tailieunhanh - Elementary Caculus

Is this second edition, many change haves been on nine years of classroom experience. There are major revisions to the first six chapters and the Epilogue, and there is one completely chapter. Chapters 14 on differential equations . In addition, the original chapters 11 and chapters 12 have been repackaged as three chapters. | ELEMENTARY CALCULUS An Infinitesimal Approach Second Edition H. Jerome Keisler University of Wisconsin Dedicated to my sons Randall Jeffrey and Thomas Copyright 2000 by H. Jerome Keisler. PREFACE TO THE SECOND EDITION In this second edition many changes have been made based on nine years of classroom experience. There are major revisions to the first six chapters and the Epilogue and there is one completely new chapter Chapter 14 on differential equations. In addition the original Chapters 11 and 12 have been repackaged as three chapters Chapter 11 on partial differentiation Chapter 12 on multiple integration and Chapter 13 on vector calculus. Chapter 1 has been shortened and much of the theoretical material from the first edition has been moved to the Epilogue. The calculus of transcendental functions has been fully integrated into the course beginning in Chapter 2 on derivatives. Chapter 3 focuses on applications of the derivative. The material on setting up word problems and on related rates has been moved from the first two chapters to the beginning of Chapter 3. The theoretical results on continuous functions including the Intermediate Extreme and Mean Value Theorems have been collected in a single section at the end of Chapter 3. The development of the integral in Chapter 4 has been streamlined. The Trapezoidal Rule has been moved from Chapter 5 to Chapter 4 and a discussion of Simpson s Rule has been added. The section on area between two curves has been moved from Chapter 6 to Chapter 4. Chapter 5 deals with limits approximations and analytic geometry. An extensive treatment of conic sections and a section on Newton s method have been added. Chapter 6 begins with new material on finding a volume by integrating areas of cross sections. Only minor changes and corrections have been made to Chapters 7 through 13. The new Chapter 14 gives a first introduction to differential equations with emphasis on solving first and second order linear differential equations.