This appendix presents a number of mathematical topics that arise in the book. The review is not meant to be comprehensive; it is limited to only items that could be helpful for understanding the flow of ideas in the chapters of this book.

Variables and Functions

Variable is the name we give to a value of something that changes. When we call a variable independent we mean that it can be any size within a prescribed physical domain of realistic values. A dependent variable is the value that we call a function of the independent variable. On a daily magnetogram, the magnitudes of the scaled H (a “dependent” variable) are dependent upon the selection of the “independent” variable of daily hourly time that we can take to be any value (in the domain) from 0 to 24. Maxwell's equations (Chapter 1) allow a unique field value to be determined from a given source-current distribution; however, given the field values, a number of possible currents might be the source. The dependent-variable field is a function of the independent-variable current. The extreme highest and lowest values of the dependent variable that occur over the domain of the independent variable define the range of the dependent variable.

The term function has a very special meaning in mathematics. When we say, for example, “the variable y is a function of the variable x” it is written as y = f(x).