CHAPTER 1: REAL ANALYSIS AND THEORY OF FUNCTIONS: A QUICK REVIEW
CHAPTER 2: NORMED VECTOR SPACES
CHAPTER 3: BANACH SPACES
CHAPTER 4: INNER-PRODUCT SPACES AND HILBERT SPACES
CHAPTER 5: THE “GREAT THEOREMS” OF LINEAR FUNCTIONAL ANALYSIS
CHAPTER 6: LINEAR PARTIAL DIFFERENTIAL EQUATIONS
CHAPTER 7: DIFFERENTIAL CALCULUS IN NORMED VECTOR SPACES
CHAPTER 8: DIFFERENTIAL GEOMETRY IN ℝn
CHAPTER 9: THE “GREAT THEOREMS” OF NONLINEAR FUNCTIONAL ANALYSIS

Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.