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Integration Review
Integration by parts (u, dv, du, v)
Partial Fractions
Trig sub
Application -
Differential Equation Review
Seperate variables and integrate both sides
solve for c
slope fields and drawing the solution for a point
exponential growth and decay for dy/dx=ky (y = ce^kt)
logistics model for dy/dx = ky(1-1/M*y) (y = M/1=ce^-kt) -
Infinite Series Review
sequences and finding equations for sequences
series: the partial sums of sequences
finding the sum of a series (a/1-r)
geometirc series, telescoping series
determining convergence of a series:
nth term test (divergance only)
ratio test (conv for <1 div for >1 and unknown at =1)
root test(conv for <1 div for >1 and unknown at =1)
DC Test
LC Test
Integration -
Taylor & Maclaurin Polynomials
approximation of a function using multiple derivatives
find derivates and value of derivatives at a point
general form:
Pn(x)= f(x) + f'(x)(x-c)^n/n! +f'(x)"(x-c)^n/n! +...f'(x)^n(x-c)^n/n! +...
maclaurin centered at 0
power series
MUST KNOW: sin, cos, e^x, ln(x+1), arcsin
look alike method: (a/1-r) -
Advanced integrations techniques
integration by parts (u, v, du, dv)
partial fractions
trig sub (not on the ap) -
Integration application
roatating a curve around an axis
integral from a to b of the area between two curves:
disc method
shell method
washer method
multiply by pi!
