課程名稱 |
複分析導論 Introduction to Complex Analysis |
開課學期 |
112-1 |
授課對象 |
理學院 數學系 |
授課教師 |
陳榮凱 |
課號 |
MATH5230 |
課程識別碼 |
221 U6560 |
班次 |
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學分 |
4.0 |
全/半年 |
半年 |
必/選修 |
必帶 |
上課時間 |
星期二6,7(13:20~15:10)星期四6,7(13:20~15:10) |
上課地點 |
新302新302 |
備註 |
此課程研究生選修不算學分。 限學士班學生 總人數上限:80人 外系人數限制:10人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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課程概述 |
Complex function theory is a valuable tool used in many branches of pure, applied mathematics and natural sciences, including geometry, number theory, partial differential equations and various topics in physics and engineering. A basic course shall enable students to understand the concept of complex analyticity, to use residue calculus for evaluation of integrals and to learn some additional topics (depending on available time) selected from Riemann mapping theorem, special functions, prime number theorem, complex dynamical systems, etc. |
課程目標 |
Contents:
1. Analytic functions of a complex variable and power series.
2. Conformal mappings.
3. Maximum modulus principle and open mapping theorem.
4. Singularities of analytic functions and Laurent series.
5. Residue theorem and its applications: argument principle, Rouche's theorem and the evaluation of integrals.
6. Compactness and convergence of the analytic functions.
7. Runge's theorem, Mittag-Leffler's theorem.
8. Analytic continuation.
9. Harmonic functions and the Dirichlet problem.
Selected topics: Entire functions, Schwarz-Christoffel integral, Quasiconformal mappings, etc. |
課程要求 |
已修過微積分及分析導論 |
預期每週課後學習時數 |
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Office Hours |
每週四 15:30~16:20 備註: Or by appointment |
指定閱讀 |
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參考書目 |
1. E. M. Stein, R. Shakarchi, Complex analysis (Princeton Lectures in Analysis, No. 2).
2. L. Ahlfors, Complex analysis. |
評量方式 (僅供參考) |
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針對學生困難提供學生調整方式 |
上課形式 |
提供學生彈性出席課程方式 |
作業繳交方式 |
學生與授課老師協議改以其他形式呈現 |
考試形式 |
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其他 |
由師生雙方議定 |
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