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Hello. I'm trying to teach myself Calculus, just in case I need it for the future (grad school). Now I took it in high school, but only passed with a C and it's been a few years.
My biggest problem is that I don't "get" Calculus, like exactly what I'm doing. I know it's the study of change over time, but my foundations are really cracked. Does anyone know of any good books or free online courses that really help complete novices? Thanks!
By need it, do you mean need to know it, or need to show you've learned it? If the latter, you may need to take a course somewhere.
Naw, the former. Thanks. I wanted to be ahead of the game in case I decide to pursue engineering of some sort in the future. To me it will be easier going in knowing what's up than later having trouble and having to drop the course. I'll definitely check that book out.
My biggest problem is that I don't "get" Calculus, like exactly what I'm doing.
I think that is a problem with mathematics teaching in general. If I give you the formulas for the Area and Circumference of a circle A=PI*r^2 and C=2*PI*r followed by the formulas for the Volume and Surface Area of a sphere V=4/3*PI*r^3 and SA=4*PI*r^2 it should be immediately obvious that
dA/dr=C and dV/dr=SA . Furthermore the reason for this relationship should be clear.
I remember studying for a Calculus II quiz in college. I was in the library and got bored, so I started flipping through my book. On the first page, there was a quote. It said "the only way to get better at math is to DO math."
The kids that struggled in my class were constantly looking for a way to absorb the information without doing too much work. Those that succeeded were either naturally gifted in math or worked like crazy solving problems. Just keep working through problems and find some study aids. Good Luck!
Yes, I've TAed over a dozen calculus classes over the years. People put in some effort the first couple weeks, then stop doing problems. This is worse when the online homework is optional or only a tiny portion of their grade. They think they can just ace the exams and get an easy A, especially the kids who took AP Calculus in high school. Once they get past the product rule, they know absolutely nothing. Most of them do no problems throughout the semester and bomb the exams. A select few put in consistent work and ace the class.
Yes, I've TAed over a dozen calculus classes over the years. People put in some effort the first couple weeks, then stop doing problems. This is worse when the online homework is optional or only a tiny portion of their grade. They think they can just ace the exams and get an easy A, especially the kids who took AP Calculus in high school. Once they get past the product rule, they know absolutely nothing. Most of them do no problems throughout the semester and bomb the exams. A select few put in consistent work and ace the class.
I really helps when quizzes/homework count for a decent proportion of the overall grade (say 10-15%-ish). It encourages students to study more, which in turn helps out tremendously on exams.
Honestly, the best way to gain a better understanding of calculus is by brushing up on your algebra and trig skills.
Getting a C in calculus shows that you had an idea of the Calculus but your skills in the algebra behind the Calculus was lacking. I'd work on your skills in manipulating expressions and trig identities.
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