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This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked examples have been added to this edition. Prerequisites include calculus and ordinary differential equations. A student who reads this book and works many of the exercises will have a sound knowledge for a second course in partial differential equations or for courses in advanced engineering and science. Two additional chapters include short introductions to applications of PDEs in biology and a new chapter to the computation of solutions. A brief appendix reviews techniques from ordinary differential equations. From the reviews of the second edition: “This second edition of the short undergraduate text provides a fist course in PDE aimed at students in mathematics, engineering and the sciences. The material is standard … Strong emphasis is put on modeling and applications throughout; the main text is supplied with many examples and exercises.” —R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007 “This is a unique book in the sense that it provides a coverage of the main topics of the subject in a concise style which is accessible to science and engineering students. … Reading this book and solving the problems, the students will have a solid base for a course in partial differential equations … .” —Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 74, 2008.

Mathematics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Community & Population Ecology. --- Ecology. --- Differential equations, partial. --- Mathematical physics. --- Mathématiques --- Ecologie --- Physique mathématique --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Community ecology, Biotic. --- Partial differential equations. --- Physics. --- Balance of nature --- Biology --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Physical mathematics --- Physics --- Partial differential equations --- Ecology --- Differential equations, Partial. --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Math --- Science

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This book includes a comprehensive review of the processes controlling marine ecosystems, communities, and populations, as well as introduces concepts, approaches, and methods in the fast-changing fields of marine ecology and oceanography. This third edition maintains the structure of previous editions, introducing marine environments, dwelling on population, community, and ecosystem levels of organization, and emphasizing relevant biogeochemical and hydrodynamic mechanisms. The content is updated to include major features that new research has revealed in recent decades, but still highlights links to originators of critical ideas in the history of marine sciences. The greatest change in this edition is an expansion of each chapter to capture new awareness, and implications, of the rapid change affecting all aspects marine environments, driven by anthropogenic forces operating through climate and oceanographic mechanisms.

Ecology --- Earth & Environmental Sciences --- Life sciences. --- Water. --- Applied ecology. --- Aquatic ecology. --- Community ecology, Biotic. --- Zoology. --- Marine sciences. --- Freshwater. --- Life Sciences. --- Freshwater & Marine Ecology. --- Water, general. --- Community & Population Ecology. --- Marine & Freshwater Sciences. --- Applied Ecology. --- Aquatic biology. --- Ecology. --- Marine Sciences. --- Biology --- Natural history --- Animals --- Environmental protection --- Nature conservation --- Ocean sciences --- Aquatic sciences --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Hydrobiology --- Water biology --- Marine ecology. --- Aquatic ecology . --- Fresh waters --- Freshwater --- Freshwaters --- Inland water --- Inland waters --- Water --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Hydrology --- Aquatic biology

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This book offers a sweeping history of Pureora Forest Park, one of the most significant sites of natural and cultural history interest in New Zealand.  The authors review the geological history of the volcanic zone, its flora and fauna, and the history of Maori and European utilization of forest resources. Chapter-length discussions cover management of the native forest by the New Zealand Forest Service; the forest village and its sawmills; the intensive timber harvesting, and the conflicts with conservationists and expensive compensation agreements that ensued. Separate chapters cover initiatives to protect the forest from introduced herbivores; to guard protected species, especially birds, from predators; the facilities for recreational hunting; the development of the Timber Trail, an 83 km cycleway through the forest and along old logging tramways, complete with detailed interpretation signs illustrating the history of logging; and the family recreation areas and tracks. The final chapter gathers conclusions and advances prospects for the future of Pureora Forest. In sum, the book demonstrates how ecological study, combined with a respect for people and for nature plus a flexible, interdisciplinary approach to both local history and current scientific priorities, can be welded into a consistently effective strategy for addressing the pressing forest-ecology questions of our time.

Ecology --- Earth & Environmental Sciences --- Biotic communities. --- Pureora Forest Park (N.Z.) --- History. --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Pureora Conservation Park (N.Z.) --- Pureora Forest (N.Z.) --- Pureora State Forest Park (N.Z.) --- Life sciences. --- Ecosystems. --- Life Sciences. --- Population biology --- Endangered ecosystems. --- Threatened ecosystems --- Biotic communities --- Nature conservation

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 In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike.   Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem.  When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply.   While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.  .

Physics. --- Socio- and Econophysics, Population and Evolutionary Models. --- Community & Population Ecology. --- Genetics and Population Dynamics. --- Biological Networks, Systems Biology. --- Ecology. --- Genetics --- Physique --- Ecologie --- Mathematics. --- Population biology -- Statistical methods. --- Random variables. --- Stochastic processes. --- Physics --- Physical Sciences & Mathematics --- Physics - General --- Population biology --- Statistical methods. --- Random processes --- Chance variables --- Stochastic variables --- Community ecology, Biotic. --- Biomathematics. --- Systems biology. --- Biological systems. --- Sociophysics. --- Econophysics. --- Probabilities --- Variables (Mathematics) --- Data-driven Science, Modeling and Theory Building. --- Systems Biology. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Ecology --- Biosystems --- Systems, Biological --- System theory --- Systems biology --- Computational biology --- Bioinformatics --- Biological systems --- Molecular biology --- Mathematics --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Economics --- Statistical physics --- Mathematical sociology --- Philosophy --- Statistical methods

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This book provides a wealth of high-quality scientific information on the patterns and processes of vegetation change across a broad range of spatial and temporal scales, concentrating on southwestern China, mostly on the Yunnan region, and extending to the Yangtze River valley near the boundaries separating Chongqing, Sichuan and Guizhou. This is the first work to present a contemporary survey and analysis of the special character and value of the subtropical vegetation of southwestern China. In addition, the author also considers present day vegetation in the context of geological events and evolution, and with reference to ecological factors and human activities. The author has conducted extensive field work in the region and the book benefits from her deep and sophisticated understanding of how vegetation dynamics evolve, how plants persist, and how plant diversity has changed over time and space in the Yunnan region. Included are comparisons and links with similar systems around the world. The book provides a clear, concise account of the patterns and processes surrounding the subtropical vegetation of southwestern China, making frequent use of line illustrations, color maps and photos to support its exhaustive analysis of this often complex topic. Special attention is paid to several Tertiary relict forests that only recently have been identified and studied. This book will serve as a point of departure for future researchers as they trace and interpret the evolution of the natural environment.

Life Sciences. --- Plant Ecology. --- Community & Population Ecology. --- Biodiversity. --- Forestry. --- Terrestial Ecology. --- Life sciences. --- Ecology. --- Forests and forestry. --- Sciences de la vie --- Biodiversité --- Ecologie --- Forêts et sylviculture --- Botany --- Earth & Environmental Sciences --- Plant Ecology --- Plant ecology --- Plants --- Ecology --- Plant ecology. --- Community ecology, Biotic. --- Forest land --- Forest lands --- Forest planting --- Forest production --- Forest sciences --- Forestation --- Forested lands --- Forestland --- Forestlands --- Forestry --- Forestry industry --- Forestry sciences --- Land, Forest --- Lands, Forest --- Silviculture --- Sylviculture --- Woodlands --- Woods (Forests) --- Agriculture --- Natural resources --- Afforestation --- Arboriculture --- Logging --- Timber --- Tree crops --- Trees --- Biological diversification --- Biological diversity --- Biotic diversity --- Diversification, Biological --- Diversity, Biological --- Biology --- Biocomplexity --- Ecological heterogeneity --- Numbers of species --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Phytoecology --- Vegetation ecology --- Ecology . --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Floristic ecology