Integrate integrable functions using integration by parts, u-substitution, trigonometric substitutions, rationalizing substitutions, partial fraction decomposition, and trigonometric identities. This includes knowing which techniques to apply to a given integral.
Compute improper integrals and numerical estimates for definite integrals.
Solve basic first-order differential equations and understand how they model simple systems.
Understand the difference between an infinite sequence and infinite series and determine if a sequence converges or diverges.
Determine whether or not an infinite series of numbers converges or diverges using a variety of tests.
Understand what it means for a power series to converge or diverge and be able to find the Taylor series for a given function. Determine how closely a Taylor polynomial approximates a function using Taylor's Remainder Theorem.
Differentiate and integrate functions in polar coordinates.