Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.

Table of Contents for A Course in Mathematical Analysis Volume 2: Functions of a Complex Variable; Differential Equations

Part One:
I. Elements of the Theory
1. General Principles. Analytic Functions
2. Power Series with Complex Terms. Elementary Transcendental Functions
3. Conformal Representation
II. The General Theory of Analytic Functions According to Cauchy
1. Definite Integrals taken between Imaginary Limits
2. Cauchy's Integral. Taylor's and Laurent's Series. Singular Points. Residues
3. Applications of the General Theorems
4. Periods of Definite Integrals
III. Single-Valued Analytic Functions
1. Weierstrass's Primary Functions. Mittag-Leffler's Theorem
2. Doubly Periodic Functions. Elliptic Functions
3. Inverse Functions. Curves of Deficiency One
IV. Analytic Extension
1. Definition of an Analytic Function by Means of One of its Elements
2. Natural Boundaries. Cuts
V. Analytic Functions of Several Variables
1. General Properties
2. Implicit Functions. Algebraic Functions
Exercises
Index
Part Two:
I. Elementary Methods of Integration
1. Formation of Differential Equations
2. Equations of the First Order
3. Equations of Higher Order
II. Existence Theorems
1. Calculus of Limits
2. The Method of Successive Approximations. The Cauchy-Lipschitz Method
3. First Integrals. Multipliers
4. Infinitesimal Transformations
III. Linear Differential Equations
1. General Properties. Fundamental Systems
2. The Study of Some Particular Equations
3. Regular Integrals. Equations with Periodic Coefficients
4. Systems of Linear Equations
IV. Non-Linear Differential Equations
1. Exceptional Initial Values
2. A Study of Some Equations of the First Order
3. Singular Integrals
V. Partial Differential Equations of the First Order
1. Linear Equations of the First Order
2. Total Differential Equations
3. Equations of the First Order in Three Variables
4. Simultaneous Equations
5. Generalities on the Equations of Higher Order
Exercises
Index

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