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.
Problem Solving Process; Algebra of Matrices; Determinants; Matrix Calculus; Mathematical Modeling; Integrable Differential Equations; Linear Homogeneous Equations; Linear Non homogeneous Equations; Energy Function Method; Reduced Linear Differential Equations; Variable Separable, Homogeneous, Bernoulli, and Essentially Time-Invariant Differential Equations; Linear Homogeneous Systems; Procedure of Finding Fundamental Matrix Solution; General Linear Homogeneous Systems; Linear Non homogeneous Systems; Companion system; The Laplace Transform; Applications of Laplace Transform; Fundamental Conceptual Algorithms and Analysis; Method of Variation of Parameters; Generalized Method of Variation of Parameters; Differential Inequalities and Comparison Method; Hybrid Method: Energy/Lyapunov and Comparison Methods; Linear Hybrid Systems; Linear Hereditary Systems; Qualitative Properties of Solution Process; Linear Stochastic Systems; Several applied Examples and Illustrations from the Biological, Chemical, Medical, Engineering, Physical and Social Sciences.