Calculus with analytic geometry [antikvár]

prerace EATURES This text is designed for a standard three-semester or four-quarter calculus course. My intent is to present the material in the clearest possible way. The primary effort has been devoted to teaching the subject matter with a level of rigor suitable for the mainstream calculus audience. Anyone who has taught calculus knows that the course contains so much material that it is impossible for an instructor to spend an adequate amount of classroom time on every topic. For this reason a calculus textbook bears a major portion of the burden in the teaching process. 1 am hopeful that this book wiU be one that can be relied on for sound, clear, and complete explanations, thereby freeing valuable classroom time for the instructor. Precalculus Material Because of the vast amount of material to be covered, it is desirable to spend as little time as possible on precalculus topics. However, it is a fact that freshmen have a wide variety of educational backgrounds and different levels of preparedness. Therefore, I have included an optional first chapter devoted to precalculus material. It is written in enough detail to enable the instructor to feel confident in moving quickly through these preliminaries. Trigonometry Deficiencies in trigonometry plague many students throughout the entire calculus sequence. Therefore, I have included a substantial trigonometry review in the appendix. It is more detailed than most such reviews because I feel that students will appreciate having this material readily available. The review is broken into two units: the first to be mastered before reading Section 1.4 and the second before Section 3.3 Illustrations This calculus text is more heavily illustrated than most. It is my experience that beginners in mathematics frequently have difficulty ex- ix