Methods of Mathematical Modelling: Continuous Systems and Differential Equations

✍ Scribed by Thomas Witelski, Mark Bowen

• Publisher: Springer
• Year: 2015
• Tongue: English
• Leaves: 309
• Series: Springer Undergraduate Mathematics Series
• Edition: 1st
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Rate Equations....Pages 3-21
Transport Equations....Pages 23-45
Variational Principles....Pages 47-83
Dimensional Scaling Analysis....Pages 85-110
Front Matter....Pages 111-111
Self-Similar Scaling Solutions of Differential Equations....Pages 113-125
Perturbation Methods....Pages 127-145
Boundary Layer Theory....Pages 147-165
Long-Wave Asymptotics for PDE Problems....Pages 167-183
Weakly-Nonlinear Oscillators....Pages 185-200
Fast/slow Dynamical Systems....Pages 201-213
Reduced Models for PDE Problems....Pages 215-232
Front Matter....Pages 233-233
Modelling in Applied Fluid Dynamics....Pages 235-249
Back Matter....Pages 251-305

✦ Subjects

Ordinary Differential Equations; Partial Differential Equations; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Calculus of Variations and Optimal Control; Optimization