Exam reviews

(Note coverage of topics has moved a bit over the years)

Applications of integration

Spring 2020

Fall 2019

Fall 2018

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

Techniques of integration

Spring 2020

Fall 2019

Fall 2018

Major topics include:

    • Integration by parts
    • Trigonometric integrals
    • Trigonometric substitution
    • Partial fractions
    • Numerical integration
    • Improper integrals

Sequences and series

Fall 2019

Spring 2019

Fall 2018

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)

Final Exam (comprehensive)

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Fall 2017 (first half)

Fall 2017 (second half)

Final exam "unboxing"