A Course in Mathematics for Students of Physics

2
Erscheinungsjahr 1991
ISBN: 978-0-521-40650-5
Verlag: Cambridge University Press

Buch, Englisch, 461 Seiten, Format (B × H): 191 mm x 235 mm, Gewicht: 859 g

This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study.

Autoren/Hrsg.

Bamberg, Paul

Sternberg, Shlomo

Fachgebiete

• Technische Wissenschaften Bauingenieurwesen Mathematische Methoden, Computeranwendungen (Bauingenieurwesen)
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

1. The theory of electric networks; 2. The method of orthogonal projection; 3. Higher-dimensional complexes; 4. Complexes situated in Rn; 5. Electrostatics in R3; 6. Currents, flows and magnetostatics; 7. The star operator; 8. Maxwell's equations; 9. Complex analysis; 10. Asymptotic analysis; Index.