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Integrodifference Equations in Spatial Ecology / Frithjof Lutscher / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)
Titre : Integrodifference Equations in Spatial Ecology Type de document : document électronique Auteurs : Frithjof Lutscher, ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2019 Collection : Interdisciplinary Applied Mathematics, ISSN 0939-6047 num. 49 Importance : XVI, 385 p. 118 illus., 4 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-29294-2 Langues : Anglais (eng) Tags : Mathematical physics Mathematics Community ecology Biotic Mathematical models Mathematical Applications in the Physical Sciences Mathematics of Planet Earth Community & Population Ecology Mathematical Modeling and Industrial Mathematics Résumé : This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike Note de contenu : Models for Spatial Population Dynamics -- Modeling with Integrodifference Equations -- Critical Patch-Size -- Positive Steady States -- The Speed of Spatial Spread -- Spatial Spread with Allee Effect -- Modeling the Dispersal Process -- Computational Aspects -- Dispersal Success -- Approximations for Spread -- The Shape of Spatial Spread -- Applications -- Structured Populations -- Two Interacting Populations -- Spatial Variation -- Temporal Variation -- Further Topics and Related Models. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=148137 Integrodifference Equations in Spatial Ecology [document électronique] / Frithjof Lutscher, ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2019 . - XVI, 385 p. 118 illus., 4 illus. in color : online resource. - (Interdisciplinary Applied Mathematics, ISSN 0939-6047; 49) .
ISBN : 978-3-030-29294-2
Langues : Anglais (eng)
Tags : Mathematical physics Mathematics Community ecology Biotic Mathematical models Mathematical Applications in the Physical Sciences Mathematics of Planet Earth Community & Population Ecology Mathematical Modeling and Industrial Mathematics Résumé : This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike Note de contenu : Models for Spatial Population Dynamics -- Modeling with Integrodifference Equations -- Critical Patch-Size -- Positive Steady States -- The Speed of Spatial Spread -- Spatial Spread with Allee Effect -- Modeling the Dispersal Process -- Computational Aspects -- Dispersal Success -- Approximations for Spread -- The Shape of Spatial Spread -- Applications -- Structured Populations -- Two Interacting Populations -- Spatial Variation -- Temporal Variation -- Further Topics and Related Models. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=148137 Sensitivity Analysis: Matrix Methods in Demography and Ecology / Hal Caswell / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2019)
Titre : Sensitivity Analysis: Matrix Methods in Demography and Ecology Type de document : document électronique Auteurs : Hal Caswell, ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2019 Collection : Demographic Research Monographs, ISSN 1613-5520 Importance : XVIII, 299 p. 134 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-030-10534-1 Langues : Anglais (eng) Tags : Demography Statistics Community ecology Biotic Biomathematics Statistics for Social Sciences Humanities Law Community & Population Ecology Mathematical and Computational Biology Résumé : This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics. Note de contenu : I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=155869 Sensitivity Analysis: Matrix Methods in Demography and Ecology [document électronique] / Hal Caswell, ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2019 . - XVIII, 299 p. 134 illus : online resource. - (Demographic Research Monographs, ISSN 1613-5520) .
