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Day 1
Today not only did we go over how to create this journal, but we also discussed the mean value theorem for integration and he limit definition of the integral. The MVT for derivation and integration are very similar. The jist is that the average value on some arbitrary span from a to b is equal to some value of c on the interval. For integration we use the form (1/(b-a)) multiplied by the integral from a to b of the function to find the average value on that interval, which is = to some f(c) -
Day 2
Today we reveiwed diferential equasions. We remember that when the rate of change is directy propotional to the population, or y'(t)=ky. When this is soled, we end up with the model: A=Ce^kt. This, unfortunately, does not work in the real world. In the real world there are carying capacities (L or M). Like this box, for example, will not hold an unlimited amount of characters (I know I have tried). This logistics Growth model does acount for real life: y'(t)=ky(1-y/M)-> y(t)=M/(1+Ae^-kt). -
Day 3
Today we reviewed sequences and series. It is paramount to remember that sequences are a list of values according to some rule, whereas series are a sumation of partial sums. When testing for convergence of a sequence, the sequence must be bounded and monotonic. When testing for convergence of a series, first see if the equasion is obviousely telescoping geometric, p-series, or alternating. Then try nth term test for DIVERGENCE. If these fail try the ratio test. -
Day 4
We continued reviewing series and remainders. If the sereis is alternating, the remainder is easy. It is just abs(S-Sn)_<a(sub (n+1)). If not alternating, the remainder of the sereis is found with the la grange form of the remainder:
max val of funct = (f^(n+1)(z))*(x-c)^(n+1)/(n+1)!
Both forms ahve the same basic idea of refering to the next term. -
Day 5
We reveiwed and practiced taylor polynomials and power series. Taylor polynomials are polynomial estimtions of complex equasions centered at a given value; they are represented by the nth derivitive of c times (x-c) divided by n! added to that of n+1, added to that of n+ 2 and so on for as many terms as desired. The higher term taylor polynomial, the more accurate the aproximation is, but the further away the center the value of x being aproximted is, the lessacurate the aproximation will be. -
Day 5
Today we reviewed strange integration techniques. Since we were assured that trig substitution will not be on the AP test, we grazed over that. Integration by parts (as a last resort) will, however, be tested on. Using LIPET we choose a value for u and dv which we then take the derivitave of and integrate respectively and then substitue into: uv- int(v du). Before resorting to such ugly things we could try integration by parts (especialy if there is a constant over a factorable polynomial). -
Day 6
YAY VOLUMES OF REVOLUTION!! There are two options for this: disc (perpendiscular) and shell (parashell). It's easyer to use shell method for any revolutions around a vertical line and disc method for any revolution around a horizontal line where the function is in terms of x so that one does not need to solve for a different variable.
shell: V= pi* int from a to b ((f(x))^2)
disc: V= 2pi* int from a to b (x*f(x)) -
Day 7
LAST TEST TOMORROW. Today we revewed all of the polar mumbo jumbo that will be tested tomorro on the polar exam....did i mention it is the LAST test of the year... besides the other classes...and the Calc AP. What we reviewed? Oh yeah... the main exuasion that is hard for me to remember that we did was arc length of a polar curve: int from (a,b) of (sqrt(r^2 +r'^2) dtheta) -
Day 8
Polar test today!!!! Did not finish multiple choice, but that which I answered I felt good about. -
Day 9
Today we went over the take home test. With this I was quite pleased because I got a solid 5 with out help from notes! This realy boosted my confidence for the big game! -
Day 10
Pre-game. We did that same activity from the begining of the year where each person finds 10 different people who know an answer to one of the review questions in the squares. We reviewed the answers and went on a walk outside; it was a lovely day. We also talked about Cerial Mom, which was necessary. -
Day 11
Because I forgot to heed the warning to check the calculator battery, I found the battery level to be 25% on test day; the battery did not die. Thank the calculus gods! I felt very prepared for the game and feel very good about my performence.
