317 pages, 67 illus
This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. Linear and non-linear algebraic equations, derivatives and integrals, ordinary differential equations, and partial differential equations are the basic kinds of structures, or mathematical models, that are discussed. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. Next the definition of the structure is presented. This is usually followed by other examples of how the structure arises in environmental science, then the analytic methods of solving and learning from the structure are discussed. This is followed by teaching numerical methods for use when the situation is difficult. In most cases, examples of using Matlab software to solve and explore the structures are also included.
From the reviews: "It ! explains how basic tools of mathematical analysis can be efficiently used to study problems arising in environmental sciences. ! The text shall attract non-mathematical audience by clarity of exposition which concentrates mostly on ideas and techniques ! . Specifically tailored to the needs of undergraduate and graduate students in environmental sciences, this unique and skillfully written book shall help them to understand and master fundamental mathematical concepts and techniques used in the analysis of applied problems." (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 1145, 2008)
Introduction to Applied Mathematics.- Derivatives and Differentiation.- Integration.- Ordinary Differential Equations.- Further Topics in ODEs.- ODE Systems.-Numerical Solution of ODEs.- Second-Order ODEs.- Linear Algebraic Equations.- Non-Linear Equations.- Partial Differential Equations.
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