An Introduction to Differential Equations: Stochastic modeling, methods, and analysis

This is a twenty-first century book designed to meet the challenges of understanding and solving interdisciplinary problems. The book creatively incorporates “cutting-edge” research ideas and techniques at the undergraduate level. The book also is a unique research resource undergraduate/graduate students and interdisciplinary researchers. It emphasizes and exhibits the importance of conceptual understandings and its symbiotic relationship in the problem solving process.The book is proactive in preparing for the modeling of dynamic processes in various disciplines. It introduces a “break-down-the problem” type of approach in a way that creates “fun” and “excitement”. The book presents many learning tools like “step-by-step procedures (critical thinking)”, the concept of “math” being a language, applied examples from diverse fields, frequent recaps, flowcharts and exercises. Uniquely, this book introduces an innovative and unified method of solving nonlinear scalar differential equations. This is called the “Energy/Lyapunov Function Method”. This is accomplished by adequately covering the standard methods with creativity beyond the entry level differential equations course.