Xiang-Sheng Wang

Differential and Difference Equations in Mathematical Biology introduces graduate and senior undergraduate students to differential and difference equations as tools for modeling biological phenomena. The book presents fundamental theory as well as recent research developments concerning the local and global analysis of continuous and discrete dynamical systems in mathematical biology. In addition to serving as a teaching text, the book is also valuable to researchers as both a reference and an introduction to the subject. Features Includes numerous exercises and examples Can serve as a primary textbook or as supplementary reading for advanced undergraduate or graduate courses in differential equations, dynamical systems, mathematical biology, and mathematical modeling Integrates research tools from ordinary differential equations (ODEs), delay differential equations (DDEs), partial differential equations (PDEs), and difference equations (DEs) in a single volume.

Differential and Difference Equations in Mathematical Biology introduces graduate and senior undergraduate students to differential and difference equations as tools for modeling biological phenomena. The book presents fundamental theory as well as recent research developments concerning the local and global analysis of continuous and discrete dynamical systems in mathematical biology. In addition to serving as a teaching text, the book is also valuable to researchers as both a reference and an introduction to the subject. Features Includes numerous exercises and examples Can serve as a primary textbook or as supplementary reading for advanced undergraduate or graduate courses in differential equations, dynamical systems, mathematical biology, and mathematical modeling Integrates research tools from ordinary differential equations (ODEs), delay differential equations (DDEs), partial differential equations (PDEs), and difference equations (DEs) in a single volume.

This volume brings together 30 chapters across five parts, offering a structured, in-depth survey of asymptotic analysis and its applications. Readers will find rigorous treatments of orthogonal polynomials, boundary layer problems, saddle-point integrals, turning point theory, Airy and Bessel expansions, special functions, and modern approaches to difference equations, differential equations, Riemann-Hilbert problems, integrals, and singular perturbation problems. Each chapter blends classical foundations with recent breakthroughs, making the book both a comprehensive reference and a graduate-level textbook with exercises for hands-on learning.Over the past three decades, asymptotic analysis has become indispensable in number theory, combinatorics, probability and statistics, mathematical physics, engineering, and applied sciences, equipping researchers and students with powerful methods for solving complex problems. This book not only surveys the latest advances in asymptotic methods but also demonstrates their practical applications across diverse mathematical models.Designed for advanced undergraduate students, graduate students, researchers, and instructors, the text can be used as a reference guide to modern asymptotic techniques or adapted into course modules, strengthening both theoretical understanding and applied problem-solving.

This volume brings together 30 chapters across five parts, offering a structured, in-depth survey of asymptotic analysis and its applications. Readers will find rigorous treatments of orthogonal polynomials, boundary layer problems, saddle-point integrals, turning point theory, Airy and Bessel expansions, special functions, and modern approaches to difference equations, differential equations, Riemann-Hilbert problems, integrals, and singular perturbation problems. Each chapter blends classical foundations with recent breakthroughs, making the book both a comprehensive reference and a graduate-level textbook with exercises for hands-on learning.Over the past three decades, asymptotic analysis has become indispensable in number theory, combinatorics, probability and statistics, mathematical physics, engineering, and applied sciences, equipping researchers and students with powerful methods for solving complex problems. This book not only surveys the latest advances in asymptotic methods but also demonstrates their practical applications across diverse mathematical models.Designed for advanced undergraduate students, graduate students, researchers, and instructors, the text can be used as a reference guide to modern asymptotic techniques or adapted into course modules, strengthening both theoretical understanding and applied problem-solving.