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5: Vector Calculus

  • Page ID
    119736
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    In this chapter, we learn to model new kinds of integrals over fields such as magnetic fields, gravitational fields, or velocity fields. We also learn how to calculate the work done on a charged particle traveling through a magnetic field, the work done on a particle with mass traveling through a gravitational field, and the volume per unit time of water flowing through a net dropped in a river. All these applications are based on the concept of a vector field. The content in this Textmap's chapter is complemented by Vector Calculus Modules in the Core and the Vector Calculus (UCD Mat 21D) Libretext.

      Thumbnail: Surface \(Σ\) with closed boundary \(∂Σ\). \(\vec{F}\) could be the \(\vec{E}\) or \(\vec{B}\) fields. \(n\) is the unit normal. (Public Domain; Maschen).

      Contributors and Attributions

      • Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.


      5: Vector Calculus is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.