Mathematical Modeling

  • Stefan Heinz

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Stefan Heinz
    Pages 1-38
  3. Stefan Heinz
    Pages 39-74
  4. Stefan Heinz
    Pages 75-114
  5. Stefan Heinz
    Pages 115-164
  6. Stefan Heinz
    Pages 165-205
  7. Stefan Heinz
    Pages 207-246
  8. Stefan Heinz
    Pages 247-293
  9. Stefan Heinz
    Pages 295-334
  10. Stefan Heinz
    Pages 335-390
  11. Stefan Heinz
    Pages 391-440
  12. Back Matter
    Pages 441-460

About this book


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.

Authors and affiliations

  • Stefan Heinz
    • 1
  1. 1.Dept. MathematicsUniversity of WyomingLaramieUSA

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