Engineering Mathematics Complex Variables Applications Chapter 5 wszhengieee
Engineering Mathematics Complex Variables & Applications Chapter 5 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? (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?
Series: Definition & Properties
Series: Definition & Properties • When does a sequence converge?
Series: Definition & Properties • What is a series? partial sum
Series: Definition & Properties • When does a series converge?
Series: Definition & Properties Absolute Convergence Converges!!!
Series: Definition & Properties • Series and Sequence 0
Taylor Series When a function at z can be represented by a series?
Taylor Series • Taylor's theorem 板书证明
Taylor Series • Maclaurin series
Taylor Series • Example
Taylor Series • Example
Laurent Series • Taylor Series If a function f fails to be analytic at a point z 0? ? ?
Laurent Series
Laurent Series • Another Equivalent Formulation
POWER SERIES: Properties • Absolute Convergence
POWER SERIES: Properties • Uniformly Convergent
POWER SERIES: Properties • What is uniformly convergent Take for example has limit at z POWER SERIES: Properties uniformly convergent
POWER SERIES: Properties • Continuity
POWER SERIES: Properties • Integration Example
POWER SERIES: Properties • Differentiation Example
POWER SERIES: Properties • Uniqueness
POWER SERIES: Properties • Uniqueness
POWER SERIES: Properties • Multiplication Taylor coefficients 前提
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