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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Differential Equations and Mathematical Biology: (Chapman & Hall/CRC Mathematical Biology Series)
Differential Equations and Mathematical Biology: (Chapman & Hall/CRC Mathematical Biology Series)

Differential Equations and Mathematical Biology: (Chapman & Hall/CRC Mathematical Biology Series)


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About the Book

The conjoining of mathematics and biology has brought about significant advances in both areas, with mathematics providing a tool for modelling and understanding biological phenomena and biology stimulating developments in the theory of nonlinear differential equations. The continued application of mathematics to biology holds great promise and in

Table of Contents:
INTRODUCTION Population Growth Administration of Drugs Cell Division Differential Equations with Separable Variables General Properties Equations of Homogeneous Type Linear Differential Equations of the First Order LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS Introduction First-Order Linear Differential Equations Linear Equations of the Second Order Finding the Complementary Function Determining a Particular Integral Forced Oscillations Differential Equations of the Order n Uniqueness Appendix: Existence Theory SIMULTANEOUS EQUATIONS WITH CONSTANT COEFFICIENTS Simultaneous Equations of the First Order Replacement of One Differential Equation by a System The General System The Fundamental System Matrix Notation Initial and Boundary Value Problems Solving the Inhomogeneous Differential Equation Appendix: Symbolic Computation MODELLING BIOLOGICAL PHENOMENA Introduction Heart Beat Blood Flow Nerve Impulse Transmission Chemical Reactions Predator-Prey Models FIRST-ORDER SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS Existence and Uniqueness Epidemics The Phase Plane Local Stability Stability Limit Cycles Forced Oscillations Appendix: Existence Theory Appendix: Computing Trajectories MATHEMATICS OF HEART PHYSIOLOGY The Local Model The Threshold Effect Phase Plane Analysis and the Heart Beat Model Physiological Considerations of the Heart Beat Cycle A Model of the Cardiac Pacemaker MATHEMATICS OF NERVE IMPULSE TRANSMISSION Excitability and Repetitive Firing Travelling Waves Qualitative Behaviour of Travelling Waves CHEMICAL REACTIONS Wavefronts for the Belousov-Zhabotinskii Reaction Phase Plane Analysis of Fisher's Equation Qualitative Behaviour in the General Case PREDATOR AND PREY Catching Fish The Effect of Fishing The Volterra-Lotka Model PARTIAL DIFFERENTIAL EQUATIONS Characteristics for Equations of the First Order Another View of Characteristics Linear Partial Differential Equations of the Second Order Elliptic Partial Differential Equations Parabolic Partial Differential Equations Hyperbolic Partial Differential Equations The Wave Equation Typical Problems for the Hyperbolic Equation The Euler-Darboux Equation EVOLUTIONARY EQUATIONS The Heat Equation Separation of Variables Simple Evolutionary Equations Comparison Theorems PROBLEMS OF DIFFUSION Diffusion through Membranes Energy and Energy Estimates Global Behaviour of Nerve Impulse Transmissions Global Behaviour in Chemical Reactions Turing Diffusion Driven Instability and Pattern Formation Finite Pattern Forming Domains BIFURCATION AND CHAOS Bifurcation Bifurcation of a Limit Cycle Discrete Bifurcation Chaos Stability The Poincare Plane Averaging Appendix: Programs GROWTH OF TUMOURS Introduction A Mathematical Model of Tumour Growth A Spherical Tumour Stability EPIDEMICS The Kermack-McKendrick Model Vaccination An Incubation Model Spreading in Space ANSWERS TO EXERCISES INDEX Each chapter also contains Exercises.

Review :
"A strength of [this book] is its concise coverage of a broad range of topics. … It is truly remarkable how much material is squeezed into the slim book's 400 pages." - SIAM Review, Vol. 46, No. 1 "It is remarkable that without the classical scheme (definition, theorem and proof) it is possible to explain rather deep results like properties of the Fitz-Hugh-Nagumo model … or the Turing model … . This feature makes the reading of this text pleasant business for mathematicians. … [This book] can be recommended for students of mathematics who like to see applications, because it introduces them to problems on how to model processes in biology, and also for theoretical oriented students of biology, because it presents constructions of mathematical models and the steps needed for their investigations in a clear way and without references to other books." - EMS Newsletter "The title precisely reflects the contents of the book, a valuable addition to the growing literature in mathematical biology from a deterministic modeling approach. This book is a suitable textbook for multiple purposes … Overall, topics are carefully chosen and well balanced. …The book is written by experts in the research fields of dynamical systems and population biology. As such, it presents a clear picture of how applied dynamical systems and theoretical biology interact and stimulate each other--a fascinating positive feedback whose strength is anticipated to be enhanced by outstanding text like the work under review." -Mathematical Reviews, Issue 2004g


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Product Details
  • ISBN-13: 9781135442026
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: Chapman and Hall
  • Language: English
  • No of Pages: 408
  • ISBN-10: 1135442029
  • Publisher Date: 26 Feb 2003
  • Binding: Digital (delivered electronically)
  • No of Pages: 408
  • Series Title: Chapman & Hall/CRC Mathematical Biology Series


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