What You will Learn?

• Area Between Curves
• Volumes of Solids of Revolution
• Volumes Using Cross-Sections
• Arclength
• Work as an Integral
• Average Value of a Function
• Proof of the Mean Value Theorem for Integrals
• Integration by Parts
• Trig Identities
• Proof of the Angle Sum Formulas
• Integrals Involving Odd Powers of Sine and Cosine
• Integrals Involving Even Powers of Sine and Cosine
• Special Trig Integrals
• Integration Using Trig Substitution
• Integrals of Rational Functions
• Improper Integrals - Type 1 & Type 2
• The Comparison Theorem for Integrals
• Sequences - Definitions and Notation
• Series Definitions
• Sequences - More Definitions
• Monotonic and Bounded Sequences Extra
• L'Hospital's Rule
• L'Hospital's Rule on Other Indeterminate Forms
• Convergence of Sequences
• Geometric Series
• The Integral Test
• Comparison Test for Series
• The Limit Comparison Test
• Proof of the Limit Comparison Test
• Absolute Convergence
• The Ratio Test
• Proof of the Ratio Test
• Series Convergence Test Strategy
• Taylor Series Introduction
• Power Series
• Convergence of Power Series
• Power Series Interval of Convergence Example
• Proofs of Facts about Convergence of Power Series
• Power Series as Functions
• Representing Functions with Power Series
• Using Taylor Series to find Sums of Series
• Taylor Series Theory and Remainder
• Parametric Equations
• Slopes of Parametric Curves
• Area under a Parametric Curve
• Arclength of Parametric Curves
• Polar Coordinates