Book description
Features mathematical modeling techniques and realworld processes with applications in diverse fields
Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets.
Written by leading scholars and international experts in the field, the book presents new and emerging topics in areas including finance and economics, theoretical and applied mathematics, engineering and machine learning, physics, chemistry, ecology, and social science. In addition, the book thoroughly summarizes widely used mathematical and numerical methods in mathematical modeling and features:
Diverse topics such as partial differential equations (PDEs), fractional calculus, inverse problems by ordinary differential equations (ODEs), semigroups, decision theory, risk analysis, Bayesian estimation, nonlinear PDEs in financial engineering, perturbation analysis, and dynamic system modeling
Case studies and realworld applications that are widely used for current mathematical modeling courses, such as the green house effect and Stokes flow estimation
Comprehensive coverage of a wide range of contemporary topics, such as game theory, statistical models, and analytical solutions to numerical methods
Examples, exercises with select solutions, and detailed references to the latest literature to solidify comprehensive learning
New techniques and applications with balanced coverage of PDEs, discrete models, statistics, fractional calculus, and more
Mathematical Modeling with Multidisciplinary Applications is an excellent book for courses on mathematical modeling and applied mathematics at the upperundergraduate and graduate levels. The book also serves as a valuable reference for research scientists, mathematicians, and engineers who would like to develop further insights into essential mathematical tools.
Table of contents
 Cover
 Half Title page
 Title page
 Copyright page
 List of Figures
 Preface
 Acknowledgments
 Editor and Contributors
 Part I: Introduction and Foundations

Part II: Mathematical Modeling with Multidisciplinary Applications
 Chapter 5: Industrial Mathematics with Applications
 Chapter 6: Binary and Ordinal Data Analysis in Economics: Modeling and Estimation
 Chapter 7: Inverse Problems in ODEs
 Chapter 8: Estimation of Model Parameters

Chapter 9: Linear and Nonlinear Parabolic Partial Differential Equations in Financial Engineering
 9.1 Financial Derivatives
 9.2 Motivation for a Model for the Price of Stocks
 9.3 Stock Prices Involving the Wiener Process
 9.4 Connection Between the Wiener Process and PDEs
 9.5 The BlackScholesMerton Equation
 9.6 Solution of the BlackScholesMerton Equation
 9.7 Free BoundaryValue Problems
 9.8 The HamiltonJacobiBellman Equation
 9.9 Numerical Methods
 9.10 Conclusion
 Exercises
 References
 Chapter 10: Decision Modeling in Supply Chain Management
 Chapter 11: Modeling Temperature for Pricing Weather Derivatives
 Chapter 12: Decision Theory under Risk and Applications in Social Sciences: I. Individual Decision Making
 Chapter 13: Fractals, with Applications to Signal and Image Modeling 307
 Chapter 14: Efficient Numerical Methods for Singularly Perturbed Differential Equations

Part III: Advanced Modeling Topics
 Chapter 15: Fractional Calculus and its Applications
 Chapter 16: The Goal Programming Model: Theory and Applications
 Chapter 17: Decision Theory under Risk and Applications in Social Sciences: II. Game Theory
 Chapter 18: Control Problems on Differential Equations
 Chapter 19: MarkovJump Stochastic Models for Tropical Convection
 Problem Solutions
 Index
Product information
 Title: Mathematical Modeling with Multidisciplinary Applications
 Author(s):
 Release date: January 2013
 Publisher(s): Wiley
 ISBN: 9781118294413
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