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Methods of Mathematical Modelling : Continuous Systems and Differential Equations / by Thomas Witelski, Mark Bowen.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Witelski, Thomas., Author.
- Bowen, Mark, Author.
- Series:
- Springer Undergraduate Mathematics Series, 2197-4144
- Language:
- English
- Subjects (All):
- Differential equations.
- Mathematical physics.
- Mathematical models.
- Mathematical optimization.
- Calculus of variations.
- Differential Equations.
- Mathematical Physics.
- Mathematical Modeling and Industrial Mathematics.
- Calculus of Variations and Optimization.
- Local Subjects:
- Differential Equations.
- Mathematical Physics.
- Mathematical Modeling and Industrial Mathematics.
- Calculus of Variations and Optimization.
- Physical Description:
- 1 online resource (XVIII, 305 p. 50 illus., 45 illus. in color.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- Summary:
- This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
- Contents:
- Rate equations
- Transport equations
- Variational principles
- Dimensional scaling analysis
- Self-similar scaling solutions of differential equations
- Perturbation methods
- Boundary layer theory
- Long-wave asymptotics for PDE problems
- Weakly-nonlinear oscillators
- Fast/slow dynamical systems
- Reduced models for PDE problems
- Modelling in applied fluid dynamics.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references and index.
- Print version record.
- ISBN:
- 3-319-23042-5
- OCLC:
- 922033492
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