Long post -
I'm used to more concrete concepts when dealing with math, particularly algebra - even when dealing with "imaginary numbers" - solving for x was simply not that big of a deal. I flamed out of Calc I in college 16 years ago, and by extension, was totally lost in a calc-based physics class I tried to take at the same time. Primarily, my issue is with understanding the concept of a "limit". I get the dictionary definition, and I even understand that it's an important concept if you want to know an objects speed under acceleration at a specific point (the answer would be a limit since at the next measurable point it would be different)... but when I sit down to write out a calculus equation and then attempt to solve for a limit, I'm hampered because I just can't internalize what I'm solving for. MIT offers their free coursework, so I attempted to read the textbook and like the "Calc for Dummies" and "Calculus the Easy Way" books I'm as confused as ever. To summarize why I'm confused, the MIT calc book - in the opening chapter - describes a velocity/time relationship as one of differentiation and integration, but specifically that when solving for velocity, it's differentiation, but when solving for time it's integration and explains it in a way that I should just know why that is. Adding to the confusion is that this difference is explained in terms where velocity is constant, so algebra can be simply used to solve the problem.
I live in Texas and am a Veteran and I have squandered my GI Bill. Thankfully we have the Hazelwood act and I'm determined to get some kind of technical degree (Comp Sci, Engineering) and I want to understand calculus like I understand addition and subtraction. I just can't figure out why it is so difficult for me and what fundamentally I'm missing where every time I read anything about it, within 3 minutes, people are talking about concepts that I have no understanding of, like after 2 paragraphs, it should be clear to me why velocity as a function of rate is a differential and time as a function of rate is an integral. I still don't know why, even after reading it a few times, to me they're all variables of a pretty straight forward equation.
I passed trig, did well on tests, but don't remember much of it. I know that sin, cos and tan functions appear regularly in calc, so I'll need to go through those to solve problems, but I'd really like to know what idea I haven't been exposed to that might allow me to focus on the mechanics of problem solving instead of staring at a jumble of fancy greek symbols and wondering "what the heck does one do with all of this???"
I'm used to more concrete concepts when dealing with math, particularly algebra - even when dealing with "imaginary numbers" - solving for x was simply not that big of a deal. I flamed out of Calc I in college 16 years ago, and by extension, was totally lost in a calc-based physics class I tried to take at the same time. Primarily, my issue is with understanding the concept of a "limit". I get the dictionary definition, and I even understand that it's an important concept if you want to know an objects speed under acceleration at a specific point (the answer would be a limit since at the next measurable point it would be different)... but when I sit down to write out a calculus equation and then attempt to solve for a limit, I'm hampered because I just can't internalize what I'm solving for. MIT offers their free coursework, so I attempted to read the textbook and like the "Calc for Dummies" and "Calculus the Easy Way" books I'm as confused as ever. To summarize why I'm confused, the MIT calc book - in the opening chapter - describes a velocity/time relationship as one of differentiation and integration, but specifically that when solving for velocity, it's differentiation, but when solving for time it's integration and explains it in a way that I should just know why that is. Adding to the confusion is that this difference is explained in terms where velocity is constant, so algebra can be simply used to solve the problem.
I live in Texas and am a Veteran and I have squandered my GI Bill. Thankfully we have the Hazelwood act and I'm determined to get some kind of technical degree (Comp Sci, Engineering) and I want to understand calculus like I understand addition and subtraction. I just can't figure out why it is so difficult for me and what fundamentally I'm missing where every time I read anything about it, within 3 minutes, people are talking about concepts that I have no understanding of, like after 2 paragraphs, it should be clear to me why velocity as a function of rate is a differential and time as a function of rate is an integral. I still don't know why, even after reading it a few times, to me they're all variables of a pretty straight forward equation.
I passed trig, did well on tests, but don't remember much of it. I know that sin, cos and tan functions appear regularly in calc, so I'll need to go through those to solve problems, but I'd really like to know what idea I haven't been exposed to that might allow me to focus on the mechanics of problem solving instead of staring at a jumble of fancy greek symbols and wondering "what the heck does one do with all of this???"