ISBN : 978-3-030-10534-1
Langues : Anglais (eng)
Tags : Demography Statistics Community ecology Biotic Biomathematics Statistics for Social Sciences Humanities Law Community & Population Ecology Mathematical and Computational Biology Résumé : This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics. Note de contenu : I Introductory and methodological: 1 Introduction. Sensitivity analysis: what and why? -- 2 Matrix calculus and notation -- II Linear models: 3 The sensitivity of population growth rate: three approaches -- 4 Sensitivity analysis of longevity and life disparity -- 5 Individual stochasticity and implicit age dependence -- 6 Age[1]stage-classified models -- III Time-varying and stochastic models: 7 Transient population dynamics -- 8 Periodic models -- 9 LTRE decomposition of the stochastic growth rate -- IV Nonlinear models: 10 Sensitivity analysis of nonlinear demographic models -- V Markov chains: 11 Sensitivity analysis of discrete Markov chains -- 12 Sensitivity analysis of continuous Markov chains Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=155869 Current Trends in Dynamical Systems in Biology and Natural Sciences / Maira Aguiar ; SpringerLink (Online service) ; Carlos Braumann ; Bob W. Kooi ; Andrea Pugliese ; Nico Stollenwerk ; Ezio Venturino / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2020)
Titre : Current Trends in Dynamical Systems in Biology and Natural Sciences Type de document : document électronique Auteurs : Maira Aguiar, ; SpringerLink (Online service) ; Carlos Braumann, ; Bob W. Kooi, ; Andrea Pugliese, ; Nico Stollenwerk, ; Ezio Venturino, Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2020 Collection : SEMA SIMAI Springer Series, ISSN 2199-3041 num. 21 Importance : XII, 243 p. 70 illus., 40 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-41120-6 Langues : Anglais (eng) Tags : Applied mathematics Engineering mathematics Biomathematics Probabilities Dynamics Ergodic theory Computer mathematics Community ecology Biotic Applications of Mathematics Mathematical and Computational Biology Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Community & Population Ecology Résumé : This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop “Dynamical Systems Applied to Biology and Natural Sciences – DSABNS”, held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. Note de contenu : 1 P. Freguglia et al., Modelling Ecological Systems from a Niche Theory to Lotka-Volterra equations -- 2 N. Petrovskaya and W. Zhang, Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species -- 3 A. Andò and D. Breda, Collocation techniques for structured populations modeled by delay equations -- 4 H. Laurie et al., Herding induced by encounter rate, with predator pressure influencing prey response -- 5 N. M. Brites and C. A. Braumann, Harvesting policies with stepwise effort and logistic growth in a random environment -- 6 C. Corbacho et al., Mathematical modeling of the population dynamics of long-lived raptor species. Application to Eurasian black vulture colonies -- 7 C. Bianchi et al., On the role of inhibition processes in modeling control strategies for composting plants -- 8 A. Martiradonna et al., Optimal control of invasive species with budget constraint: qualitative analysis and numerical approximation -- 9 S. Aniţa et al., A Shape Optimization Problem Concerning the Regional Control of a Class of Spatially Structured Epidemics - Sufficiency Conditions -- 10 A. d’Onofrio and P. Manfredi, The interplay between voluntary vaccination and reduction of risky behavior: a general behavior-implicit SIR model for vaccine preventable infections -- 11 F. Florian and R. Vermiglio, PC-based sensitivity analysis of the basic reproduction number of population and epidemic models -- 12 M. J. Wieteska, Linear dynamics of mRNA expression and hormone concentration levels in primary cultures of bovine granulosa cells. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149895 Current Trends in Dynamical Systems in Biology and Natural Sciences [document électronique] / Maira Aguiar, ; SpringerLink (Online service) ; Carlos Braumann, ; Bob W. Kooi, ; Andrea Pugliese, ; Nico Stollenwerk, ; Ezio Venturino, . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2020 . - XII, 243 p. 70 illus., 40 illus. in color : online resource. - (SEMA SIMAI Springer Series, ISSN 2199-3041; 21) .
