The authors' aim is to offer the reader the fundamentals of numerous mathematical methods with accompanying practical environmental applications. The material in this book addresses mathematical calculations common to both the environmental science and engineering professionals. It provides the reader with nearly 100 solved illustrative examples and the interrelationship between both theory and applications is emphasized in nearly all of the 35 chapters. One key feature of this book is that the solutions to the problems are presented in a stand-alone manner. Throughout the book, the illustrative examples are laid out in such a way as to develop the reader's technical understanding of the subject in question, with more difficult examples located at or near the end of each set. In presenting the text material, the authors have stressed the pragmatic approach in the application of mathematical tools to assist the reader in grasping the role of mathematical skills in environmental problem-solving situations. The book is divided up into 5 parts: Introduction; Analytical Analysis; Numerical Analysis; Statistical Analysis; and Optimization. The analytical analysis includes graphical, trial-and-error, search, etc. methods. The numerical analysis includes integration, differentiation, differential equation, Monte Carlo, etc. The statistical analysis includes probability, probability distribution, decision trees, regression analysis, etc. Optimization includes both traditional approaches and linear programming.

An accessible introduction to the mathematical methods essential for understanding processes in the Earth and environmental sciences.

Advanced mathematics used in engineering is studied here in this text which examines the relationship between the principles in natural processes and those employed in engineered processes. The text covers principles, practices and the mathematics involved in the design and operation of environmental engineering works. It also presents engineering

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

Modern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There is also an 'Application' section at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of 'put' and 'call' options in financial markets. The book presents several modern important and computationally efficient topics, including feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods.A unique and novel feature of the book is the introduction of a recently developed method for solving partial differential equations (PDEs), called the unified transform. PDEs are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics to ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge.The unified transform greatly facilitates this task. For example, two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, the unified transform derives in a simple manner a generalization of the d'Alembert solution, valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, the unified transform constructs a new solution to this ubiquitous PDE, with important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples.Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering.

This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.

Designed for engineering graduate students, this book connects basic mathematics to a variety of methods used in engineering problems.