This book offers readers the methods that are necessary to apply the power of calculus to analyze real problems. While most calculus textbooks focus on formula-based calculus, this book explains how to do the analysis of calculus, rates of change, and accumulation from data. The author’s introductory approach prepares students with the techniques to handle numerically-based problems in more advanced classes or in real-world applications. This self-contained book uses the computer algebra system Maple for computation, and the material is easily adaptable for calculators or other computer...

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique....

This book revises and expands upon the prior edition,  The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries.  Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an  a priori  estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly...

This book provides the essential theoretical tools for stochastic modeling. The authors address the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes. This book also presents specific examples with simulation methods that apply the topics to different areas of knowledge. These examples include practical applications, such as modeling the COVID-19 pandemic and animal movement modeling. This book is concise and rigorous, presenting the material in an easily accessible manner that allows...

This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beans and their applications to sup norm estimates, L^p estimates,  averages, and Weyl laws.  Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment is currently spread through a variety of rather technical papers. The authors present a treatment of these tools that is accessible to a wider...