Special Edition for Rutgers University
The NEW 7th edition of Calculus blends the best aspects of calculus reform along with the goals and methodology of traditional calculus. The format of this text is enhanced, but is not dominated by new technology. Its innovative presentation includes:
- Conceptual Understanding through Verbalization
- Mathematical Communication
- Cooperative Learning Group Research Projects
- Integration of Technology
- Greater Text Visualization
- Supplementary Materials
- Interactive art - Many pieces of art in the book link online to dynamic art to illustrate such topics as limits, slopes, areas, and direction fields
- An early presentation of transcendental functions: Logarithms, exponential functions, and trigonometric functions
- Differential equations in a natural and reasonable way
- Utilization of the humanness of mathematics
- Precalculus mathematics being taught at most colleges and universities correctly reflected
- A student solutions manual, instructor’s manual, and accompanying website
It’s all about Problems, problems, problems, and even more problems:
- Modeling Problems require the reader to make assumptions about the real world.
- Think Tank Problems prove the proposition true or to find a counterexample to disprove the proposition.
- Exploration Problems go beyond the category of counterexample problem to provide opportunities for innovative thinking.
- Historical Quest Problems invite the students to participate in the historical development of mathematics. History becomes active rather than passive.
- Journal Problems have been reprinted from leading mathematics journals in an effort to show that “mathematicians work problems too.”
- Putnam Examination Problems have been included to challenge not only the “best of the best” but to offer stimulating content for everybody.
- Uniform Problem Sets 60 in every set allow for easy and consistent problem assignment.
- Cumulative Problem Sets for Chapters 1-5.
- Huge Chapter Supplementary Problem Set of 99 miscellaneous problems in each chapter.
- Proficiency Examination Problem Sets consisting of both concept and practice problems.
1 Functions and Graphs
1.1 What Is Calculus?
1.3 Lines in the Plane; Parametric Equations
1.4 Functions and Graphs
1.5 Inverse Functions; Inverse Trigonometric Functions
Chapter 1 Review
Book Report Ethnomathematics by Marcia Ascher
Chapter 1 Group Research Project
2 Limits and Continuity
2.1 The Limit of a Function
2.2 Algebraic Computation of Limits
2.4 Exponential and Logarithmic Functions
Chapter 2 Review
Chapter 2 Group Research Project
3.1 An Introduction to the Derivative: Tangents
3.2 Techniques of Differentiation
3.3 Derivatives of Trigonometric, Exponential, and Logarithmic Functions
3.4 Rates of Change: Modeling Rectilinear Motion
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Related Rates and Applications
3.8 Linear Approximation and Differentials
Chapter 3 Review
Book Report Fermat’s Enigma by Simon Singh
Chapter 3 Group Research Project
4 Additional Applications of the Derivative
4.1 Extreme Values of a Continuous Function
4.2 The Mean Value Theorem
4.3 Using Derivatives to Sketch the Graph of a Function
4.4 Curve Sketching with Asymptotes: Limits Involving Infinity
4.5 l’Hˆopital’s Rule
4.6 Optimization in the Physical Sciences and Engineering
4.7 Optimization in Business, Economics, and the Life Sciences
Chapter 4 Review
Chapter 4 Group Research Project
5.2 Area as the Limit of a Sum
5.3 Riemann Sums and the Definite Integral
5.4 The Fundamental Theorems of Calculus
5.5 Integration by Substitution
5.6 Introduction to Differential Equations
5.7 The Mean Value Theorem for Integrals; Average Value
5.8 Numerical Integration: The Trapezoidal Rule and Simpson’s Rule
5.9 An Alternative Approach: The Logarithm as an Integral
Chapter 5 Review
Chapter 5 Group Research Project
Cumulative Review Problems—Chapters 1–5
A: Introduction to the Theory of Limits
B: Selected Proofs
C: Significant Digits
D: Short Table of Integrals
J: Answers to Selected Problems