PARTIAL DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELING: A Practical Guide to Formulating, Solving, and Interpreting PDEs and Boundary Value Problems for Scientists and Engineers - Couverture souple

Wright, Juan

Couverture souple

ISBN 13 : 9798161393475

Editeur : Independently published, 2026

Synopsis

Become an expert at Partial differential Equation & Mathematical modeling

A solution to a partial differential equation is only useful if you can say what it means for the system it describes. This book is built around that principle, and it is organised so that every method you learn is immediately put to work on a physical question.

Readers who come to this subject already know the frustration it can produce. Techniques are learned in isolation, boundary conditions are copied from examples rather than reasoned from the physics, and a result is accepted because the algebra closed rather than because it makes sense. When the problem changes even slightly, none of it transfers.

This guide is written to make the knowledge transfer. Formulation comes first, methods follow in the order in which they become necessary, and interpretation is treated as a stage of the work rather than an afterthought.

By working through this book you will be able to:

• Turn a stated physical situation into a complete boundary value problem, with a governing equation, a domain, boundary conditions, and initial conditions that belong together.

• Choose the method a problem actually calls for, distinguishing the situations that suit separation of variables, characteristics, transform methods, source representations, or numerical approximation.

• Solve diffusion, wave, and steady-state problems on intervals, rectangles, disks, annuli, wedges, cylinders, and spheres, including problems with nonuniform material properties.

• Handle sources and forcing through concentrated-source representations, the method of images, and time-dependent superposition.

• Analyse nonlinear behaviour that linear theory cannot describe, including the formation and speed of discontinuities, admissibility, rarefactions, similarity solutions, and travelling fronts.

• Implement numerical schemes as precise mathematical procedures, assess their stability, and recognise when a refined grid is telling you something real.

• Extract the quantities a decision depends on from a solution, and state the limits of the model that produced them.

The topics covered include the modeling cycle and conservation laws, dimensional analysis and reduced models, characteristics and traffic-flow models, classification and well-posedness, orthogonal expansions and convergence, eigenvalue problems and expansion theory, special functions for curved geometries, source and transform methods, shocks and reaction-diffusion fronts, finite difference schemes with their stability conditions, weak formulations and finite elements, and a full modeling case study carried from formulation to validated prediction.

Written for engineering and science students at upper-undergraduate and graduate level, and for practising engineers and self-directed readers with a background in multivariable calculus and ordinary differential equations, the book assumes seriousness rather than prior expertise. Algorithms are described as mathematical steps rather than as code, so the material does not age with any particular software.

Take the next step from solving equations to modeling systems, and start building results you can defend.

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Détails de l'édition

• Éditeur: Independently published
• Date d'édition: 2026
• Langue: anglais
• ISBN 13: 9798161393475
• Reliure: Broché
• Nombre de pages: 434
• Coordonnées du fabricant: Printed by Amazon on behalf of the author; https://www.amazon.fr/hz/contact-us; ; c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy; Luxembourg; L-1855; Luxembourg