Ebook: Mathematical Modeling with Multidisciplinary Applications

Features mathematical modeling techniques and real-world 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 real-world 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 upper-undergraduate 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.

Content:
Chapter 1 Differential Equations (pages 1–22): Xin‐She Yang
Chapter 2 Mathematical Modeling (pages 23–44): Xin‐She Yang
Chapter 3 Numerical Methods: An Introduction (pages 45–56): Xin‐She Yang
Chapter 4 Teaching Mathematical Modeling in Teacher Education: Efforts and Results (pages 57–80): Thomas Lingefjärd
Chapter 5 Industrial Mathematics with Applications (pages 81–122): Alfredo Bermúdez and Luz M. García García
Chapter 6 Binary and Ordinal Data Analysis in Economics: Modeling and Estimation (pages 123–150): Ivan Jeliazkov and Mohammad Arshad Rahman
Chapter 7 Inverse Problems in ODEs (pages 151–167): H. Kunze and D. La Torre
Chapter 8 Estimation of Model Parameters (pages 169–190): Robert Piché
Chapter 9 Linear and Nonlinear Parabolic Partial Differential Equations in Financial Engineering (pages 191–228): L. A. Boukas, K. I. Vasileiadis, S. Z. Xanthopoulos and A. N. Yannacopoulos
Chapter 10 Decision Modeling in Supply Chain Management (pages 229–255): Huajun Tang
Chapter 11 Modeling Temperature for Pricing Weather Derivatives (pages 257–284): Fred Espen Benth
Chapter 12 Decision Theory under Risk and Applications in Social Sciences: I. Individual Decision Making (pages 285–306): E. V. Petracou and A. N. Yannacopoulos
Chapter 13 Fractals, with Applications to Signal and Image Modeling (pages 307–328): H. Kunze and D. La Torre
Chapter 14 Efficient Numerical Methods for Singularly Perturbed Differential Equations (pages 329–354): S. Natesan
Chapter 15 Fractional Calculus and its Applications (pages 355–396): Ivo PetráŠ
Chapter 16 The Goal Programming Model: Theory and Applications (pages 397–419): Belaid Aouni, Cinzia Colapinto and Davide La Torre
Chapter 17 Decision Theory under Risk and Applications in Social Sciences: II. Game Theory (pages 421–447): E. V. Petracou and A. N. Yannacopoulos
Chapter 18 Control Problems on Differential Equations (pages 449–470): Chuang Zheng
Chapter 19 Markov‐Jump Stochastic Models for Tropical Convection (pages 471–523): Boualem Khouider