Derek Raine - Mathematical Physics

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An Introduction

Derek Raine, PhD et al.

MERCURY LEARNING AND INFORMATION

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Copyright 2019 by MERCURY LEARNING AND INFORMATION LLC. All rights reserved.

Original title and copyright: Mathematical Methods for Physical Science by Derek Raine et al. Copyright 2018 Pantaneto Press. All rights reserved.

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D. Raine et al. Mathematical Physics.

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10.1Functions of two variables
Functions of two variables

The book differs from other introductions to mathematical methods at this level in several important regards.

First, it does not follow the usual presentation of a description of the theory followed by examples and exercises. Rather we use examples to introduce the theory. This approach is not new; it goes back to the methods by which the scribes of Ancient Babylon learned mathematics: by example problems and, to judge from the numbers of surviving cuneiform tablets, lots of them!

Second, to help the reader digest the text, it is broken up into quite short sections (often a page or so) followed by exercises. It may be tempting to skip the exercises (especially if one is used to doing only a selection of end-of-chapter problems), on the grounds that one can get through the book more quickly that way. This is true, in the same sense that watching a film speeded up 8 will get to the end more quickly, but it will be without much understanding of the plot. There are optional additional exercises at the end of each chapter; the ones in the text represent the minimum we think you need.

Third, however, we have tried to avoid too many plug-and-chugexercises, that is, exercises which you solve by following the text but substituting some different numbers (pattern matching). These are useful to reinforce memory, but they are not very useful to develop or test understanding. Rather, we have tried to make the exercises diagnostic in the sense that they do test understanding, that is, they test the ability to use what has been learned in a slightly different context.An instructor can therefore use these to target support for students.

Finally, and related to the previous point, while we hope it is perfectly possible to use this book for self-study, it was not designed for that purpose. It is intended for use as a course text. In this regard it might be useful to say a little about the background to the writing of the book - especially if you are intrigued to know why there are so many authors. We would also like to thank contributions to various versions of the text from Paul Abel, Mike Dampier, Andrew King and Tim Yeoman.

About forty years ago, it was agreed that our conventional presentation of mathematical methods for our physics students - lectures, marked homework and examinations - was not as effective at we might have hoped. So, instead of spending lecture time going through theory and exercises on the board, we produced a text as, in effect, the lecture notes, and refocused class time on weekly workshops and small group tutorials. Lectures were restricted to a weekly one-hour introduction to the topics for that week. We made the examinations harder, by requiring passes separately in the major topics (calculus of one variable, many variables, linear algebra, differential equations, vector calculus) and the pass rates soared. The initial text has been refined over the years (hence the number of authors) and this book is another, more outward-facing, version, which we are pleased to have the opportunity to share with you.