Calculus for Scientists And Engineers: An Analytical Approach

This text attempts to lay emphasis on the whys of mathematics rather than on the hows. The material covered is the same as is generally found in a first course in calculus, namely, the study of functions of a real variable, but the approach is different. A conscious effort is made to give strong motivation for the abstract concepts covered and thereby help a beginner overcome most of the aversion one has for abstraction. For example, instead of merely giving the epsilon-delta definition of a limit, a whole section is devoted to explain how the definition evolved and why it is a most natural formulation of the basic concept of a limit. This should help the student get over the clumsiness of the definition, which can be quite repulsive otherwise. Even though the emphasis is more on the whys than on the hows of mathematics, the latter are not entirely ignored. There is adequate exposure to the techniques through the exercises. The answers to these exercises will enable sincere students to acquire the hows as well. As a result, the book should appeal to a variety of readers. It can be used as a regular text for a first course in calculus. On the other hand, those who already have a working knowledge of calculus will benefit by gaining deeper insights. Yet another class of students who may find the book useful, are those who want to pursue mathematics as their major subject. Some students experience difficulty making the transition from calculus to analysis. The treatment given here will enable them to get over the rough edges.