This third edition of University Calculus provides a streamlined treatment of the material in a standard three-semester or four-quarter course taught at the university level. As the title suggests, the book aims to go beyond what many students may have seen at the high school level. By emphasizing rigor and mathematical precision, supported with examples and exercises, this book encourages students to think more clearly than if they were using rote procedures.
Generalization drives the development of calculus and is pervasive in this book. Slopes of lines generalize to slopes of curves, lengths of line segments to lengths of curves, areas and volumes of regular geometric figures to areas and volumes of shapes with curved boundaries, rational exponents to irrational ones, and finite sums to series. Plane analytic geometry generalizes to the geometry of space, and single variable calculus to the calculus of many variables. Generalization weaves together the many threads of calculus into an elegant tapestry that is rich in ideas and their applications.
Mastering this beautiful subject is its own reward, but the real gift of mastery is the ability to think through problems clearly—distinguishing between what is known and what is assumed, and using a logical sequence of steps to reach a solution. We intend this book to capture the richness and powerful applicability of calculus, and to support student thinking and understanding for mastery of the material. New to this Edition In this new edition, we have followed the basic structure of earlier editions. Taking into account helpful suggestions from readers and users of previous editions, we continued to improve clarity and readability.
We also made the following improvements:
• Updated and added numerous exercises throughout, with emphasis on the mid-level and more in the life science areas
• Reworked many figures and added new ones
• Moved the discussion of conditional convergence to follow the Alternating Series Test
• Enhanced the discussion defining differentiability for functions of several variables with more emphasis on linearization
• Showed that the derivative along a path generalizes the single-variable chain rule
• Added more geometric insight into the idea of multiple integrals and the meaning of the Jacobian in substitutions for their evaluations
• Developed surface integrals of vector fields as generalizations of line integrals
• Extended and clarified the discussion of the curl and divergence, and added new figures to help visualize their meanings
Author: Joel R. Hass
Pub Date: 1/3/2015
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