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.