ISBN : 978-3-030-41120-6
Langues : Anglais (eng)
Tags : Applied mathematics Engineering mathematics Biomathematics Probabilities Dynamics Ergodic theory Computer mathematics Community ecology Biotic Applications of Mathematics Mathematical and Computational Biology Probability Theory and Stochastic Processes Dynamical Systems and Ergodic Theory Computational Mathematics and Numerical Analysis Community & Population Ecology Résumé : This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop “Dynamical Systems Applied to Biology and Natural Sciences – DSABNS”, held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. Note de contenu : 1 P. Freguglia et al., Modelling Ecological Systems from a Niche Theory to Lotka-Volterra equations -- 2 N. Petrovskaya and W. Zhang, Accurate Recognition of Spatial Patterns Arising in Spatio-Temporal Dynamics of Invasive Species -- 3 A. Andò and D. Breda, Collocation techniques for structured populations modeled by delay equations -- 4 H. Laurie et al., Herding induced by encounter rate, with predator pressure influencing prey response -- 5 N. M. Brites and C. A. Braumann, Harvesting policies with stepwise effort and logistic growth in a random environment -- 6 C. Corbacho et al., Mathematical modeling of the population dynamics of long-lived raptor species. Application to Eurasian black vulture colonies -- 7 C. Bianchi et al., On the role of inhibition processes in modeling control strategies for composting plants -- 8 A. Martiradonna et al., Optimal control of invasive species with budget constraint: qualitative analysis and numerical approximation -- 9 S. Aniţa et al., A Shape Optimization Problem Concerning the Regional Control of a Class of Spatially Structured Epidemics - Sufficiency Conditions -- 10 A. d’Onofrio and P. Manfredi, The interplay between voluntary vaccination and reduction of risky behavior: a general behavior-implicit SIR model for vaccine preventable infections -- 11 F. Florian and R. Vermiglio, PC-based sensitivity analysis of the basic reproduction number of population and epidemic models -- 12 M. J. Wieteska, Linear dynamics of mRNA expression and hormone concentration levels in primary cultures of bovine granulosa cells. Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=149895 Stable Isotopes to Trace Migratory Birds and to Identify Harmful Diseases / Gerrit J. Viljoen / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2016)
Titre : Stable Isotopes to Trace Migratory Birds and to Identify Harmful Diseases : An Introductory Guide Type de document : document électronique Auteurs : Gerrit J. Viljoen, ; A. G. Luckins, ; SpringerLink (Online service) ; Ivancho Naletoski, Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2016 Importance : XII, 49 p. 15 illus., 4 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-319-28298-5 Langues : Anglais (eng) Tags : Animal ecology Community ecology Biotic Environmental monitoring Animal Ecology Community & Population Ecology Monitoring Environmental Analysis Résumé : This manuscript discusses the potentials of the approaches as mentioned below to monitor the AIVs in WMW. Molecular diagnostic platforms enable for accurate detection of the AIVs in the feces of infected birds. Similar technologies can be used to determine the bird species through DNA barcoding, enabling non-invasive research on the epidemiology of the disease. Wild migratory waterfowl (WMW) play significant role in the transmission of avian influenza viruses (AIVs) on large distances. Understanding bird migrations may therefore significantly contribute towards understanding of the disease epidemiology, however most conventional approaches to trace WMW migrations are based on capturing, tagging (mostly ringing or GPS devices) and their re-capturing to link the departure and arrival places. Stable isotope ratios in metabolically inert tissues (feathers, beaks, claws) reflect the ratios present at the point of intake (drinking or feeding), thus enabling for tracing bird origins at stopover places. Molecular diagnostic platforms such as the polymerase chain reaction (PCR) enable for accurate detection of the AIVs in the feces of infected birds. Similar technologies (genetic sequencing) can be used to determine the bird species through DNA barcoding. Simple and easy collection of feather and fecal samples at the stopover places may generate a full information package on which species of WMW carries the AIVs (PCR+DNA barcoding on the feces), as well as the origin of these species (SI+DNA barcoding on the feathers). Therefore, such approaches enable for research on the epidemiology and the ecology of the AIVs in WMW using a non-invasive platform, which does not require capturing of WMW. This manuscript discusses the potentials of these approaches to monitor the AIVs in WMW Note de contenu : FOREWORD -- 2. GENERAL INTRODUCTION -- 2.1. Background analysis -- 2.2. Migratory Birds and HPAI -- 2.3. Using SIA to understand the dissemination of HPAI – The way ahead! -- 3. ANIMAL MIGRATION TRACKING METHODS -- 3.1. Extrinsic Markers -- 3.2. Intrinsic Markers -- 3.3. The Stable Isotopes of Water on a Spatial Scale -- 3.4. Deriving isoscapes in the absence of GNIP data -- 3.5. Use of Stable Isotopes in Migration Studies -- 3.6. Approaches for Determining Migratory Connectivity -- 4. PRACTICAL CONSIDERATIONS -- 4.1. Sample Collection and Tissue Preparation -- 4.2. Other Stable Isotopes for Migration Research -- 5. REFERENCES Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=156339 Stable Isotopes to Trace Migratory Birds and to Identify Harmful Diseases : An Introductory Guide [document électronique] / Gerrit J. Viljoen, ; A. G. Luckins, ; SpringerLink (Online service) ; Ivancho Naletoski, . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2016 . - XII, 49 p. 15 illus., 4 illus. in color : online resource.
