BC topics

BC topics

Techniques of Integration

Trig Identities

Trig Integrals

Trig Substitution

Partial Fractions

Sequences and Series

Telescoping Series

Comparison Tests

Alternating Series

Taylor Polynomials and Taylor's Theorem

Power Series

Taylor Series for Familiar Functions

Parametric Equations

Polar Coordinates

Derivitives of Polar Functions

Vectors

Topics: functions and graphs, a rigorous development limits, continuity, derivatives and differentiability, applications of the derivative, curve sketching, related rates, implicit differentiation, parametric equations, polar functions, vector functions, l’Hospital’s rule, Riemann sums, indefinite and definite integrals, techniques of integration, applications of integration, the Fundamental Theorem of Calculus, numerical approximations to definite integrals, improper integrals, differential equations, polynomial approximations, Taylor series, limit comparison test, alternating series error bound and absolute and conditional convergence and divergence of infinite sequences and series.