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James Stewart's CALCULUS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Eighth Edition of SINGLE VARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Eighth Edition. From the student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.
- The data in examples and exercises have been updated. New examples have been added. The solutions to some of the existing examples have been amplified.
- Several new application-based problems in the book have been added to help students strengthen the understanding of concepts and make the leap to discovering the impact of Calculus in its various applications.
- A new project has been added: Controlling Red Blood Cell Loss During Surgery. This project describes the ANH procedure, in which blood is extracted from the patient before an operation and is replaced by saline solution.
- More than 20% of the exercises in each chapter are new.
- Stewart's writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus.
- Every concept is supported by thoughtfully worked examples—many with step-by-step explanations—and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.
- Examples are not only models for problem solving or a means of demonstrating techniques; they also encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.
- The text's clean, user-friendly design provides a clear presentation of calculus. The art program, with its functional and consistent use of color, helps students identify and review mathematical concepts more easily.
- The topic of Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration.
- Stewart draws on physics, engineering, chemistry, biology, medicine, and social science to motivate students and demonstrate the power of calculus as a problem-solving tool in a wide variety of fields.
- Stewart's presentation repeatedly provides answers to the question, “When will I use this?” Students will find many examples of how calculus is used as a problem-solving tool in fields such as physics, engineering, chemistry, biology, medicine, and the social sciences.
- Stewart's text offers an extensive collection of more than 8,000 quality exercises. Each exercise set is carefully graded, progressing from skill-development problems to more challenging problems involving applications and proofs. The wide variety of types of exercises includes many technology-oriented, thought-provoking, real, and engaging problems.
- Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. These exercises stimulate critical thinking and reinforce the concepts of calculus.
- A wealth of engaging projects reinforces concepts. "Writing Projects" ask students to compare present-day methods with those of the founders of calculus. "Discovery Projects" anticipate results to be discussed later. "Applied Projects" feature content that engages student interest and demonstrates the real-world use of mathematics. "Laboratory Projects" anticipate results to be discussed later or encourage discovery through pattern recognition.
- Comprehensive review sections follow each chapter and further support conceptual understanding. A "Concept Check" and "True/False Quiz" allow students to prepare for upcoming tests through ideas and skill-building.
- "Strategies" sections (based on George Polya's problem-solving methodology) help students select what techniques they'll need to solve problems in situations where the choice is not obvious, and help them develop true problem-solving skills and intuition.
- Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena.
- More challenging exercises called "Problems Plus" follow the end-of-chapter exercises. These sections reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.
- Four carefully crafted diagnostic tests in algebra, analytic geometry, functions, and trigonometry appear at the beginning of the text. These provide students with a convenient way to test their pre-existing knowledge and brush up on skill techniques they need to successfully begin the course. Answers are included, and students who need to improve will be referred to points in the text or on the book's website where they can seek help.
To the Student.
A Preview of Calculus.
1. FUNCTIONS AND LIMITS.
Four Ways to Represent a Function.
Mathematical Models: A Catalog of Essential Functions.
New Functions from Old Functions.
The Tangent and Velocity Problems.
The Limit of a Function.
Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit.
Principles of Problem Solving.
Derivatives and Rates of Change.
Writing Project: Early Methods for Finding Tangents.
The Derivative as a Function.
Applied Project: Building a Better Roller Coaster.
Derivatives of Trigonometric Functions.
The Chain Rule.
Applied Project: Where Should a Pilot Start Descent?
Laboratory Project: Families of Implicit Curves.
Rates of Change in the Natural and Social Sciences.
Linear Approximations and Differentials.
Laboratory Project: Taylor Polynomials.
3. APPLICATION OF DIFFERENTIATION.
Maximum and Minimum Values.
Applied Project: The Calculus of Rainbows.
The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes.
Summary of Curve Sketching.
Graphing with Calculus and Calculators.
Applied Project: The Shape of a Can.
Applied Project: Planes and Birds: Minimizing Energy.
Areas and Distances.
The Definite Integral.
Discovery Project: Area Functions.
The Fundamental Theorem of Calculus.
Indefinite Integrals and the Net Change Theorem.
Writing Project: Newton, Leibniz, and the Invention of Calculus.
The Substitution Rule.
5. APPLICATIONS OF INTEGRATION.
Areas Between Curves.
Applied Project: The Gini Index.
Volumes by Cylindrical Shells.
Average Value of a Function.
Applied Project: Calculus and Baseball.
A Numbers, Inequalities, and Absolute Values.
B Coordinate Geometry and Lines.
C Graphs of Second-Degree Equations.
E Sigma Notation.
F Proofs of Theorems.
G Complex Numbers.
H Answers to Odd-Numbered Exercises.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Includes multiple-choice and short-answer test items that key directly to the text. (Includes single variable and multivariable content).
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Complete Solutions Manual, Chapters 1-11 for Stewart's Single Variable Calculus, 8th
This manual includes worked-out solutions to every exercise in Single Variable Calculus, 8e (Chapters 1-11 of Calculus, 8e). This manual can be found on the Instructors Companion Site.
Complete Solutions Manual, Chapters 10-17 for Stewart's Multivariable Calculus, 8th
This manual includes worked-out solutions to every exercise in Multivariable Calculus, 8e (Chapters 10-17 of Calculus, 8e). This manual can be found on the Instructors Companion Site.
Fast Track to a 5 for Stewart’s Calculus, 8th
Student Solutions Manual, Chs. 10-17
This manual includes worked-out solutions to every odd-numbered exercise in Multivariable Calculus, 8e (Chapters 1-11 of Calculus, 8e).