ISBN : 978-3-319-28298-5
Langues : Anglais (eng)
Tags : Animal ecology Community ecology Biotic Environmental monitoring Animal Ecology Community & Population Ecology Monitoring Environmental Analysis Résumé : This manuscript discusses the potentials of the approaches as mentioned below to monitor the AIVs in WMW. Molecular diagnostic platforms enable for accurate detection of the AIVs in the feces of infected birds. Similar technologies can be used to determine the bird species through DNA barcoding, enabling non-invasive research on the epidemiology of the disease. Wild migratory waterfowl (WMW) play significant role in the transmission of avian influenza viruses (AIVs) on large distances. Understanding bird migrations may therefore significantly contribute towards understanding of the disease epidemiology, however most conventional approaches to trace WMW migrations are based on capturing, tagging (mostly ringing or GPS devices) and their re-capturing to link the departure and arrival places. Stable isotope ratios in metabolically inert tissues (feathers, beaks, claws) reflect the ratios present at the point of intake (drinking or feeding), thus enabling for tracing bird origins at stopover places. Molecular diagnostic platforms such as the polymerase chain reaction (PCR) enable for accurate detection of the AIVs in the feces of infected birds. Similar technologies (genetic sequencing) can be used to determine the bird species through DNA barcoding. Simple and easy collection of feather and fecal samples at the stopover places may generate a full information package on which species of WMW carries the AIVs (PCR+DNA barcoding on the feces), as well as the origin of these species (SI+DNA barcoding on the feathers). Therefore, such approaches enable for research on the epidemiology and the ecology of the AIVs in WMW using a non-invasive platform, which does not require capturing of WMW. This manuscript discusses the potentials of these approaches to monitor the AIVs in WMW Note de contenu : FOREWORD -- 2. GENERAL INTRODUCTION -- 2.1. Background analysis -- 2.2. Migratory Birds and HPAI -- 2.3. Using SIA to understand the dissemination of HPAI – The way ahead! -- 3. ANIMAL MIGRATION TRACKING METHODS -- 3.1. Extrinsic Markers -- 3.2. Intrinsic Markers -- 3.3. The Stable Isotopes of Water on a Spatial Scale -- 3.4. Deriving isoscapes in the absence of GNIP data -- 3.5. Use of Stable Isotopes in Migration Studies -- 3.6. Approaches for Determining Migratory Connectivity -- 4. PRACTICAL CONSIDERATIONS -- 4.1. Sample Collection and Tissue Preparation -- 4.2. Other Stable Isotopes for Migration Research -- 5. REFERENCES Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=156339 Applied Partial Differential Equations / John David Logan / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2004)
Titre : Applied Partial Differential Equations Type de document : document électronique Auteurs : John David Logan (1944-....) ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2004 Collection : Undergraduate Texts in Mathematics, ISSN 0172-6056 Importance : XII, 212 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4419-8879-9 Langues : Anglais (eng) Tags : Mathematics Community ecology Biotic Partial differential equations Physics Partial Differential Equations Mathematical Methods in Physics Community & Population Ecology Résumé : This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers 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. