Mathematical Methods

For Students of Physics and Related Fields
2. Auflage 2009
ISBN: 978-0-387-09503-5
Verlag: Springer

Buch, Englisch, 832 Seiten, HC runder Rücken kaschiert, Format (B × H): 183 mm x 260 mm, Gewicht: 1782 g

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.

Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.

This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Zielgruppe

Graduate

Autoren/Hrsg.

Hassani, Sadri

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Coordinates and Calculus.- Coordinate Systems and Vectors.- Differentiation.- Integration: Formalism.- Integration: Applications.- Dirac Delta Function.- Algebra of Vectors.- Planar and Spatial Vectors.- Finite-Dimensional Vector Spaces.- Vectors in Relativity.- Infinite Series.- Infinite Series.- Application of Common Series.- Integrals and Series as Functions.- Analysis of Vectors.- Vectors and Derivatives.- Flux and Divergence.- Line Integral and Curl.- Applied Vector Analysis.- Curvilinear Vector Analysis.- Tensor Analysis.- Complex Analysis.- Complex Arithmetic.- Complex Derivative and Integral.- Complex Series.- Calculus of Residues.- Differential Equations.- From PDEs to ODEs.- First-Order Differential Equations.- Second-Order Linear Differential Equations.- Laplace’s Equation: Cartesian Coordinates.- Laplace’s Equation: Spherical Coordinates.- Laplace’s Equation: Cylindrical Coordinates.- Other PDEs of Mathematical Physics.- Special Topics.- Integral Transforms.- Calculus of Variations.- Nonlinear Dynamics and Chaos.- Probability Theory.