# Introduction

## Abstract

This chapter is an overview of the sorts of problems that can be addressed using the methods from this book. It also discusses the major differences between mathematical modeling and mathematics, and reviews some basic terminology that is used throughout the book. The appendix provides a much more in-depth review of engineering mathematics. This book is meant to be self-contained in the sense that only prior knowledge of college-level calculus, linear algebra, and differential equations is assumed. Therefore, if it is read sequentially and something does not make sense, then the appendix most likely contains the missing piece of knowledge. Standard references on classical mathematics used in engineering and physics include [2, 5], which also can be consulted to fill in any missing background.

Even after consulting the appendix and the cited references, some of the concepts presented toward the end of each chapter may be difficult to grasp on the first reading. That is okay. To a large extent, it should be possible to skip over some of the more difficult concepts in any given chapter, and still understand the fundamental ideas in subsequent chapters. In order to focus the reader on the most important ideas in each chapter, the equations that are necessary to successfully navigate through later chapters are circumscribed with a box. This also makes it easier to refer back to key equations.

## Keywords

Equivalence Class Control Volume Commutative Diagram Divergence Theorem Probability Flow## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Amari, S., Nagaoka, H.,
*Methods of Information Geometry*. Translations of Mathematical Monographs 191, American Mathematical Society, Providence, RI, 2000.Google Scholar - 2.Arfken, G.B., Weber, H.J.,
*Mathematical Methods for Physicists*, 6th ed., Academic Press, San Diego, 2005.Google Scholar - 3.Birkhoff, G., MacLane, S.,
*A Survey of Modern Algebra*, A.K. Peters, Wellesley, MA, 1997.Google Scholar - 4.Joshi, A.W.,
*Matrices and Tensors in Physics*, 3rd ed., John Wiley and Sons, New York, 1995.Google Scholar - 5.Kreyszig, E.,
*Advanced Engineering Mathematics*, 9th ed., John Wiley and Sons, New York, 2005.Google Scholar - 6.Lai, W.M., Rubin, D., Krempl, E.,
*Introduction to Continuum Mechanics*, 3rd ed., Butterworth Heineman, New York, 1996.Google Scholar - 7.Mace, G.E.,
*Continuum Mechanics*, Schaum's Outline Series, McGraw-Hill, New York, 1970.Google Scholar - 8.Malvern, L.E.,
*Introduction to the Mechanics of a Continuous Medium*, Prentice-Hall, Englewood Cliffs, NJ, 1969.Google Scholar - 9.Munkres, J.R.,
*Topology*, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2000.Google Scholar - 10.Neyfeh, A.,
*Problems in Perturbation*, John Wiley and Sons, New York, 1985.Google Scholar - 11.Pinsky, M.A.,
*Introduction to Partial Differential Equations with Applications*, McGraw-Hill, New York, 1984.Google Scholar - 12.Pitts, D.R., Sissom, L.E.,
*Heat Transfer*, Schaum's Outline Series, McGraw-Hill, New York, 1977.Google Scholar - 13.Zhou, Y., Chirikjian, G.S., “Probabilistic models of dead-reckoning error in nonholonomic mobile robots,”
*Proceedings of the IEEE International Conference on Robotics and Automation*, Taipei, Taiwan, Sept 14–19, 2003, pp. 1594–1599.Google Scholar