Calculus, Updated / Text Only (2ND 02 Edition)

The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student — one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.

The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems.

0 Preliminaries

0.1 The Real Numbers and the Cartesian Plane

0.2 Lines and Functions

0.3 Graphing Calculators and Computer Algebra Systems

0.4 Solving Equations

0.5 Trigonometric Functions

0.6 Exponential and Logarithmic Functions

0.7 Transformations of Functions

0.8 Preview of Calculus

1 Limits and Continuity

1.1 The Concept of Limit

1.2 Computation of Limits

1.3 Continuity and its Consequences

1.4 Limits Involving Infinity

1.5 Formal Definition of the Limit

1.6 Limits and Loss-of-Significance Errors

2 Differentiation

2.1 Tangent Lines and Velocity

2.2 The Derivative

2.3 Computation of Derivatives: The Power Rule

2.4 The Product and Quotient Rules

2.5 Derivatives of Trigonometric Functions

2.6 Derivatives of Exponential and Logarithmic Functions

2.7 The Chain Rule

2.8 Implicit Differentiation and Related Rates

2.9 The Mean Value Theorem

3 Applications of Differentiation

3.1 Linear Approximations adn L'Hopital's Rule

3.2 Newton's Method

3.3 Maximum and Minimum Values

(and more...)