Buch, Englisch, 396 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 746 g
Reihe: Textbooks in Mathematics
Analytical Methods and Applications
Buch, Englisch, 396 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 746 g
Reihe: Textbooks in Mathematics
ISBN: 978-1-032-47508-0
Verlag: CRC Press
Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor.
This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses.
Highlights:
- Offers a complete first course on PDEs
- The text’s flexible structure promotes varied syllabi for courses
- Written with a teach-by-example approach which offers numerous examples and applications
- Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions
- The text’s graphical material makes excellent use of modern software packages
- Features numerous examples and applications which are suitable for readers studying the subject remotely or independently
Zielgruppe
General
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Introduction
Basic definitions
Examples
First-order equations
Linear first-order equations
General solution
Initial condition
Quasilinear first-order equations
Characteristic curves
Examples
Second-order equations
Classification of second-order equations
Canonical forms
Hyperbolic equations
Elliptic equations
Parabolic equations
The Sturm-Liouville Problem
General consideration
Examples of Sturm-Liouville Problems
One-Dimensional Hyperbolic Equations
Wave Equation
Boundary and Initial Conditions
Longitudinal Vibrations of a Rod and Electrical Oscillations
Rod oscillations: Equations and boundary conditions
Electrical Oscillations in a Circuit
Traveling Waves: D'Alembert Method
Cauchy problem for nonhomogeneous wave equation
D'Alembert's formula
The Green's function
Well-posedness of the Cauchy problem
Finite intervals: The Fourier Method for Homogeneous Equations
The Fourier Method for Nonhomogeneous Equations
The Laplace Transform Method: simple cases
Equations with Nonhomogeneous Boundary Conditions
The Consistency Conditions and Generalized Solutions
Energy in the Harmonics
Dispersion of waves
Cauchy problem in an infinite region
Propagation of a wave train
One-Dimensional Parabolic Equations
Heat Conduction and Diffusion: Boundary Value Problems
Heat conduction
Diffusion equation
One-dimensional parabolic equations and initial