- Rationale and Outline of Lecture Notes
- Domains of Physical Phenomena
- Dimensions and Units
- Experimental Uncertainties
- Order of Magnitude Estimates
- Mode of Presentation

However, we have no direct experience to decide for example, what is the size of a typical atom. Or how many atoms and molecules constitute a living cell. Or how far are the distant galaxies. To obtain a more complete classification of nature, we need recourse to scientific experiments. As one can imagine, to even arrive at such a classification of physical phenomena, we need to know what discipline studies the phenomena in question.

Table 2.1 gives a sample of phenomena on different length scales and Table 2.2 does the same for different time scales. Various theories of physics are applicable for different domains of phenomena. All theories of physics are an approximate description of nature, although it is worth noting the remarkable fact that so far no experiment has been able to find any inaccuracy with quantum mechanics. For objects that are not too big or too small, Newtonian, or classical physics is a valid approximation. In the Figure 2.1 we chart out the various length and time scales, or equivalently, length and velocity scales for which the various theories are good approximations. Figure 1.1 lists all the theories of physics, and as one moves towards the right, the theories encompass a greater range of phenomena and are more accurate as well. The crowning glory of theoretical physics is embodied in string theory. String theory has as yet no experimental evidence in support of its correctness. Nevertheless, it has made a number of theoretical advances, the most important being the successful synthesis of quantum theory with the geometry of spacetime. Einstein's theory of gravitation is incorrect at short distances, and emerges from string theory as an approximation valid at large distances of the more fundamental equations of string theory. A remarkable prediction of string theory is that the physical universe is at least ten dimensional, with only four dimensions being visible to our senses, and the remaining six dimensions existing in the unseen.

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Given the mass of of water is , we have that the mass of water in the tank is approximately tons. Although this is not an exact answer, we have an estimate of what to expect. Hence it would be disastrous if we designed the tank to hold say ton of water.

- Elementary algebra, in particular the ability to use and manipulate symbols. For example, symbols or and so on normally mean that these two quantities are in some way related, and that is why they have been named in a manner to reflect their connection.
- Elementary trigonometry, in particular familiarity with sines and cosines.
- Elementary geometry, in particular, the properties of triangles.
- Elementary knowledge of vectors. Throughout the text,
vectors will always be denoted by boldface, namely a symbol
**v**means that v is a vector and that . - Complex numbers are necessary in the study of quantum theory, and we will review the essential properties of these.
- We will almost always use the symbol to denote points of space and to parametrize time.