Applied Partial Differential Equations

• Κύριος συγγραφέας: Logan, J. David (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: 3rd ed. 2015.
• Σειρά: Undergraduate Texts in Mathematics,
• Θέματα: Mathematics.; Community ecology, Biotic.; Partial differential equations.; Physics.; Partial Differential Equations.; Mathematical Methods in Physics.; Community & Population Ecology.

This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this thi...

Πίνακας περιεχομένων:

• Preface to the Third Edition
• To the Students
• 1: The Physical Origins of Partial Differential Equations
• 1.1 PDE Models
• 1.2 Conservation Laws
• 1.3 Diffusion
• 1.4 Diffusion and Randomness
• 1.5 Vibrations and Acoustics
• 1.6 Quantum Mechanics*
• 1.7 Heat Conduction in Higher Dimensions
• 1.8 Laplace’s Equation
• 1.9 Classification of PDEs
• 2. Partial Differential Equations on Unbounded Domains
• 2.1 Cauchy Problem for the Heat Equation
• 2.2 Cauchy Problem for the Wave Equation
• 2.3 Well-Posed Problems
• 2.4 Semi-Infinite Domains
• 2.5 Sources and Duhamel’s Principle
• 2.6 Laplace Transforms
• 2.7 Fourier Transforms
• 3. Orthogonal Expansions
• 3.1 The Fourier Method
• 3.2 Orthogonal Expansions
• 3.3 Classical Fourier Series.-4. Partial Differential Equations on Bounded Domains
• 4.1 Overview of Separation of Variables
• 4.2 Sturm–Liouville Problems - 4.3 Generalization and Singular Problems
• 4.4 Laplace's Equation
• 4.5 Cooling of a Sphere
• 4.6 Diffusion inb a Disk
• 4.7 Sources on Bounded Domains
• 4.8 Poisson's Equation*.-5. Applications in the Life Sciences.-5.1 Age-Structured Models
• 5.2 Traveling Waves Fronts
• 5.3 Equilibria and Stability
• References
• Appendix A. Ordinary Differential Equations
• Index. .