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Reaction Kinetics: Exercises, Programs and Theorems

Mathematica for Deterministic and Stochastic Kinetics

  • Textbook
  • © 2018

Overview

Authors:
  1. János Tóth

    1. Chemical Kinetics Laboratory, Eötvös Loránd University, Budapest, Hungary

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  2. Attila László Nagy

    1. Department of Stochastics, Budapest University of Technology and Economics, Budapest, Hungary

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  3. Dávid Papp

    1. Department of Mathematics, North Carolina State University, Raleigh, USA

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  • Offers a step-by-step introduction to the modern mathematical theory of deterministic and stochastic reaction kinetics for newcomers both from chemistry and mathematics
  • Includes detailed descriptions and a Mathematica package to help readers with their symbolic and numerical work in all areas of reaction kinetics. The package can be downloaded from http://extras.springer.com.
  • Features a rich collection of recent references, the solutions to all the exercises, and a large set of unsolved problems for researchers

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Introduction

    • János Tóth, Attila László Nagy, Dávid Papp
    Pages 1-2

  3. Part I

    1. Front Matter

      Pages 3-3
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    2. Preparations

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 5-17

    3. Graphs of Reactions

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 19-37

    4. Mass Conservation

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 39-53

    5. Decomposition of Reactions

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 55-73

  4. Part II

    1. Front Matter

      Pages 75-75
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    2. The Induced Kinetic Differential Equation

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 77-114

    3. Stationary Points

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 115-147

    4. Time-Dependent Behavior of the Concentrations

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 149-216

    5. Approximations of the Models

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 217-256

  5. Part III

    1. Front Matter

      Pages 257-257
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    2. Stochastic Models

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 259-321

  6. Part IV

    1. Front Matter

      Pages 323-323
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    2. Inverse Problems

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 325-344

    3. Past, Present, and Future Programs for Reaction Kinetics

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 345-357

    4. Mathematical Background

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 359-379

    5. Solutions

      • János Tóth, Attila László Nagy, Dávid Papp
      Pages 381-456

  7. Back Matter

    Pages 457-469
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Keywords

About this book

Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation.  The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth ofsolved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

Authors and Affiliations

  • Chemical Kinetics Laboratory, Eötvös Loránd University, Budapest, Hungary

    János Tóth

  • Department of Stochastics, Budapest University of Technology and Economics, Budapest, Hungary

    Attila László Nagy

  • Department of Mathematics, North Carolina State University, Raleigh, USA

    Dávid Papp

About the authors

János Tóth graduated from mathematics at Eötvös Loránd University and started to work for the Institute of Medical Chemistry. His main interest is in applied mathematics (differential equations and stochastic processes) in chemistry, chemical engineering, biochemistry, pharmacology and combustion. He is best known for his work on the inverse problem, on the stochastic model of the Michaelis-Menten reaction, and on lumping. Presently an honorary professor of the Budapest University of Technology and Economics, he was a visiting researcher at Princeton University, Pierre et Marie Curie Université, INRA, INERIS. He has published over 100 papers and four books. He has designed and taught subjects in mathematical chemistry. In 2017 he received the MaCKiE Lifetime Achievement Award.

Attila László Nagy graduated with highest honors from Budapest University of Technology and Economics as applied mathematician. He received his MSc under the guidance of János Tóth in 2011 by defending his thesis on stochastic parameter estimation methods. Since then he has been working both in the field of interacting particle systems and mathematical chemistry, and is now a PhD candidate. So far five publications of his have appeared in various journals including the Annals of Probability and the Journal of Mathematical Chemistry. Over the years he has taught several mathematics-related subjects mainly for engineering students at the undergraduate level. Recently, he has been working in the industry, currently as a business analyst. 


Dávid Papp received his PhD from Rutgers University in 2011. Following postdoctoral researcher positions at Northwestern University and Massachusetts General Hospital, he is now an Assistant Professor of Mathematics at North Carolina State University. His research interests are in mathematical optimization and its applications in medicine, engineering, and statistics. He has written 30 publications. Over the years he has designed and taught various applied mathematics courses both at the undergraduate and PhD level.

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