Xiang-Sheng Wang - Böcker

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.FeaturesIncludes numerous exercises and examplesCan serve as a primary textbook or as supplementary reading for advanced undergraduate or graduate courses in differential equations, dynamical systems, mathematical biology, and mathematical modelingIntegrates 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.FeaturesIncludes numerous exercises and examplesCan serve as a primary textbook or as supplementary reading for advanced undergraduate or graduate courses in differential equations, dynamical systems, mathematical biology, and mathematical modelingIntegrates research tools from ordinary differential equations (ODEs), delay differential equations (DDEs), partial differential equations (PDEs), and difference equations (DEs) in a single volume.

Machine learning has become a cornerstone of modern data-driven science and technology. For mathematics students and researchers, understanding the mathematical foundations behind machine learning is essential, even if they never work directly with real-world datasets.This book provides a rigorous yet accessible introduction to the core mathematical ideas that underpin machine learning. Topics such as linear and nonlinear regression, regularization techniques, and the fundamentals of neural networks are explained in detail from a clear mathematical perspective.Unlike many existing texts that emphasize coding and practical implementation, this book focuses on theoretical results and conceptual understanding. It is designed for readers who want to grasp the mathematics behind machine learning without writing code.Who should read this book?Mathematics students and researchers interested in machine learning but with little programming experience.Scientists and engineers who have applied machine learning in practice and now seek a deeper understanding of its mathematical foundations.

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.