An Introduction to Differential Equations

Stochastic Modeling, Methods and Analysis(Volume 2)

Volume 1: Deterministic Modeling, Methods and Analysis

For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background.

An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus.

Errata
Errata (32 KB)

Contents:

• Elements of Stochastic Processes and Itô–Doob Stochastic Calculus
• First-Order Differential Equations
• First-Order Nonlinear Differential Equations
• First-Order Systems of Linear Differential Equations
• Higher-Order Differential Equations
• Topics in Differential Equations

Readership: Advanced undergraduate students, interdisciplinary researchers; researchers in the mathematical sciences.
Key Features:

• Volume 2 prepares the undergraduate students and interdisciplinary readers to meet the demands and challenges in the global competitive and dynamic world of the twenty-first century
• This book is an easily accessible source for the advanced tools and knowledge surrounding the development of the stochastic models of dynamic processes under both internal and external random environmental perturbations
• The book provides generalizations of the deterministic results, namely, the Principle of Superposition, Abel-Jacobi-Liouville Theorem and its extensions to their stochastic version or by further clarification/proof of the results/observations (the concept of the Ito-Doob type stochastic adjoint differential equations)
• The book is innovative in its efforts to present the concepts, topics, and methods with adequate preparation for deterministic calculus with a brief supplement of Ito-Doob calculus
• The book also serves as a reference source for research in developing stochastic models and the methods of solving other different types of stochastic differential equations in literature
• This is the first time that an undergraduate level book serves as a source for research reference book in the literature
• The book takes a proactive approach to motivating the reader
• Volume 2 uses the unique format introduced in Volume 1
• The book also targets readers with interdisciplinary backgrounds and interests
• The observations in the book attempt to nurture the curiosity of a reader and to minimize the gap between conceptual and computational understanding