This appears in quantum-mechanical calculations of transition probabilities and also includes a lot of unpleasant numerical work. Accurate numerical studies of high-Reynolds-number flows are notoriously difficult to create and program.Īlternatively, Rₑ could stand for electronic transition dipole moment in a molecule. Large values of Re are indicative of turbulent flow, which cannot usually be retrieved analytically, and so numerical modeling is necessary. Named for Osborne Reynolds, Re characterizes the relative sizes of inertial and viscous effects in a moving fluid.
Rₑ: Someone needs to do a lot of tedious numerical work hopefully it's not you The Reynolds number (which is usually denoted by "Re," not "R e" as it appears in the comic) is the most important dimensionless group in fluid mechanics. This means that effects that are proportional to some power of ħ cannot be explained classically, and instead are "a quantum thing". Conversely, you can also formally set ħ=0 to get classical results from quantum formulae. ħ is equal to the energy of a photon divided by its frequency, and angular momentum in quantum mechanical systems is measured in quantized integer or half-integer units of ħ.Ĭlassical physics appears as a limit of quantum physics if all "actions" (quantities of dimension energy * time, momentum * length, or angular momentum) are much larger than ħ. Ħ: Oh wow, this is apparently a quantum thing ħ (pronounced "h-bar") is a symbol used for (the reduced) Planck's constant, a universal, fundamental constant in quantum physics. Although PDEs would typically be first taught at an undergraduate level, difficult partial derivatives would be encountered in graduate-level work. Problems with partial derivatives, especially partial differential equations, can be extremely challenging. ∂⁄ ∂x: A grad student is working very hard The replacement of the standard "d" letters with the curly letters "∂" denotes the partial derivative, which generalizes the ordinary derivative to multi-variable calculus. A hard-working undergraduate in the relevant fields would churn through exercises using this symbol. This is one of the basic operations in calculus and consequently is ubiquitous in the work of undergraduates in the sciences. Later Randall made a similar comic, 2586: Greek Letters, regarding the use of Greek letters in math.ĭ⁄ dx: An undergrad is working very hard d/dx is the symbol for a single-variable derivative. In the mid-20th century when they were in use, the dangers of radiation weren't as well understood as today, so an area with radiation that was noteworthy back then is probably dangerous, hence the no trespassing part. The title text refers to two non-SI units of radiation measurement, röntgen and rem. Many of the individual descriptions look like verbiage that might be found on informational or warnings signs or placards, although typically with a silly edge. Each piece of notation is presented as "symbolizing" not what it specifically means, but a typical context in which it might be encountered, see below. This comic refers to elements of (mostly mathematical or engineering) notation commonly used in various fields of math and science.
#Meanings of calculus symbols plus
Some expressions can be represented as the principal part that you need plus a remainder term. The purpose of introducing these symbols is to make complicated mathematical expressions simpler.
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