Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models.
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‘Before courses in math modeling became de rigueur, Richard Haberman had already demonstrated that mathematical techniques could be unusually effective in understanding elementary mechanical vibrations, population dynamics, and traffic flow, as well as how such intriguing applications could motivate the further study of nonlinear ordinary and partial differential equations. My students and I can attest that this carefully crafted book is perfect for both self-study and classroom use.’ Robert E. O'Malley, Jr., University of Washington
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This review is from: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow (Classics in Applied Mathematics) (Paperback)
I used this as a text for an upper division math course in math modeling. I would suggest you have a good grounding in analytical geometry, differential equations and partial differential equations before tackling this subject. This was one of the hardest math courses I took in school. While the concepts will short circuit your brain, the book is reasonably well written.
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First Sentence:
Science attempts to establish an understanding of all types of phenomena. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
possible equilibrium populations, initial traffic density, fanlike characteristics, simple isoclines, density wave velocity, nonzero equilibrium population, phase plane equation, density wave moves, density wave velocities, neighboring characteristics, local wave velocity, nonlinear pendulum, linearized pendulum, discrete logistic equation, plane differential equation, earliest shock, maximum traffic flow, nth car, stable equilibrium population, linearized stability analysis, unstable equilibrium position, traffic variables, constant coefficient difference equations, logistic growth model, car velocity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fundamental Diagram of Road Traffic, Lincoln Tunnel, New York, United States, Merritt Parkway, John Wiley, Discrete One-Species Models, Further Reading, Operations Research, Pmax Pmax, World War New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Science attempts to establish an understanding of all types of phenomena. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
possible equilibrium populations, initial traffic density, fanlike characteristics, simple isoclines, density wave velocity, nonzero equilibrium population, phase plane equation, density wave moves, density wave velocities, neighboring characteristics, local wave velocity, nonlinear pendulum, linearized pendulum, discrete logistic equation, plane differential equation, earliest shock, maximum traffic flow, nth car, stable equilibrium population, linearized stability analysis, unstable equilibrium position, traffic variables, constant coefficient difference equations, logistic growth model, car velocity Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fundamental Diagram of Road Traffic, Lincoln Tunnel, New York, United States, Merritt Parkway, John Wiley, Discrete One-Species Models, Further Reading, Operations Research, Pmax Pmax, World War New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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