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Day 1: AB review
In doing Reimann Sums, it is important to remmeber to use the approxiamtely sign instead of equals sign! Difference between Average Value: f(c) = 1/(b-a)*integral from a to b of f(x) dx and Mean Value: f'(c) = (f(b)-f(a)) / (b-a) 2nd Fundamental Theorem of Calculus: Dont forget to take the derivative of the bounds! -
Day 2: Slope fields, Eulers Method, Differential Equations
Growth and Decay: "The rate of change is proportional to the amount present" means dy/dt = ky , which integrated is y = Ce^(kt) Logistics Differential Equations: remember the two different forms (e^-kMt or e^-kt) , max rate of change is at half the max value -
Day 3: Day 2 continuted
Be able to identify Slope fields with their representative equations Eulers method - make a table of x, y, dy/dx, dy -
Day 4: Sequence and Series
Characteristics of Sequences: domain is set of positive integers, converges if bounded and monotonic
writing equation for terms of a sequence: odd integers (2n+1), even (2n), alternating ((-1) ^n), 1, 2, 6, 24 (n!) Telescoping series: may have to reqrite with partial fractions, terms cancel. Can find the values the series converges to Root and Ratio test:
if (lim n--> infinity expression < 1)
series converges
if (lim n--> infinity expression == 1)
series is inconclusive -
Day 5: Taylor Series and McClaurin Polynomials
LaGrange Error Bound (not for alternating series):
R=abs((f(z)*(x-a)^n-1)/(n+1)!) When a series is cenetered at a value - must solve for the derivates of f(x) at that value, not at 0 and write polynomial with those coefficients -
Day 6: Advanced Integration Techniques
Integration by Parts: integral of uv = uv - integral of v du
in choosing u: LIPET
Tabular method: signs alternate, starting with + Partial Fractions, Infinite Integrals -
Day 7: Integral Applications: Area, Volume, Water in Water out
Maximizing/Minimizing distance formula
Washer: V = pi*integral of f^2(x)
Shell method V = 2pi*integral of distance from axis*f(x) -
Polar Test Review
Area : integral from a to b of r^2 d@
Surface Area of Revolution: SA = 2pi*integral of (rsin@*sqrt(r^2 +r'^2))d@
about the POLAR AXIS SA = 2pi*integral of (rcos@*sqrt(r^2 +r'^2))d@
about PI/2 -
Polar Test Day
I don't remember if i wrote the correct area of a surface of revolution equation for around the polar aixs (rsin@) and around pi/2 (rcos@)
Overall, the test was not bad. -
Review
Over the weekend: Do practice problems and start creating study guide -
Review Day
Doing the "what do you do...when you see worksheet" has helped me review some of the AB that we have not touched, such as water in water out problems, which although not difficult to think about, may throw me off when I see it unexpectedly on the test. I should review integrating trig fucntions such as integral of tan = -ln(cos@). -
Review: The Day Before!
Mr. Hyman suggested that we shoukld take it easy and look at the KYSC sheet and the "what do you do...when you see sheet", but the KYSC sheet feels sparse, so I reviewed my study guide and did some practice problems -
AP DAY!
The difficulty of the test was as expected. I did not understand what part C of question 6 was asking for, and i think i did not do the grass clipping question correctly (the values i got did not seem probable). The other free responses were not bad.
