I am very interested in the field of Computer Science. I don't have any degrees or experience in the field, but the field somehow fascinates me. I am very good in math, very analytical, I like numbers, solving logical problems and stuff like that. In school I was very good in algebra, but geometry gave me a heartache :( I see in the pre-requisite classes at colleges and Universities' programs, there are classes such as Calculus I & II w/Analytic Geometry © MAC 2311 & 2312 (or MAC 2281 & MAC 2282). Analytic Geometry sounds interesting, but I was never good in Geometry in grade school...so, I have NOOOO basic knowledge of it whatsoever...will I have problems studying this degree with no PRIOR major knowledge of Geometry? Also, physics I did not like, either and chemistry...but I can take them up at college...Can you, also, please, tell me if there is anything you really had to be good at at grade school to start learning Computer Science? Thanks a lot!!
"Analytic geometry" when part of the title of a calculus course is simply referring to geometry with the use of the Cartesian coordinate system. In other words, the course is about calculus. Aspects relating to "analytic geometry" include the finding of areas of regions on the plane (whose edges are described by functions), the finding of volumes of rotationally symmetric figures (described as a rotation of a function about the x-axis or y-axis), the finding of perimeters or lengths of curves, and of course the computing of slopes of curves.
For example:
You'll be able to compute that the area between the curves y=x^2, x=5, and y=0, is 125/3.
You'll be able to compute that the slope of the tangent line to the curve y=sin(2x) at the point (a, sin(2a)) is given by the formula 2cos(2a).
With enough creativity, you could prove that the (infinitely long) region between the graphs of y=0 and y=e^(-x^2) has area equal to sqrt(pi).
None of this involves Euclidean geometry, it's algebraic in nature. For example, for none of these problems would you bother drawing a picture. If you showed your work, it would look like this:
int(0..5) x^2 dx = [x^3/3](x=0..5) = 5^3/3 - 0^3/3 = 125/3.
d/dx [sin(2x)] = d/dx [2x] cos(2x) = 2cos(2x). So.. 2cos(2a).
int(-inf..inf) e^(-x^2) dx = sqrt[int(..) e^(-x^2) dx int(..) e^(-y^2) dy] = sqrt[int(..) int(..) e^(-x^2-y^2) dx dy] = sqrt[int(0..2pi) int(0..inf) r e^(-r^2) dr dtheta] = sqrt[2pi int(0..inf) r e^(-r^2) dr] = sqrt[2pi [-e^(-r^2)/2](0..inf)] = sqrt[2pi [-e^(-inf)/2 - -e^0/2] = sqrt[2pi [-0/2 - -1/2]] = sqrt[2pi * 1/2] = sqrt(pi).
See? It's quite simple and straightforward.