複變函數論 Complex Analysis | 應用數學系吳培元老師

Complex Analysis

複變函數論

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課程影音
課程綱要
課程行事曆

本課程主要目的是探討解析函數之微分及積分性質，作為後續研究之基礎。

課程用書：Complex Variables and Applications,James Ward Brown & Ruel V. Churchill,6th edition, McGraw-Hill, 1996.

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授課老師	應用數學系吳培元老師
課程學分	3學分
授課年度	96學年度
授課對象	大學部三年級學生
預備知識	高等微積分
課程提供	課程影音課程綱要課程行事曆

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音
	第一章 Complex Numbers Section1 Sums and Products Section2 Basic Algebraic Properties Further Properties Section3 Moduli Section4 Complex Conjugates	線上觀看
	Section5 Polor Form Section6 Exponential Form Section7 Powers and Roots	線上觀看
	第一章 Complex Numbers Section8 Regions in the Complex Plane 第二章 Analytic Functions Section9 Functions of a Complex Variable Section10 Mappings Section11 Mappings by the Exponential Function	線上觀看
	Section12 Limits Section13 Theorems in Limits Section14 Derivatives Section15 Differentiation Formulas	線上觀看
	Section16 Limits Involving the Points at Infinity Section17 Continuity Section18 Differentiatility	線上觀看
	Section18 Differentiatility Section19 Differentiatility Formulas Section20 Cauchy-Riemann Equations Section21 Reflectiotn Principle Section22 C-R equation in Polar Form Section23 Analytic Function	線上觀看
	Section23 Analytic Functions Section24 Harmonic Functions	線上觀看
	Section25 Harmonic Functions-1 Section26 Uniquely Determined Analytic Functions Section27 Refelction Principle 第三章 Elementary Functions Section28 The Exponential Func	線上觀看
	Section29 The Logarithmic Function Section31 Branches and Derivatives of Logarithms Section32 Complex Exponents Functions Section33 Trigonometric Functions	線上觀看
	Section34 Hyperbolic Functions Section35 Inverse Trigonometric and Hyperbolic Functions Section36 Derviatives of Functions Section37 Integrals Section38 Contours Section39 Contours Integrals	線上觀看
	Section40 Examples Section41 Antiderivatives Section42 Fundamental Theory of Integral Section43 Examples	線上觀看
	Section44 Cauchy-Goursat Theorem (VersionI)	線上觀看
	Section45 Cauchy-Goursat Theorem (VersionII) Section46 Cauchy-Goursat Theorem (VersionIII) Section47 Cauchy Integral Formula Section48 Derivatives of Analytic Functions Section49 Liouvilles Theorem	線上觀看
	Section50 Maximum Modulus Principle	線上觀看
	Section50 Maximum Modulus Principle 第五章 Series Section51 Convergence of Sequences Section52 Convergence of Series Section53 Taylor Series Section54 Examples	線上觀看
	Section55 Laurent Series Section56 Examples	線上觀看
	Section56 Examples Section57 Absolate amd Uniform Convergence of Power Series	線上觀看
	Section58 Continuity of Sums of Power Series Section59 Integration and Differentiation of Power Series	線上觀看
	Section59 Integration and Differentiation of Power Series Section60 Uniqueness of Series Representations Section61 Multiplication and Division of Power Series 第六章 Residues and Poles Section62 Residues Section63 Cauchy	線上觀看
	Section61 Multiplication and Division of Power Series 第六章 Residues and Poles Section62 Residues Section63 Cauchys Residue Theorem	線上觀看
	Section63 Cauchys Residue Theorem Section64 Using a single Residue Section65 The Three Types of Isolated Singular Points	線上觀看
	Section66 Residues at Poles Section67 Examples Section68 Zeros of Analytic Functions	線上觀看
	Section69 Zeros and Poles Section70 Behavior of f Near Isolated Singular Points	線上觀看
	Section70 Behavior of f Near Isolated Singular Points 第七章 Residues and Poles Section71 Evaluation of Improper Integrals Section72 Example	線上觀看
	Section73 Improper Integrals from Fourier Analysis Section74 Jordans Lemma Section75 Indented PAths Section76 An Indentation Around a Branch Point	線上觀看
	Section77 Integration Along a Branch Cut Section78 Definite Integrals Involving Sines and Cosines	線上觀看
	Section79 Argument Principle Section80 Rouches Theorem Section81 Inverse Laplace Transforms Section82 Examples	線上觀看
	第八章 Mapping by Elementary Functions Section86 Linear Fractional Transformations 第九章Conformal Mapping Section94 Preservation of Angles	線上觀看

目前顯示第 1 至第 28 個資料列，總計 28 個資料列

課程目標

本課程主要目的是探討解析函數之微分及積分性質，作為後續研究之基礎。

課程章節

章節	主題內容
第一章	Complex numbers
第二章	Analytic functions
第三章	Elementary functions
第四章	Integrals
第五章	Series
第六章	Residues and poles
第七章	Applications of residues
第八章	Mapping by elementary functions

課程書目

Complex Variables and Applications,James Ward Brown & Ruel V. Churchill,6th edition, McGraw-Hill, 1996.

本課程行事曆提供課程進度與考試資訊參考。

學期週次	參考課程進度
第一週	Complex numbers
第二週	Complex numbers
第三週	Analytic functions
第四週	Analytic functions
第五週	Elementary functions
第六週	Elementary functions
第七週	Integrals
第八週	Integrals
第九週	期中考
第十週	Series
第十一週	Series
第十二週	Residues and poles
第十三週	Residues and poles
第十四週	Applications of residues
第十五週	Applications of residues
第十六週	Applications of residues
第十七週	Mapping by elementary functions
第十八週	期末考