Power Series - Derivatives & Integrals | Calculus 2 Lesson 32 - JK Math

How to Differentiate & Integrate Power Series (Calculus 2 Lesson 32)
In this video we learn how to find the derivative and integral of a power series by using the power rule for derivatives and integration. Additionally, we discuss how to find the radius and interval of convergence for these derivatives and integrals, and how they compare to the radius and interval of convergence of the original power series.
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This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Derivative of a Power Series
7:45 Integral of a Power Series
13:59 Brief Discussion of Radius & Interval of Convergence
15:01 Example Part 1 - Finding Derivative
16:38 Example Part 2 - Finding Integral
18:15 Example Part 3 - Radius & Interval for Original Series
25:03 Example Part 4 - Radius & Interval for Derivative
27:54 Example Part 5 - Radius & Interval for Integral
32:46 Example Part 6 - Checking Endpoints for Original Series
36:31 Example Part 7 - Checking Endpoints for Derivative
39:29 Example Part 8 - Checking Endpoints for Integral
45:47 Example Part 9 - Conclusion
46:26 Outro
📝 Examples Video: • Power Series - Derivat...
⏩ Next Lesson: • Power Series - Represe...
📺 Calculus 2 Playlist: • Calculus 2
📺 Calculus 1 Playlist: • Calculus 1
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