Some new topics, such as differential equations, were added, and some traditional topics whose inclusion could not be justified after discussions with mathematicians, engineers, physicists, chemists, biologists, and economists were omitted. Top Client Disciplines Faculty in engineering, physics, chemistry, biology and economics have had considerable input into these texts, both in choice of topics and choice of applications. In the Second Edition, comments were solicited once again from a large number of mathematicians and instructors in client disciplines. Suggestions were incorporated while maintaining a commitment to a focused treatment of a limited number of topics. Top Guiding Principles Exercises in the texts are of central importance since students learn most when they are most active.
Problems are varied and some are challenging.
Most cannot be worked by following a template in the texts. Problem Driven Formal definitions and procedures evolve form the investigation of practical problems. Whenever possible, the authors start with a practical problem and derive the general results from it. These practical problems are usually, but not always, real world applications. The real world problems are open-ended, meaning that there may be more than one solution depending on a students' analysis.