Customer Reviews

Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical Sciences

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1 star:		(1)

 

 

Whether your personal focus is upon mathematics, engineering, physics, or even computer science or the arts, this work provides a superb instructional foundation for applied mathematics.

Beginning with differentiation and integration, the text continues on its mathematical journey, taking the reader through complex numbers, linear algebra, differential equations, even LaPlace transforms and Fourier series. It then ends with overview chapters on such varied topics as graph theory, set theory, boolean algebra, probability and statistics. In addition there is a section devoted to using symbolic computing with applications such as Mathematica, which are essential to anyone interested in learning or using mathematics today.

The overall look of the book is exquisite. The typefaces, equations and graphs are a pleasure to the eye (even as they grow substantially in complexity). The prose discusses the subject matter with rigor, yet is easy to read and guides gradually and carefully.

Anyone wishing to review the fundamentals of mathematics or to further the education started through school will find this book to be a joy to go through. Solutions to many exercises are provided in an appendix.

The softcover edition is highly durable. Upon completion of every chapter the reader will have substantial expertise in or exposure to major branches and topics of mathematics. For this wealth of information to have so low a cost is remarkable.

Highest possible recommendation, with superlative marks in virtually all categories of review.

** UPDATE FOR THIRD EDITION :

The formatting of the book has been changed subtly but noticeably, maintaining the original elegance. Content has been changed and restructured minimally.

Perhaps the most significant change, is that every one of the hundreds of exercises in the 41 chapters of this book has now been solved, and is available at the publisher's website in Acrobat (.PDF) format. The link is provided in the book itself.

Additionally, there are far more Mathematica projects than earlier editions, several per each chapter in fact, and again, programmatic-solutions for all of these are provided at another site, its link also in the book. These are in .NB (Mathematica NoteBook) format, and can be read by any text-editor including Notepad. They can also be viewed and tested using Mathematica Reader, a free program distributed by Mathematica's author, available for Windows, Mac OS, and Linux.

These significant updates fully address what was arguably the only previous weakness in this fine work.

First, if you haven't noticed yet, this is NOT an advanced math book. Don't expect detailed demonstrations or complexe problems to solve. It is a global reference for engineers or anyone dealing with intermediate maths. If you want to explore the subjects covered in this book with deep details, you should buy a book per chapter.

The content is well divided in numerous chapters, each covering a specific field like geometry, linear and vector algebra, calculus, Laplace and Fourier transforms and series, statistics (less useful, a complete reference is better). The book starts with a good introduction recalling important concepts required to understand the following chapters (partial fractions expansion, functions, complex numbers, matrix, algebra, etc.) Once you master these, you can move throughout the chapters and master or revise the math techniques with the great examples (well explained, they generally cover most of the possible cases).

A complete set of problems with answers is available at the end of each chapter. The book is well illustrated, but a few graphs could have been more clear.

A great reference book for any math user. Complete, it is an extended summary of a dozen of other "specific subject" books.

If you need as few texts as possible that cover all the maths you need for engineering purposes, this book is a must buy. Adding Kreyzig's Advanced Engineering Mathematics and maybe a Statistics text to it and you should have no problems with 99% of the maths for the rest of your life (unless you want to do substantial computer program design, in which a discrete maths text may help).

A few problems though: a proper treatment on sequences and series is absent, l'Hopital's rule is not discussed either (both presumably because they are too pure maths for engineering, but some advanced engineering maths courses do use them), and there are some topics (like Simpson's rule) that are only discussed in problems sections but not in the main text.

Good comprehensive coverage of most things you'll need in 1st and 2nd year sci/tech courses in top end Uni's. However it lacks the rigorous formality of the more hardcore texts for Math degrees but will serve you well for engineering and physics related stuff (like it says on the cover).

It's useful to note that this book won't guide you through the concepts and problems in an 'idiot's guide' step-by-step fashion. It's written under the assumption that you've done some higher+ maths for a while and have had some experiencing in muddling through things on your own. Moreover, much of the format is laid out in a summary type fashion with breif intros and a few examples culminating in a lucid statement of concepts. This approach is usefull especially after you've waded through heavy class notes and are gagging for something concise that puts the stuff in a nutshell....much needed clarity, like finally seeing through the smoke.

The exercise problems are tough, ball breakingly hard in fact! Often leaping beyond the seemingly easy illustrations of the examples. You'll need help from other resources to get through them. Maybe this is deliberate as it get's you desperately banging your head against the wall and /if when you finally get the method right - you won't make the same mistake again.

keep this book after you're done, it'll serve as a good reference thing as well.

One big disappointment about the book is that, not only are few solutions to problems provided, there are a relatively large number of errors in the solutions which are presented. This is very frustrating to students trying to learn this material. Given that the text is in its second edition, this is really not understandable.

The book is surprisingly inexpensive, however. Perhaps it cost less to publish since proofreaders were not utilized.