  Physics as a discipline embeds conceptual meaning about the physical world in
mathematical formalism. The meaning associated with mathematical symbols
depends on context, and physicists can shift conceptual meaning by manipulating
those symbols. We present an analysis of the different physical meanings
associated with the equal sign "=" that can be inferred from introductory and
upper--level physics textbooks. Five distinct meanings/categories are
identified: causality, balancing, definitional, assignment, and calculation,
each with operational definitions that help identify their presence. The
different uses can be seen to link mathematical equations to intuitive
conceptual ideas, and significant differences in the frequency with which these
are used exist between textbooks of different levels.
