One of the most ancient purposes to which mathematics has been put is engineering. The ancient Egyptians used their knowledge of geometry and math to calculate the dimensions and positions of their pyramids and to survey land for the purposes of farming and taxation. In our modern world of computers and technology, the number of uses for mathematics in engineering is greater than ever before. The textbook Advanced Engineering Mathematics, currently in its 10th edition, is one of the foremost of its kind for use in engineering mathematics courses at the college level. It is written by Ernin Kreyszig, Hernan Kreyszig and Edward J. Norminton.
The Fundamentals of Materials Science and Engineering: An Integrated Approach, 5th Edition is the latest update of a textbook that has been widely renowned for its comprehensive coverage of all the material with which it deals and for the accuracy with which it sets them forth. The exercises for the students are also outstanding. Two notable features of Advanced Engineering Mathematics are:
- simplicity of examples: These have been introduced in this edition. The examples are specially chosen for their simplicity and ease of understanding, while at the same time being instructive
- Modern standard notation is used throughout the book so that the student can relate what he or she is reading to the material in other courses that he may be taking.
Advanced Engineering Mathematics is divided into seven parts:
- ordinary differential equations
- linear algebra and vector calculus
- Fourier analysis and partial differential equations
- complex analysis and potential theory
- numerical analysis
- optimisation and graphs
- probability and statistics
These parts are subdivided into a total of twenty-five chapters. At the end of the book is a collection of four manuals:
- the Maple and Mathematica Computer Guides
- the Student Solutions Manual and Study Guide
- an instructor’s manual
The book has four underlying themes:
- modelling
- the judicious use of software for numerics
- the beauty of engineering mathematics
- to clearly identify the conceptual structure of subject matters
The 10th edition of Advanced Engineering Mathematics can be viewed at the website of Wiley Direct, a company that provides information about textbooks published in Australia, in two formats. One is the simple e-text format, which can be viewed both online and offline on a computer, tablet (including iPad) or smartphone. The student can make notes and highlights in any part of the e-book and they will remain synched thereto. The other format, e-book with Wiley Plus, is somewhat more expensive, but it brings with it all the advantages that come with a standard Wiley textbook, which include a wide variety of tools that can be used for self-study, to help the student develop his or her knowledge of the field further.