Methods of mathematical modelling : continuous systems and differential equations
Mathematical models sähkökirjat
Springer
2015
EISBN 9783319230429
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.
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.
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.
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.
