Product Description
Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for what the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics. ... Read more

Customer Reviews (2)

inverse problems
This book is excellant,gives you oportunity to fully understand content.Also worth mentioning are numerous examples which shows how theory is intertwined with applications.

Problems from perspectives I has not thought of
While the basics of inverting functions are part of the pre-calculus curriculum, applying inverse operations is not given the attention that it should. Granted that differentiation and integration are inverse operations and that inverting matrices is part of the linear algebra class, this truly does not do justice to how ubiquitous inverse problems are.
Three general principles generally apply when looking at functions and their inverses.

* One direction is much harder than the other.
* One direction does not yield a unique solution.
* It may not be possible to perform the inverse of a function.

For example, while differentiation yields a unique answer, antidifferentiation has an infinite family of solutions. Multiplying two numbers together is easy, factoring is hard.
Many of the problems in this book arise from the study of physical phenomena. This is only fitting, in that collecting data and constructing an equation to model it is a classic form of inverse problem. The range of problems is considerable and quite impressive. While some are fairly standard issue, there were many that took approaches that I have never considered.
There are several levels to the problems: precalculus, calculus, differential equations and linear algebra. With solutions to most included, this is a treasure chest of unusual problems perfect for advanced presentations, extra credit and the occasional examination puzzler. Some of the problems require the use of a symbolic mathematics package and MATLAB is the one used throughout. However, with so many problems, the absence of MATLAB would not be sorely felt.
As a steady reader of math books, I sometimes grow tired of seeing only slight variations of the same old problems. In this book, I saw many different problems from perspectives that I was unaware of. That was exciting, stimulating and refreshing. I wish there were more just like it. I can almost guarantee that if you teach precalculus, calculus, differential equations or linear algebra, there will be something in here that you can use to improve the quality of the course. ... Read more

Product Description

This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. It gives an introduction to the most important models, followed by a detailed description of numerical techniques. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology.

Customer Reviews (1)

Good scope; figures and index fall short
For a cross-disciplinary mathematical biologist who is to be an end-user of cardiac models, this book gave a quick introduction to electrocardiograms, electromechanics, and pertinent computing algorithms. It provides worked examples which should be useful in conjunction with a dedicated course book e.g. on partial differential equations. Regrettably, many terms and abbreviations used in the text are absent in the index, detracting from the book's value as a quick reference. The illustrations could be much better, considering the multidimensional, multivariate nature of the system. Instead, they suffer from unlabeled axes, nonuniform color maps in multi-panel figures, or wasteful use of color plates where different linestyles would suffice. All in all, not a feast for the eye but a reasonably concise, fairly well-structured primer on a specific sub-area of a huge research field. ... Read more

Product Description
Here's a six-volume Reading Skills Activities Library featuring 1,200 ready-to-use activity sheets to reinforce basic reading skills. Each volume includes a reproducible Reading Skills Check List for each level, organized sequentially and formatted for easy record keeping. Ideal for in-class reinforcement, homework assignments and peer- or aide-assisted instruction. ... Read more

Customer Reviews (1)

This one book does it all!
If you're looking for a book full of activities to help your child with vocabulary, word skills, comprehension, research, phonics and more, this book is for you!


Sections include vocabulary (defining words, synonyms, antonyms, homophones, etc.), word attack (syllabication, vowel sounds, using a dictionary, context clues), and comprehension (locating information, note taking, organizing material correctly, using reference material effectively, etc.)Each grade level in this series includes more than 200 reproducible activities to help children master the sequential reading skills at that level.Complete answer keys for all activities are included. ... Read more