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Essential Calculus

By James Stewart

2nd Edition © 2013
Discipline:Mathematics
Course:Calculus
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This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

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AboutTable of contentsResourcesPricing & formatsRelated products

About this product

This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

The text presents a concise approach to calculus for instructors who want to focus on essential principles and who feel no need for frills.

Brevity is achieved through condensed exposition, fewer examples in some sections, fewer technology and conceptual problems, and fewer appendixes. Problems Plus and Projects have been moved to the author's website at www.stewartcalculus.com.

Certain topics, for example, the treatment of the integral and the remainder term in Taylor Series, are presented in a manner that is more traditional than in Stewart's other books.

The text presents exponential, logarithmic, and inverse trigonometric functions late, with the logarithm defined as an integral. Instructors wishing to cover such functions earlier should consider ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS.

Table of contents

Chapters

Cover Page
Title Page
Copyright Page
Preface
To the Student
Diagnostic Tests
A. Diagnostic Test: Algebra
B. Diagnostic Test: Analytic Geometry
C. Diagnostic Test: Functions
D. Diagnostic Test: Trigonometry
1. Functions and Limits*Preview this chapter
2. Derivatives
3. Applications of Differentiation
4. Integrals
5. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
6. Techniques of Integration
7. Applications of Integration
8. Series
9. Parametric Equations and Polar Coordinates
10. Vectors and the Geometry of Space
11. Partial Derivatives
12. Multiple Integrals
13. Vector Calculus
Media Index
A. Trigonometry
B. Sigma Notation
C. Proofs
Reference Pages
Show more

1. Functions and LimitsPreview this chapter ↗

1.1
Functions and Their Representations
Preview this section ↗
Representations of Functions ↗
Piecewise Defined Functions ↗
Symmetry ↗
Increasing and Decreasing Functions ↗
1.1. Exercises ↗
1.2
A Catalog of Essential Functions
Preview this section ↗
Mathematical Modeling ↗
Transformations of Functions ↗
Combinations of Functions ↗
1.2. Exercises ↗
1.3
The Limit of a Function
Preview this section ↗
Intuitive Definition of a Limit ↗
One-Sided Limits ↗
Precise Definition of a Limit ↗
1.3. Exercises ↗
1.4
Calculating Limits
Preview this section ↗
1.4. Exercises ↗
1.5
Continuity
Preview this section ↗
1.5. Exercises ↗
1.6
Limits Involving Infinity
Preview this section ↗
Infinite Limits ↗
Limits at Infinity ↗
Infinite Limits at Infinity ↗
Precise Definitions ↗
1.6. Exercises ↗
Chapter 1. Review ↗

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