Exam reviews
(Coverage of topics has moved a bit over the years)
Major topics include:
Volume (cross sections; washer; shell)
Arc length
Surface area
Work; pumping; fluid force
Mass; moments of mass; center of mass
Parameterized curves
Polar coordinates (graphing; symmetry)
Area in polar coordinates
Major topics include:
Integration by parts
Trigonometric integrals
Trigonometric substitution
Partial fractions
Numerical integration
Improper integrals
Major topics include:
Sequences (w/ limits)
Geometric and telescoping series
Divergence test (or n-th term test), comparison test, limit comparison test, integral test, p-series test, ratio test, root test, alternating series test
Absolute and conditional convergence
Power series; radius/interval of convergence
Calculus of power series
Taylor polynomials and error
Taylor series for sin(x), cos(x), exp(x), 1/(1-x), (1+x)^a
Applications of Taylor series (high order derivatives; polynomial approximation)