Mathematical Methods for Oscillations and Waves

Erscheinungsjahr 2020
ISBN: 978-1-108-48822-8
Verlag: Cambridge University Press

Buch, Englisch, 350 Seiten, Format (B × H): 197 mm x 251 mm, Gewicht: 747 g

Anchored in simple and familiar physics problems, the author provides a focused introduction to mathematical methods in a narrative driven and structured manner. Ordinary and partial differential equation solving, linear algebra, vector calculus, complex variables and numerical methods are all introduced and bear relevance to a wide range of physical problems. Expanded and novel applications of these methods highlight their utility in less familiar areas, and advertise those areas that will become more important as students continue. This highlights both the utility of each method in progressing with problems of increasing complexity while also allowing students to see how a simplified problem becomes 're-complexified'. Advanced topics include nonlinear partial differential equations, and relativistic and quantum mechanical variants of problems like the harmonic oscillator. Physics, mathematics and engineering students will find 300 problems treated in a sophisticated manner. The insights emerging from Franklin's treatment make it a valuable teaching resource.

Autoren/Hrsg.

Franklin, Joel

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse

Inhaltsverzeichnis

Preface; 1. Harmonic oscillator; 2. Damped harmonic oscillator; 3. Coupled oscillators; 4. The wave equation; 5. Integration; 6. Waves in three dimensions; 7. Other wave equations; 8. Numerical methods; Appendix A. Solving ODE's: a roadmap; Appendix B. Vector calculus: curvilinear coordinates; References; Index.

Über Autor(innen)

Franklin, Joel
Joel Franklin is a professor in the Physics Department of Reed College, Oregon. His research focuses on mathematical and computational methods with applications to classical mechanics, quantum mechanics, electrodynamics, general relativity and modifications to general relativity He is also the author of Advanced Mechanics and General Relativity (Cambridge, 2010), Computational Methods for Physics (Cambridge, 2013), and Classical Field Theory (Cambridge, 2017).