Free PDF Mathematical Modelling: A case studies approach (Student Mathematical Library), by C. Sean Bohun, Samantha McCollum, Thea van Roode, Reinh
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Mathematical Modelling: A case studies approach (Student Mathematical Library), by C. Sean Bohun, Samantha McCollum, Thea van Roode, Reinh
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Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem.
The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel.
Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; others are more modest.
The text was designed to be suitable for a one-term course for advanced undergraduates. The selection of topics and the style of exposition reflect this choice. The authors have also succeeded in demonstrating just how enjoyable the subject can be.
This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.
- Sales Rank: #1415243 in Books
- Brand: Brand: American Mathematical Society
- Published on: 2004-12-24
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x 5.75" w x .50" l, .58 pounds
- Binding: Paperback
- 196 pages
- Used Book in Good Condition
Review
The book is written in a nice manner, the exposition is very friendly and intriguing ... [a] delightful introductory text. --Zentralblatt MATH
IBMvR is a welcome addition to the collection of texts for modeling courses. It fits well [in] its intended audience, all of whom appreciate its small size and reasonable price. I would use it again as the text for my junior/senior-level course, and it should be on anyone's shortlist for such a course. --MAA Reviews
Most helpful customer reviews
4 of 4 people found the following review helpful.
Mathematical Models Serve Society
By Man Kam Tam
One of the purpose of the book "Mathematical Modeling: A Case Studies Approach" is to demonstrate the usefulness of mathematical modeling. A case in point would be the chapter two of the book. The title of the chapter is "Will the valve hold?" The chapter is about an engineer attempting to determine whether a valve would hold when a temporary rock plug was removed from a water tunnel. The story occurred on the year 1961. The engineer had only 24 hours to determine whether the valve would hold or not. In order to solve the problem, he built a mathematical model, which modeled the motion of the water. Having developed an equation to model the motion of water, the next challenge was to solve the equation. Unfortunately, the equation could not be solved, because it was ill-posed. Therefore, he had (1) to revise the model and (2) to change the initial conditions. Eventually, the engineer determined whether the value would hold.
Other interesting modeling includes determining (1) the energy released by a nuclear bomb (through the video of a nuclear explosion), (2) the time required to cook a turkey, (3) the fairness of salary (according to the philosophy of Aristotle), (4) the loan payment and annuity, (5) the maximal sustainable catch of fish, (6) the microscopic and the macroscopic models of traffic dynamic, and (7) the crystallization processes. Many classical mathematical models, concepts, and methods are presented on the book. For example, they are the Kolmogorov-Avrami model for crystallization, well-posedness, numerical solvability, stability, financial mathematics, dimensional analysis, Lotka-Volterra model, functional equations, differential-delay equations, scalar conservation law, shock and rarefaction waves.
1 of 1 people found the following review helpful.
Math Modeling
By Gary L. Roach
I got this book for a 400/500 level applied mathematics course. This had to be one of the toughest math course I have ever taken. It isn't the books fault, it's the subject. You had better have a good grounding in Linear Algebra, Differential Equations and Partial DE to use this book. Here again it isn't the books fault. It's the subject. The book covers a broad spectrum of math modeling techniques that include things like crystal growth, rain drop patterns and traffic models. It's a fascinating book but you will need every piece of math you ever knew. I do wonder whether this should have been restricted to a graduate level course.
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