Geometric Mechanics on Riemannian Manifolds Applications to partial Differential Equations

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic os...

 Global Analysis in Mathematical Physics Geometric and Stochastic Models

This book gives a common treatment to three areas of application of Global analysis to Mathematical Physics previously considered quite distant from each other. These areas are the geometry of manifolds applied to classical mechanics, stochastic different...

 Numerical methods for ordinary differential equations

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This book is a fully revised update of the author's classic 1987 text, Numerical Analysis of Ordinary Differential Equations, and in...

 Modern Differential Geometry Curves and Surfaces with Mathematica

Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray's famous textbook, covers how to define and compute standard geometric functions using...

 Introduction to Numerical Methods in Differential Equations

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understa...

 Applied partial differential equations

Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathema...

 Differential Equations on Fractals A Tutorial

Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with...

 From Geometry to Quantum Mechanics In Honor of Hideki Omori

This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics that have been arranged in celebration of Hideki Omori's recent retirement from Tokyo University of Science and in honor ...

 The universality of the radon transform

Written by a leading scholar in mathematics, this monograph discusses the Radon transform. This topic has wide ranging applications, in particular X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography. Read...

 Differential Equations and Their Applications

This text is a clearly written and complete introductory study of differential equations and their applications. Suitable for a one- or two-semester course on the subject, the material is fully comprehensible to anyone who has studied college-level calcul...

 Notions of Convexity

The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory...

 Theory of fuzzy differential equations and inclusions

This volume details the current state of the theory of fuzzy differential equations and inclusions and a systematic account of recent developments. The chapters are presented in a clear and logical way and provide preliminary material of fuzzy set theory;...

 Heat Kernels and Dirac Operators

In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction ...

 Handbook of Mathematics and Computational Science

Introduction 1. Numerical computation (arithmetics and numerics) 2. Equations and inequalities (algebra) 3. Geometry and trigonometry in the plane 4. Solid geometry 5. Functions 6. Vector analysis 7. Coordinate systems 8. Analytic geometr...

 Optimal control theory for applications

The published material represents the outgrowth of teaching analytical optimization to aerospace engineering graduate students. To make the material available to the widest audience, the prerequisites are limited to calculus and differential equations. It...