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Representing Functions with Power Series
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Classroom Contents
Calculus 2 - Full College Course
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- 1 Area Between Curves
- 2 Volumes of Solids of Revolution
- 3 Volumes Using Cross-Sections
- 4 Arclength
- 5 Work as an Integral
- 6 Average Value of a Function
- 7 Proof of the Mean Value Theorem for Integrals
- 8 Integration by Parts
- 9 Trig Identities
- 10 Proof of the Angle Sum Formulas
- 11 Integrals Involving Odd Powers of Sine and Cosine
- 12 Integrals Involving Even Powers of Sine and Cosine
- 13 Special Trig Integrals
- 14 Integration Using Trig Substitution
- 15 Integrals of Rational Functions
- 16 Improper Integrals - Type 1
- 17 Improper Integrals - Type 2
- 18 The Comparison Theorem for Integrals
- 19 Sequences - Definitions and Notation
- 20 Series Definitions
- 21 Sequences - More Definitions
- 22 Monotonic and Bounded Sequences Extra
- 23 L'Hospital's Rule
- 24 L'Hospital's Rule on Other Indeterminate Forms
- 25 Convergence of Sequences
- 26 Geometric Series
- 27 The Integral Test
- 28 Comparison Test for Series
- 29 The Limit Comparison Test
- 30 Proof of the Limit Comparison Test
- 31 Absolute Convergence
- 32 The Ratio Test
- 33 Proof of the Ratio Test
- 34 Series Convergence Test Strategy
- 35 Taylor Series Introduction
- 36 Power Series
- 37 Convergence of Power Series
- 38 Power Series Interval of Convergence Example
- 39 Proofs of Facts about Convergence of Power Series
- 40 Power Series as Functions
- 41 Representing Functions with Power Series
- 42 Using Taylor Series to find Sums of Series
- 43 Taylor Series Theory and Remainder
- 44 Parametric Equations
- 45 Slopes of Parametric Curves
- 46 Area under a Parametric Curve
- 47 Arclength of Parametric Curves
- 48 Polar Coordinates
