Calculus II - 25

A college course for Calculus II:
Inverse Trigonometric Functions
Review inverse functions and inverse trigonometric functions Derivatives of inverse trigonometric functions
Integrals leading to inverse trigonometric functions
Applications of the Definite Integral
Area between curves
Volumes by slicing (disks and washers) Volumes by cylindrical shells
Work; arc length
Techniques of Integration
Review of integration by substitution
Integration by parts
Trigonometric integrals (powers of sine, cosine, secant, tangent) Trigonometric substitutions
Integration of rational functions by partial fractions

Other Integration Topics and L’Hospital’s Rule
L’Hospital’s Rule
Improper integrals
Approximate integration (trapezoidal rule and Simpson’s Rule)
Polar Coordinates
Introduce polar coordinates
Graphs in polar coordinates
Areas and arc lengths in polar coordinates

Infinite Sequences and Series
Introduction of sequences and series
Convergence and divergence of sequences and series Geometric series
The integral test, p-series
Comparison test, limit comparison test
Alternating series
Ratio test, root test
Absolute and conditional convergence
Power series
Differentiation and integration of power series Taylor and Maclaurin series
Taylor’s formula with remainder