- 預備知識:微積分、基礎數學、高等微積分
- 適合年級: 三年級
- 課程簡介:
複變函數論是一個重要的領域,在物理、數論、組合等...都有許多應用。複變函數論主要是學習解析方程,而在大學的學習範圍主要為其基礎的領域,包含解析方程、線積分、奇異值、殘值定理、保角映射、 解析延拓等...。
- Definition of Complex Numbers.<br/>
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Topology of the Complex Plane.<br/>
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Power Series.<br/>
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Analytic Functions and Cauchy-Riemann Equations.<br/>
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Line Integrals.<br/>
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Closed Curve Theorem for Entire Functions.<br/>
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Properties of Entire Functions.<br/>
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Properties of Analytic Functions<br/>
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Cauchy’s Theorem<br/>
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Isolated Singularities.<br/>
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Laurent Series.<br/>
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The Residue Theorem.<br/>
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Introduction into Conformal Mappings.<br/>
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Riemann Mapping Theorem.<br/>
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Analytic Continuation.
- J. Bak and D. J. Newman (1999). Complex Analysis, Springer, corr. 2nd printing edition.<br/>
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H. A. Priestley (2003). Introduction to Complex Analysis, OUP Oxford 2nd edition.
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