Johnson and Kiokemeister's Calculus with Analytic Geometry

This sixth edition of CALCULUS AND ANALYTIC GEOMETRY preserves the basic features of the previous editions. While maintaining the same logical and critical spirit that has characterized all previous versions of this text, the authors have introduced additional material to provide more intuitive background for the presentation of difficult topics. This interplay between intuition and rigor is obviously essential to a full understanding of the calculus. It has been the authors’ purpose to achieve a reasonable balance between these qualities. As in the fifth edition, derivatives and integrals make an early appearance. Introductory material on algebra and analytic geometry is presented in a preliminary chapter, Chapter 0. This chapter will be a review for many students. After a short chapter on functions, limits are presented in Chapter 2. This chapter is assembled in such a way that the limit theorems can be passed over quickly if the teacher so desires. Chapters 3 and 4 are concerned with derivatives and the usual applications to extrema and motion of a particle. Although integrals are defined in Chapter 5 in terms of upper and lower sums, the fundamental theorem 1s soon given so that integrals can be evaluated as antiderivatives. By the end of Chapter 6, the calculus of algebraic functions has been introduced. The next three chapters cover the calculus of transcendental functions. A substantial number of geometrical and physical applications is then presented in Chapter 10. Chapters 11 and 12, on improper integrals, infinite series, and related topics, may be postponed until later without breaking the continuity of the course. Chapters 13 through 16 focus on two- and three-dimensional vectors, plane and space curves, surfaces, and elementary multidimensional calculus. Chapter 17 is an optional chapter on line integrals, Green’s theorem, and change of variable in multiple integrals. The final chapter is on differential equations. Calculus with Analytic Geometry Contents Preface Chapter 0 ELEMENTS OF ANALYTIC GEOMETRY Chapter 1 FUNCTIONS Chapter 2 LIMITS Chapter 3 DERIVATIVES Chapter 4 APPLICATIONS OF THE DERIVATIVE Chapter 5 INTEGRALS Chapter 6 APPLICATIONS OF THE INTEGRAL Chapter 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Chapter 8 TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS Chapter 9 FORMAL INTEGRATION Chapter 10 FURTHER APPLICATIONS OF THE CALCULUS Chapter 11 INDETERMINATE FORMS, IMPROPER INTEGRALS, AND TAYLOR'S FORMULA Chapter 12 INFINITE SERIES Chapter 13 PLANE CURVES, VECTORS, AND POLAR COORDINATES Chapter 14 THREE-DIMENSIONAL ANALYTIC GEOMETRY Chapter 15 DIFFERENTIAL CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES Chapter 16 MULTIPLE INTEGRATION Chapter 17 FURTHER TOPICS IN INTEGRATION Chapter 18 DIFFERENTIAL EQUATIONS APPENDIXES Appendix A FACTS AND FORMULAS FROM TRIGONOMETRY Appendix B TABLE OF INTEGRALS Appendix C NUMERICAL TABLES Appendix D ANSWERS TO ODD-NUMBERED EXERCISES INDEX R. E. Johnson, F. L. Kiokemeister, E. S. Wolk. Includes Index.