This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in workin...

Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, sh...

A concise guide to representing complex Earth systems using simple dynamic modelsMathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes th...

Introduction to Geophysical Fluid Dynamics provides an introductory-level exploration of geophysical fluid dynamics (GFD), the principles governing air and water flows on large terrestrial scales. Physical principles are illustrated with the aid of the simplest existing models, and the computer methods are shown in juxtaposition with the equations to which they apply. It explores contemporary topics of climate dynamics and equatorial dynamics, including the Greenhouse Effect, global warmin...

The book is about a medium of discrete elements that permeate all space giving rise to physical reality. However, it is not about new physics. To the contrary, it enforces all major current theories, for they are all interpretable in terms of the behaviour and mechanics of the proposed fabric of space, which makes them much easier to comprehend. Thus, unlike our current understanding of physical reality, in both classical and quantum mechanics, in which fundamental quantities such as mass,...

The dramatic advances in the efficiency of digital computers during the past decade have provided hydrologists with a powerful tool for numerical modeling of groundwater systems. Introduction to Groundwater Modeling presents a broad, comprehensive overview of the fundamental concepts and applications of computerized groundwater modeling. The book covers both finite difference and finite element methods and includes practical sample programs that demonstrate theoretical points described in ...

This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include s...

This book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.

This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex syste...

A solid introduction to mathematical modeling for a range of chemical engineering applications, covering model formulation, simplification and validation. It explains how to describe a physical/chemical reality in mathematical language and how to select the type and degree of sophistication for a model. Model reduction and approximation methods are presented, including dimensional analysis, time constant analysis and asymptotic methods. An overview of solution methods for typical classes o...

Numerical models have become essential tools in environmental science, particularly in weather forecasting and climate prediction. This book provides a comprehensive overview of the techniques used in these fields, with emphasis on the design of the most recent numerical models of the atmosphere. It presents a short history of numerical weather prediction and its evolution, before describing the various model equations and how to solve them numerically. It outlines the main elements of a m...

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students ...