Multiplicative Analytic Geometry

This book is devoted to multiplicative analytic geometry. The book reflects recent investigations in the topic. The reader can use the main formulae for investigations of multiplicative differential equations, multiplicative integral equations, and multiplicative geometry.

The authors summarize the most recent contributions in this area. The goal of the authors is to bring the most recent research on the topic to capable senior undergraduate students, beginning graduate students of engineering and science, and researchers in a form to advance further study. The book contains seven chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems.

Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. In the period from 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics and finance.

Multiplicative Analytic Geometry builds upon multiplicative calculus and advances the theory to the topics of analytic and differential geometry.