# Mathematics for Electromagnetism

May 19th, 2015
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Many physical quantities are a function of more than one variable (e.g. the pressure of a gas depends upon both temperature and volume, a magnetic field may be a function of the three spatial co-ordinates (x,y,z) and time (t)). Hence when differentiating a function there is usually a choice of which variable we differentiate with respect to.

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Mathematics for Electromagnetism (PHY205) The following provides a brief description and summary of the mathematics required for PHY205, Electromagnetism. Its main objective is to provide a revision of the most important and relevant points. It is not intended to teach the mathematics from scratch. For more detailed treatments consult your first year mathematics notes or textbooks. Some of the electromagnetism textbooks provide a chapter or appendix covering the required mathematics. Partial Differentiation Many physical quantities are a function of more than one variable (e.g. the pressure of a gas depends upon both temperature and volume, a magnetic field may be a function of the three spatial co-ordinates (x,y,z) and time (t)). Hence when differentiating a function there is usually a choice of which variable we differentiate with respect to. For example consider the function f which depends upon the variables x and y (f(x,y)). We can differentiate f with respect to x or y. When we differentiate with respect to a given variable we proceed in the same manner as in basic differentiation for functions which depend upon one variable. However for functions of more than one variable all other variables are treated as if they are constants. The symbols for the differential are modified ( is used instead of d). The derivatives of f with respect to x or y are written as respectively. Example f(x,y)=3x3+yx2+4xy2+5y3 We can also take

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