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MTH 324 Lecture # 23 Power Series
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Previous Lecture’s Review
Derivatives of an analytic function Cauchy’s inequality Liouville’s theorem Fundamental theorem of Algebra Morera’s theorem 2
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Review of real power series Sequence and series of complex numbers
Lecture’s Outline Review of real power series Sequence and series of complex numbers Complex power series Operations on series 3
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Review of real sequence and series:
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Sequence: 7
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Criterion for convergence:
Example: 8
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Solution: 9
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Series: Remark: 11
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Geometric series : Example: 12
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Example: Solution: 15
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Theorem: (Necessary condition for convergence)
Proof: 16
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Divergence Test Example: 17
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Absolute and conditional convergence
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Tests for convergence Ratio test: 19
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Root test: 20
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Circle of convergence:
Power series: Circle of convergence: 21
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Remark: 22
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Example: Solution: 23
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Example: Solution: 25
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Theorem: Proof: 28
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References A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan. Complex variables and applications by James Brown and Ruel Churchill
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