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3_Sep_08 - Electricity and Magnetism I(P331 M R Shepherd...

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Electricity and Magnetism I (P331) M. R. Shepherd September 3, 2008 1 Vector Calculus 1.1 Notation 1.1.1 Denoting a vector Throughout the text vectors are typically noted in boldface upright characters. For example, the vector electric field is given by E . Scalars are noted by normal italic letters; the scalar potential is given, for example, by V . It is really impossible to designate boldface letters on the blackboard so you will often see me write E instead of E . 1.1.2 Functions We will also be dealing primarily with quantities that are a function of spatial coordinates. To be more compact, instead of writing E ( x, y, z ) or E ( x, y, z ), we will simply write E or E . It is important to remember that these quantities are functions and have a spatial (and, later in the course, time) dependence. 1.1.3 Unit vectors Note also that unit vectors appear with a hat. For example the quantity ˆ x means a vector with a length of one unit pointing in the direction of the x -axis. Some of you may be used to the notation ˆ i , ˆ j , ˆ k to denote the unit vectors of the x , y , and z axes. Our text uses ˆ x , ˆ y , ˆ z .
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