How to Analyze Power Series - Calc 2 / AP Calculus Lesson & Examples

Learn how to expand and work with Power Series in AP Calculus BC Unit 10 and College Calc 2.
We build series from functions, use the geometric series to study convergence, differentiate and integrate term by term, and find intervals of convergence graphically and algebraically.
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🤓 My Calculus Courses
Calc 1: https://www.youtube.com/playlist?list=PLO0QMMwWEgs_naFuE_d6xdmU8Xh7gG2zg
Calc 2: https://www.youtube.com/playlist?list=PLO0QMMwWEgs91-5x5cXg7zCGIMb40iQ4C
Calc 3: https://www.youtube.com/playlist?list=PLO0QMMwWEgs__vBQQymjNqmD9lkEcnvvv
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🎯 Learning Goals
- Main Objective: Expand out power series and connect them to the functions they represent
- Side Quest 1: Use the geometric power series to first explore the convergence of power series
- Side Quest 2: Term-by-term differentiate or integrate to generate new power series
- Side Quest 3: Begin to understand the interval of convergence for power series both graphically and algebraically
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⏱️Video Timestamps
00:00 Intro
01:10 Geometric Series Warm-Up, Conceptually
01:53 Geometric Series Warm-Up, Procedurally
03:24 Connecting the Geometric Series to the Power Series
07:00 Power Series Graphically
12:12 Expanding Power Series Examples
15:57 Defining the Power Series
18:03 Expanding Power Series In Reverse Examples
19:30 Term-by-Term Integration for Arctangent
22:46 Term-by-Term Differentiation and Integration for Power Series
23:12 Term-by-Term Integration for Natural Log
24:11 Early First Encounter with e^x Power Series (Non-Geometric)
25:36 General Non-Geometric Power Series Example
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🧭 Where You Are in the Chapter
L1. Power Series ← YOU ARE HERE :)
L2. Radius and Interval of Convergence
L3. Taylor Series
L4. Lagrange Error Bound
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🗺️ Your Calculus Roadmap
https://drive.google.com/file/d/1ID3SH6rwtTmjBOIpT9gg-kHggSVWr8Ng/view
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📝 Grab the Notes & Key
→ Free Blank Notes:
UNDER CONSTRUCTION
→ First Lecture Google Drive Link:
UNDER CONSTRUCTION
→ If you’d like to support me, get my answer keys, and more!:
UNDER CONSTRUCTION
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🏷️ Tags and Keywords
power series calculus, expand power series from functions, geometric power series convergence, interval of convergence calculus, term by term differentiation integration series, AP calculus BC unit 10 power series, calc 2 series examples, college calculus power series, calculus help online, math exam prep, STEM education, convergence and divergence series

Видео How to Analyze Power Series - Calc 2 / AP Calculus Lesson & Examples канала Math Man McGreal