Mathematical Biology An introduction 3rd Edition by James D Murray ISBN 0387952233 9780387952239 by Murray J.d. 9780387952239, 0387952233 instant download after payment.

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ISBN 10: 0387952233 
ISBN 13: 9780387952239
Author: James D Murray

It has been over a decade since the release of the now classic original edition of Murray's Mathematical Biology. Since then mathematical biology has grown at an astonishing rate and is well established as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biomedical sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems that arise in biology and gives some indication of the wide spectrum of questions that modeling can address. Due to the tremendous development in the field this book is being published in two volumes. This first volume is an introduction to the field, the mathematics mainly involves ordinary differential equations that are suitable for undergraduate and graduate courses at different levels. For this new edition Murray is covering certain items in depth, giving new applications such as modeling marital interactions andtemperature dependence sex determination

Mathematical Biology An introduction 3rd Table of contents:

Part I: Foundations and Fundamental Models

Chapter 1: What is Mathematical Biology?

• The Interdisciplinary Nature of Mathematical Biology
• Why Use Mathematics in Biology? (Quantification, Prediction, Understanding)
• A Brief History of Mathematical Biology
• Key Areas of Application

Chapter 2: Continuous Models: Differential Equations

• Basic Concepts of Differential Equations:
  • Ordinary Differential Equations (ODEs)
  • Partial Differential Equations (PDEs)
  • Initial Value Problems and Boundary Value Problems
• Population Dynamics:
  • Exponential Growth and Decay
  • Logistic Growth Model
  • Predator-Prey Models (Lotka-Volterra)
  • Competition Models
• Pharmacokinetics and Drug Delivery
• Enzyme Kinetics (Michaelis-Menten)

Chapter 3: Discrete Models: Difference Equations

• Introduction to Difference Equations:
  • Iteration and Recursion
  • Stability and Equilibria
• Discrete Population Models:
  • Logistic Map and Chaos
  • Age-Structured Populations
• Genetic Models (Hardy-Weinberg Principle)

Chapter 4: Linear Algebra in Biology

• Vectors and Matrices: Basic Operations
• Systems of Linear Equations: Solving Biological Problems
• Eigenvalues and Eigenvectors: Applications in Population Growth and Stability Analysis

Chapter 5: Probability and Statistics in Biology

• Basic Probability Concepts:
  • Conditional Probability, Bayes' Theorem
• Random Variables and Distributions:
  • Binomial, Poisson, Normal Distributions
• Statistical Inference:
  • Hypothesis Testing, Confidence Intervals
• Stochastic Processes: Introduction to Random Walks and Markov Chains

Part II: Advanced Topics and Applications

Chapter 6: Spatial Models and Pattern Formation

• Reaction-Diffusion Systems:
  • Turing Patterns and Morphogenesis
  • Spread of Diseases
• Cell Motility and Chemotaxis
• Ecological Spatial Patterns:
  • Animal Territories, Vegetation Patterns

Chapter 7: Modeling Disease Dynamics (Epidemiology)

• Compartmental Models:
  • SIR (Susceptible-Infectious-Recovered) Model
  • SIS, SIRS, SEIR Models
• Basic Reproduction Number (R0)
• Vaccination Strategies
• Modeling Disease Outbreaks (e.g., COVID-19, Flu)

Chapter 8: Evolutionary Biology and Genetics

• Population Genetics Models:
  • Allele Frequencies, Selection, Mutation, Drift
• Game Theory in Biology:
  • Evolutionary Stable Strategies (ESS)
  • Cooperation and Conflict
• Phylogenetic Tree Reconstruction

Chapter 9: Cellular and Molecular Biology

• Gene Regulatory Networks:
  • Boolean Networks, ODE Models
• Signal Transduction Pathways
• Enzyme Cascades
• Mathematical Models of the Cell Cycle

Chapter 10: Neuroscience

• Neuron Models:
  • Hodgkin-Huxley Model
  • Integrate-and-Fire Models
• Neural Networks and Oscillations
• Modeling Brain Activity

Chapter 11: Ecology and Ecosystems

• Food Webs and Trophic Dynamics
• Biogeochemical Cycles (e.g., Carbon, Nitrogen)
• Ecological Resilience and Stability
• Conservation Biology Applications

Part III: Computational Methods and Future Directions

Chapter 12: Computational Tools for Mathematical Biology

• Numerical Methods for ODEs and PDEs:
  • Euler's Method, Runge-Kutta
• Simulation Techniques:
  • Agent-Based Modeling
  • Monte Carlo Methods
• Software Tools:
  • MATLAB, Python (SciPy, NumPy), R, Mathematica

Chapter 13: Data-Driven Mathematical Biology

• Parameter Estimation and Model Fitting
• Machine Learning in Biological Data Analysis
• Big Data and Systems Biology

Chapter 14: Challenges and Future Directions

• Bridging Scales: From Molecules to Ecosystems
• Uncertainty Quantification and Sensitivity Analysis
• Personalized Medicine and Predictive Biology
• Ethical Considerations in Mathematical Biology

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