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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

Chapter 1.  
Introduction  
l.  Algebraic and Geometric Structures  
1.1.  Vector Spaces  
1.2.  Metric Spaces  
1.3.  Mappings  
1.4.  Linear Transformations on C into Itself ; Matrices  
1.5.  Fixed Point Theorems  
1.6.  Functional Inequalities  
II.  Analytical Structures  
1.7.  Holomorphic Functions  
1.8.  Power Series  
1.9.  Cauchy Integrals  
1.10.  Estimates of Growth  
1.11.  Analytic Continuation; Permanency of Functional Equations  
Chapter 2.  
Existence and Uniqueness Theorems  
2.1.  Equations and Solutions  
2.2.  The Fixed Point Method  
2.3.  The Method of Successive Approximations  
2.4.  Majorants and Majorant Methods  
2.5.  The Cauchy Majorant  
2.6.  The Lindelöf Majorant  
2.7.  The Use of Dominants and Minorants  
2.8.  Variation of Parameters  
Chapter 3.  
Singularities  
3.1.  Fixed and Movable Singularities  
3.2.  Analytic Continuation; Movable Singularities  
3.3.  Painlevé's Determinateness Theorem; Singularities  
3.4.  Indeterminate Forms  
Chapter 4.  
Riccati's Equation  
4.1.  Classical Theory  
4.2.  Dependence on Internal Parameters; Cross Ratios  
4.3.  Some Geometric Applications  
4.4.  "Abstract of the Nevanlinna Theory, I "  
4.5.  "Abstract of the Nevanlinna Theory, II "  
4.6.  The Malmquist Theorem and Some Generalizations  
Chapter 5.  
Linear Differential Equations: First and Second Order  
5.1.  General Theory: First Order Case  
5.2.  General Theory: Second Order Case  
5.3.  RegularSingular Points  
5.4.  Estimates of Growth  
5.5.  Asymptotics on the Real Line  
5.6.  Asymptotics in the Plane  
5.7.  Analytic Continuation; Group of Monodromy  
Chapter 6.  
Special Second Order Linear Dulerential Equations  
6.1.  The Hypergeometric Equation  
6.2.  Legendre's Equation  
6.3.  Bessel's Equation  
6.4.  Laplace's Equation  
6.5.  The Laplacian; the HermiteWeber Equation; Functions of the Parabolic Cylinder  
6.6.  The Equation of Mathieu; Functions of the Elliptic Cylinder  
6.7.  Some Other Equations  
Chapter 7.  
Representation Theorems  
7.1.  Psi Series  
7.2.  Integral Representations  
7.3.  The Euler Transform  
7.4.  Hypergeometric Euler Transforms  
7.5.  The Laplace Transform  
7.6.  Mellin and MellinBarnes Transforms  
Chapter 8.  
Complex Oscillation Theory  
8.1.  Stunnian Methods; Green's Transform  
8.2.  Zerofree Regions and Lines of Influence  
8.3.  Other Comparison Theorems  
8.4.  Applications to Special Equations  
Chapter 9.  
Linear nth Order and Matrix Differential Equations  
9.1.  Existence and Independence of Solutions  
9.2.  Analyticity of Matrix Solutions in a Star  
9.3.  Analytic Continuation and the Group of Monodromy  
9.4.  Approach to a Singularity  
9.5.  RegularSingular Points  
9.6.  The Fuchsian Class; the Riemann Problem  
9.7.  IrregularSingular Points  
Chapter 10.  
The Schwarzian  
10.1.  The Schwarzian Derivative  
10.2.  Applications to Conformal Mapping  
10.3.  Algebraic Solutions of Hypergeometric Equations  
10.4.  Univalence and the Schwarzian  
10.5.  Uniformization by Modular Functions  
Chapter 11.  
First Order Nonlinear Differential Equations  
11.1.  Some BriotBouquet Equations  
11.2.  Growth Properties  
11.3.  Binomial BriotBouquet Equations of Elliptic Function Theory  
Appendix. Elliptic Functions  
Chapter 12.  
Second Order Nonlinear Differential Equations and Some Autonomous Systems  
12.1  Generalities; BriotBouquet Equations  
12.2  The Painlevé Transcendents  
12.3  The Asymptotics of Boutroux  
12.4  The Emden and the ThomasFermi Equations  
12.5  Quadratic Systems  
12.6  Other Autonomous Polynomial Systems  
Bibliography  
Index  