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced. J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001) Note de contenu : 1: The Physical Origins of Partial Differential Equations -- 1.1 Mathematical Models -- 1.2 Conservation Laws -- 1.3 Diffusion -- 1.4 PDEs in Biology -- 1.5 Vibrations and Acoustics -- 1.6 Quantum Mechanics* -- 1.7 Heat Flow in Three Dimensions -- 1.8 Laplace?s Equation -- 1.9 Classification of PDEs -- 2: Partial Differential Equations on Unbounded Domains -- 2.2 Cauchy Problem for the Wave Equation -- 2.3 Ill-Posed Problems -- 2.4 Semi-Infinite Domains -- 2.5 Sources and Duhamel?s Principle -- 2.6 Laplace Transforms -- 2.7 Fourier Transforms -- 2.8 Solving PDEs Using Computer Algebra Systems* -- 3: Orthogonal Expansions -- 3.1 The Fourier Method -- 3.2 Orthogonal Expansions -- 3.3 Classical Fourier Series -- 3.4 Sturm-Liouville Problems -- 4: Partial Differential Equations on Bounded Domains -- 4.1 Separation of Variables -- 4.2 Flux and Radiation Conditions -- 4.3 Laplace?s Equation -- 4.4 Cooling of a Sphere -- 4.5 Diffusion in a Disk -- 4.6 Sources on Bounded Domains -- 4.7 Parameter Identification Problems* -- 4.8 Finite Difference Methods* -- 5: Partial Differential Equations in the Life Sciences -- 5.1 Age-Structured Models -- 5.2 Traveling Wave Fronts -- 5.3 Equilibria and Stability -- Appendix: Ordinary Differential Equations -- Table of Laplace Transforms -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=117537 Applied Partial Differential Equations [document électronique] / John David Logan (1944-....) ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2004 . - XII, 212 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4419-8879-9
Langues : Anglais (eng)
Tags : Mathematics Community ecology Biotic Partial differential equations Physics Partial Differential Equations Mathematical Methods in Physics Community & Population Ecology Résumé : This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers 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. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced. J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001) Note de contenu : 1: The Physical Origins of Partial Differential Equations -- 1.1 Mathematical Models -- 1.2 Conservation Laws -- 1.3 Diffusion -- 1.4 PDEs in Biology -- 1.5 Vibrations and Acoustics -- 1.6 Quantum Mechanics* -- 1.7 Heat Flow in Three Dimensions -- 1.8 Laplace?s Equation -- 1.9 Classification of PDEs -- 2: Partial Differential Equations on Unbounded Domains -- 2.2 Cauchy Problem for the Wave Equation -- 2.3 Ill-Posed Problems -- 2.4 Semi-Infinite Domains -- 2.5 Sources and Duhamel?s Principle -- 2.6 Laplace Transforms -- 2.7 Fourier Transforms -- 2.8 Solving PDEs Using Computer Algebra Systems* -- 3: Orthogonal Expansions -- 3.1 The Fourier Method -- 3.2 Orthogonal Expansions -- 3.3 Classical Fourier Series -- 3.4 Sturm-Liouville Problems -- 4: Partial Differential Equations on Bounded Domains -- 4.1 Separation of Variables -- 4.2 Flux and Radiation Conditions -- 4.3 Laplace?s Equation -- 4.4 Cooling of a Sphere -- 4.5 Diffusion in a Disk -- 4.6 Sources on Bounded Domains -- 4.7 Parameter Identification Problems* -- 4.8 Finite Difference Methods* -- 5: Partial Differential Equations in the Life Sciences -- 5.1 Age-Structured Models -- 5.2 Traveling Wave Fronts -- 5.3 Equilibria and Stability -- Appendix: Ordinary Differential Equations -- Table of Laplace Transforms -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=117537 Complexity, Analysis and Control of Singular Biological Systems / Qingling Zhang / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2012)
PermalinkMathematical Biology / James D. Murray ; SpringerLink (Online service) / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2002)
PermalinkMathematical Biology / James D. Murray ; SpringerLink (Online service) / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2003)
PermalinkMeta-Ecosystem Dynamics / Frederic Guichard / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2021)
PermalinkSocioeconomic and Environmental Implications of Agricultural Residue Burning / Parmod Kumar / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2015)
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