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Mathematical Modeling

By Heinz, Stefan
Mathematical Modeling

Details

Authors: Heinz, Stefan
Format: Paperback
GTIN13: 9783642443886
ISBN10: 3642443885
Page Count: 460
Dimensions: 6.14x0.97x9.21
Publisher: Springer
Jacket Notes:

The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions.

Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed.

Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods.

Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed - which is an important problem of current research.

Description

Mathematical modelling had become such an integral tool modern science and technology that practically all students take a course or otherwise need to master it. This textbook for undergraduate and graduate students of engineering, biology, chemistry, physics and even economics derives from the author's decade of teaching university courses It features systematic development of deterministic and stochastic modeling approaches; systematic discussions of single problems: the analysis of observations, characteristic properties and changes of one variable, and the laws that govern the evolution of one and several variables; and hierarchical development of models such as discussion of statistically most-likely probability density functions, the relations between difference and differential equations, the Brownian motion model and diffusion models, the delay logistic model, non-Markovian and Markovian velocity models, etc. Comprehensive in scope, it includes the derivations with all required details (exercises are used to provide additional details), complete discussions of problems, and practice in application of the developed concepts via 570 exercise questions organized in 220 problems. Detailed solutions given in the Instructor's Solutions Manual, which is available to instructors via springer.com. Prerequisites include 2-3 semesters of college-level calculus and familiarity with computer-algebra software (e.g. Matlab, Maple, or Mathematica). The author explains how the ten chapters can be combined to provide material for an undergraduate course Introduction to Mathematical Modeling or graduate-level courses Deterministic Mathematical Modeling and Stochastic Mathematical Modeling.

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