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1: Review of Vector Analysis

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  • Page ID
    48111

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    Electromagnetic field theory is the study of forces between charged particles resulting in energy conversion or signal transmission and reception. These forces vary in magnitude and direction with time and throughout space so that the theory is a heavy user of vector, differential, and integral calculus. This chapter presents a brief review that. highlights the essential mathematical tools needed throughout the text. We isolate the mathematical details here so that in later chapters most of our attention can be devoted to the applications of the mathematics rather than to its development. Additional mathematical material will be presented as needed throughout the text.

    • 1.1: Coordinate Systems
      A coordinate system is a way of uniquely specifying the location of any position in space with respect to a reference origin. Any point is defined by the intersection of three mutually perpendicular surfaces. The coordinate axes are then defined by the normals to these surfaces at the point.
    • 1.2: Vector Algebra
      A scalar quantity is a number completely determined by its magnitude, such as temperature, mass, and charge, the last being especially important in our future study.
    • 1.3: The Gradient and the Del Operator
      Often we are concerned with the properties of a scalar field f(x, y, z) around a particular point.
    • 1.4: Flux and Divergence
      If we measure the total mass of fluid entering the volume in Figure 1-13 and find it to be less than the mass leaving, we know that there must be an additional source of fluid within the pipe. If the mass leaving is less than that entering, then
    • 1.5: The Curl and Stokes' Theorem
      We have used the example of work a few times previously to motivate particular vector and integral relations.
    • 1.6: Problems

    Thumbnail: An illustration of Stokes' theorem, with surface \(Σ}\), its boundary \(∂Σ\) and the normal vector \(\vec{n}\). (CC BY-SA 3.0; Cronholm144 via Wikipedia)

    This page titled 1: Review of Vector Analysis is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Markus Zahn (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.