posted May 14, 2019, 4:20 AM by Matthew Grenfell
[
updated Jun 3, 2020, 3:51 AM
]
- Use integration by parts to evaluate integrals
- Evaluate trigonometric integrals (e.g., integrate sin^3(x),
sec^2(x)tan^2(x), and so on)
- Evaluate integrals by making trig substitutions
- Evaluate integrals using partial fractions
- Determine the convergence/divergence of improper integrals
and evaluate if convergent
- Use various tests to determine the convergence/divergence of
series, including the integral test, comparison tests, and ratio test
- Determine the convergence/divergence of a geometric series or
alternating series
- Determine a power series representation of a given function
- Determine the radius of convergence and interval of
convergence for a power series
- Determine a Maclaurin or Taylor series representation of a
function
- Determine a Taylor polynomial of a certain degree for a given
function
- Determine the solution of a separable differential equation
- Graph curves defined by parametric equations
- Determine the derivative at a point on a parametric curve
- Describe and work with points and curves in polar coordinates
- Determine areas of common regions using polar coordinates
- More integration by parts
- Approximate integration techniques (Midpoint Rule, Trapezoidal
Rule, Simpson's Rule)
- Sequences
- More power series/Taylor series (preferably deriving a Taylor
series from scratch)
- Approximating error of an integration technique or Taylor
polynomial
- More on parametric curves and calculus with parametric
equations
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