In this more technical chapter, the notions of space, time, and experimental evidence are introduced as the foundation on which (theoretical) physics rests. Vector and tensor algebra and analysis are discussed, including the theorems of Gauss, Stokes, and Green, and also the Christoffel symbols. Use is made of general, Cartesian, spherical, and cylindrical coordinates, but also rectilinear oblique covariant and contravariant coordinates and Euler angles. We discuss the kind of coordinate transformation properties used in differential equations in many more advanced theories. The chapter ends with error analysis, the normal (Gauss) distribution, averages, standard deviations, and error propagation.
This is a preview of subscription content, log in to check access.
Suggestions for Further Reading
J. Arfken, H.J. Weber, Mathematical Methods for Physicists, 6th edn. (Elsevier Academic, Burlington MA, 2005)zbMATHGoogle Scholar
E. Ph Blanchard, Brüning: Mathematical Methods in Physics: Distributions, Hilbert Space Operators, and Variational Methods (Springer Science + Business, Media, 2003)CrossRefGoogle Scholar
S. Hassani, Mathematical Physics-A Modern Introduction to Its Foundations (Springer, Berlin, 2013)zbMATHGoogle Scholar
A. Sommerfeld: Lectures on Theoretical Physics 6-Partial Differential Equations in Physics (Academic, London, 1949/1953)CrossRefGoogle Scholar