MTH132: Calculus with Analytic Geometry II

Calculate derivatives of parametric functions. (2.3.2)

Calculate derivatives of functions written in polar coordinates. (2.3.4)

Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives. (4.1.1, 4.1.2)

For integrands requiring substitution or rearrangements into equivalent forms: determine indefinite integrals and evaluate definite integrals. (4.1.3)

For integrands requiring integration by parts: determine indefinite integrals and evaluate definite integrals. (4.1.4)

For integrands requiring integration by linear partial fractions: determine indefinite integrals and evaluate definite integrals. (4.1.5)

Evaluate definite integrals analytically using the Fundamental Theorem of Calculus. (4.3.3)

Evaluate an improper integral or determine that the integral diverges. (4.3.4)

Calculate areas of regions defined by polar curves using definite integrals. (4.3.5)

Calculate areas in the plane using the definite integral. (5.1.1)

Determine the average value of a function using definite integrals. (5.1.2)

Calculate volumes of solids with known cross sections using definite integrals. (5.1.3)

Calculate volumes of solids of revolution using definite integrals. (5.1.3)

Determine the length of a curve in the plane defined by a function, using a definite integral. (5.1.4)

Determine whether a series converges or diverges. (6.1.1, 6.1.2, 6.3)

Represent a given function as a power series. (6.1.3)

Represent a function as a Taylor series or a Maclaurin series. (6.2.1, 6.2.2)

Interpret Taylor series and Maclaurin series. (6.2.1)

Represent a function at a point as a Taylor polynomial. (6.2.1)

Approximate function values using a Taylor polynomial. (6.2)

Determine the error bound associated with a Taylor polynomial approximation. (6.2.2)

Approximate the sum of a series. (6.3.7)

Determine the radius of convergence and interval of convergence for a power series. (6.3.9)