Calculus

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 skills they need to successfully begin the course.

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.

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.

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.

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 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.

Comprehensive review sections follow each chapter and further support conceptual understanding.

"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.

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.

The data in examples and exercises have been updated. New examples have been added and the solutions to some of the existing examples have been amplified.

Several new application based problems in the book have been added to help the students strengthen the understanding of concepts and make the leap to discovering the impact of Calculus in its various applications.

Three new projects have been added: the project, Controlling Red Blood Cell Loss During Surgery describes the ANH procedure, in which blood is extracted from the patient before an operation and is replaced by saline solution. This dilutes the patient's blood so that fewer red blood cells are lost during bleeding and the extracted blood is returned to the patient after surgery. The project, Planes and Birds: Minimizing Energy asks how birds can minimize power and energy by flapping their wings versus gliding. In the project, The Speedo LZR Racer Suit, it is explained that this suit reduces drag in the water and, as a result, many swimming records were broken. Students are asked why a small decrease in drag can have a big effect on performance.

Chapter 15 (Multiple Integrals) has been streamlined by combining the first two sections so that iterated integrals are treated earlier.

More than 20% of the exercises in each chapter are new.