Abstract
In this chapter, we define and discuss volume integrals in \(\, D\)-dimensional space, curvilinear, and surface integrals of the first and second types in 3D.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Reminder: \(\,\mathrm{diam}\,(V_i)\,\) is a maximal (supremum) of the distances between the two points of the figure \(\,(V_i)\).
- 2.
In Exercise 2, we ask to verify that \(\, dx^{i}\,\) really transform as contravariant vector components.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Shapiro, I.L. (2019). Curvilinear, Surface, and D-Dimensional Integrals. In: A Primer in Tensor Analysis and Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26895-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-26895-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26894-7
Online ISBN: 978-3-030-26895-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)