This book presents an introduction to a wide range of techniques and applications for dynamical mathematical modelling, modelling that is useful in studying how things change over time. The book uses topics from algebra and encourages students to develop a different way of thinking about mathematics and how to use it in their field of interest. Their are no mathematical prerequisites beyond algebra.
Rezensionen / Stimmen
"A very nice book! It assumes minimal mathematical preparation and nevertheless arrives at very interesting and sophisticated results."--Maurice Kreevoy, University of Minnesota
"Suitable for general audiences....Excellent examples and problems from many areas." --American Mathematical Monthly
"The material presented in this textbook will help the reader apply discrete dynamics to many fields, such as business, economics, biology, genetics, engineering, and physics....[Sandefur] supplies interesting problems in all chapters; the answers to all even-numbered problems are given in the text. This book can serve as a valuable tool for researchers developing dynamic models." --Computing Reviews
"A closely related textbook by the same author [Discrete Matematical Systems] was reviewed here previously....Modeling is more self-contained than Systems, in that it includes sections on elementary counting and probability and a short chapter on vectors and matrices (which are used in the final chapter to study dynamical systems of several linear equations). It also has new sections on elementary fractal geometry and on using spreadsheets to
explore dynamical systems empirically. The latter section is especially well-written and could serve as an effective and entertaining tutorial on the use of spreadsheet software....Modeling could be a good choice for-to
take an example-an honors course in dynamics at the high-school level. The exposition in both texts is outstanding....I hope that they both remain available in the future." --The UMAP Journal-The Journal of Undergraduate Mathematics and Its Applications
Sprache
Verlagsort
Zielgruppe
Illustrationen
Maße
Höhe: 164 mm
Breite: 243 mm
Dicke: 37 mm
Gewicht
ISBN-13
978-0-19-508438-2 (9780195084382)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Professor of MathematicsProfessor of Mathematics, Georgetown University, Washington, DC 20057
Chapter 1: Introduction to dynamic modeling ; 1. Modeling drugs in the bloodstream ; 2. Terminology ; 3. Equilibrium values ; 4. Dynamic economic applications ; 5. Applications of dynamics using spreadsheets ; Chapter 2: First order dynamical systems ; 1. Solutions to linear dynamical systems with applications ; 2. Solutions to an affine dynamical system ; 3. An introduction to genetics ; 4. Solution to affine dynamical systems with applications ; 5. Applications to finance ; Chapter 3: Introduction to probability ; 1. The multiplication to probability ; 2. Introduction to probability ; 3. Multistage tasks ; 4. An introduction to Markov chains ; Chapter 4: Nonhomogeneous dynamical systems ; 1. Exponential terms ; 2. Exponential terms, a special case ; 3. Fractal geometry ; 4. Polynomial terms ; 5. Polynomial terms, a special case ; Chapter 5: Higher order linear dynamical systems 183 ; 1. An introduction to second order linear equations ; 2. Multiple roots ; 3. The gambler's ruin ; 4. Sex-linked genes ; 5. Stability for second order affine equations ; 6. Modeling a vibrating string ; 7. Second order nonhomogeneous equations ; 8. Gambler's ruin revisited ; 9. A model of a national economy ; 10. Dynamical systems with order greater than two ; 11. Solutions involving trigonometric functions ; Chapter 6: Introduction to nonlinear dynamical systems ; 1. A model of population growth ; 2. Using linearization to study stability ; 3. Harvesting strategies ; 4. More linearization ; Chapter 7: Vectors and matrices ; 1. Introduction to vectors and matrices ; 2. Rules of linear algebra ; 3. Gauss-Jordan elimination ; 4. Determinants ; 5. Inverse matrices ; Chapter 8: Dynamical systems of several equations ; 1. Introduction to dynamical systems of several equations ; 2. Characteristic values ; 3. First order dynamical systems of several equations ; 4. Regular Markov chains ; 5. Absorbing Markov chains ; 6. Applications of absorbing Markov chains ; 7. Long term behavior of solutions ; 8. The heat equation ; 9. Bibliography
