University calculus, early transcendentals (Q2917617)

The book is devoted to the simple introduction to certain ideas of modern mathematics taught at German university.NEWLINENEWLINEThis is a second (revised and extended) edition of a big project for the creation of an early stage university calculus textbook (first edition made by Pearson Education in 2007).NEWLINENEWLINEThe main attention of the authors is to present in a not too formal way the main concepts of university calculus (i.e., function theory in one and several variables). The following sentence from the Preface to the second edition characterises the main goal staying behind the authors (p. ix): ``Today, an increasing number of students become familiar with the terminology and operational methods of calculus in high school. However, their conceptual understanding of calculus is often quite limited when they enter college. We have acknowledged this reality be concentrating on concepts and their applications throughout.''NEWLINENEWLINEHow this ideas are realised in the book? It should be said, all possible ways are useful for this. First, any deep rigour (proofs of main theorems, in particular) is placed at the end of the book. Second, the book is full of examples. Third, the geometrical point of view is used extensively. Fourth, a lot of reference materials is spread along the book (tables, formulas etc.) Fifth, the main book is supplied by extra editions which are cited in the Preface and, thus, can be easily found (Instructor's edition, Instructor's solution manual, Student's solution manual and others). Last but not the least, modern technology is used for visualization and problem solving.NEWLINENEWLINEThis book can be considered as a text-book on calculus for self-education. A large number of exercises which end each chapter, special chapters named ``Questions for review'', an instructive discussion of simple applied problems (mostly taken from physics), all this serves to help readers to achieve their educational goals.NEWLINENEWLINEThe material which is taught in this book is more or less standard (as it is presented in any curricula on calculus in universities). The first part (Chapters 1--10) is devoted to the study of functions of one variable (``Functions'', ``Limit and continuity'', ``Differentiation'', ``Applications of derivatives'', ``Integration'', ``Applications of definite integrals'', ``Integrals and transcendental functions'', ``Techniques of integration'', ``Infinite sequences and series'', ``Parametric equations and polar coordinates''). The second part (Chapters 11--17) is devoted to the calculus of functions of several variables and begins is fact already in Chapter 10. Other chapters are the following: ``Vectors and the geometry of space'', ``Vector-valued functions and motion in space'', ``Partial derivatives'', ``Multiply integrals'', ``Integration in vector fields'', ``First-order differential equations'', ``Second-order differential equations''. Moreover, the last two chapters are presented only on-line.NEWLINENEWLINEExtra material (including a discussion of the questions and concepts which are most difficult for understanding, the proofs of main theorems) is collected in the appendices. Some other reference material is presented at the end of the book, too.