James Ward Brown密歇根大學(xué)迪爾本分校數(shù)學(xué)系教授，美國(guó)數(shù)學(xué)學(xué)會(huì)會(huì)員。1964年于密歇根大學(xué)獲得數(shù)學(xué)博士學(xué)位。他曾經(jīng)主持研究美國(guó)國(guó)家自然科學(xué)基金項(xiàng)目，獲得過(guò)密歇根大學(xué)杰出教師獎(jiǎng)，并被列入美國(guó)名人錄。Ruel V.Churchill已故密歇根大學(xué)知名教授。早在60多年前，就開始編寫一系列經(jīng)典教材。除本書外，還與James Ward Brown合著《Fourier Series and Boundary Value Problems》。
圖書目錄
Preface 1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products and Quotients Roots of Complex Numbers Examples Regions in the Complex Plane 2 Analytic Functions Functions of a Complex Variable Mappings Mappings by the Exponential Function Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Differentiation Formulas Cauchy-Riemann Equations Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Branches and Derivatives of Logarithms Some Identities Involving Logarithms Complex Exponents Trigonometric Functions Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions 4 Integrals Derivatives of Functions w(t) Definite Integrals of Functions w(t) Contours Contour Integrals Some Examples Examples with Branch Cuts Upper Bounds for Moduli of Contour Integrals Antiderivatives Proof of the Theorem Cauchy-Goursat Theorem Proof of-the Theorem 5 Series 6 Residues and Poles 7 Applications of Residues 8 Mapping by Elementary Functions 9 Conformal Mapping 10 Applications of Conformal Mapping 11 The Schwarz-Chrstoffer Transformation 12 Integral Formulas of the Poisson Type Appendixes Index
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