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Engineering Mathematics

Complex Variables & Applications Chapter 5. Engineering Mathematics. 郑伟诗 wszheng@ieee.org, http://sist.sysu.edu.cn/~zhwshi/. Outlilne. 1 、 Definition of Series & Properties. 2 、Taylor Series. 3 、Laurent Series. 4 、Power Series. Series: Definition & Properties. What are we caring?

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Engineering Mathematics

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  1. Complex Variables & Applications Chapter 5 Engineering Mathematics • 郑伟诗 • wszheng@ieee.org, • http://sist.sysu.edu.cn/~zhwshi/

  2. Outlilne 1、Definition of Series & Properties 2、Taylor Series 3、Laurent Series 4、Power Series 1/2/2020, Page 2

  3. Series: Definition & Properties What are we caring? (1) Is this sequence converged? When? How? (2) Moreover, are the Sum of these point converged? (3) Can a function f at z be approximated by a series?

  4. Series: Definition & Properties 1/2/2020, Page 4

  5. When does a sequence converge? Series: Definition & Properties 1/2/2020, Page 5

  6. What is a series? Series: Definition & Properties partial sum 1/2/2020, Page 6

  7. When does a series converge? Series: Definition & Properties 1/2/2020, Page 7

  8. Absolute Convergence Series: Definition & Properties Converges!!! 1/2/2020, Page 8

  9. Series and Sequence Series: Definition & Properties 0 1/2/2020, Page 9

  10. When a function at z can be represented by a series? Taylor Series 1/2/2020, Page 10

  11. Taylor's theorem Taylor Series 板书证明 1/2/2020, Page 11

  12. Maclaurin series Taylor Series 1/2/2020, Page 12

  13. Example Taylor Series 1/2/2020, Page 13

  14. Example Taylor Series 1/2/2020, Page 14

  15. Taylor Series Laurent Series If a function f fails to be analytic at a point z0??? 1/2/2020, Page 15

  16. Laurent Series 1/2/2020, Page 16

  17. Another Equivalent Formulation Laurent Series 1/2/2020, Page 17

  18. Absolute Convergence POWER SERIES: Properties 1/2/2020, Page 18

  19. Uniformly Convergent POWER SERIES: Properties 1/2/2020, Page 19

  20. What is uniformly convergent Take for example POWER SERIES: Properties has limit at z POWER SERIES: Properties uniformly convergent 1/2/2020, Page 20

  21. Continuity POWER SERIES: Properties 1/2/2020, Page 21

  22. Integration POWER SERIES: Properties Example 1/2/2020, Page 22

  23. Differentiation POWER SERIES: Properties Example 1/2/2020, Page 23

  24. Uniqueness POWER SERIES: Properties 1/2/2020, Page 24

  25. Uniqueness POWER SERIES: Properties 1/2/2020, Page 25

  26. Multiplication POWER SERIES: Properties Taylor coefficients 前提 1/2/2020, Page 26

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