Calculus with Early Transcendental Functions

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Success in your calculus course starts here! James Stewart's Calculus texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With Calculus With Early Transcendental Functions, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course! Key Features 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. Stewart's text has 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. Projects include: 'Writing Projects' that ask students to compare present-day methods with those of the founders of calculus; 'Laboratory Projects' featuring content that engages student interest; 'Applied Projects' that capture students' imagination and demonstrate the real-world use of mathematics; and 'Discovery Projects' that anticipate results to be discussed later. Use of technology is optional appropriate use is recommended as a powerful stimulus to enhance mathematical discovery. Students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem-solving. Many opportunities to execute complicated computations, and to verify the results of other solution methods using technology are presented. In addition to describing the benefits of using technology, the text also pays special attention to its possible misuse or misinterpretation. Notable section: Graphing with Calculus and Calculators (Section 4.6). Many exercises in the text can be solved using technology icons identify exercises where a graphing utility or a computer algebra system are recommended. Comprehensive review sections follow each chapter. A 'Concept Check' and 'True/False Quiz' allow the student to prepare for upcoming tests through ideas and skill-building. These are included to further support the idea of 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. These sections also help them develop true problem-solving skills and intuition. "Problems Plus" are collections of more challenging exercises, found at the end of every chapter. These exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text. 'Problems Plus' sections patiently show students how to approach a challenging problem. Historical and biographical margin notes enliven the course and show students that mathematics was developed to help explain and represent natural phenomena. Stewart's writing style speaks clearly and directly to the student, guiding them through key ideas, theorems, and problem solving steps. He encourages students 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. A clean, user-friendly design provides a clear presentation of calculus. The art program and its functional and consistent use of color helps students identify and review mathematical concepts more easily. Early transcendental functions (exponential and logarithmic) are introduced in Chapter 1. The topic of Differential Equations is unified by the theme of modeling. Qualitative, numerical, and analytic approaches are given equal consideration. 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. Many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution. Table of Contents 1. Functions and Models 2. Limits and Derivatives 3. Differentiation Rules 4. Applications of Differentiation 5. Integrals 6. Applications of Integration 7. Techniques of Integration 8. Further Applications of Integration 9. Differential Equations 10. Parametric Equations and Polar Coordinates 11. Infinite Sequences and Series 12. Vectors and the Geometry of Space 13. Vector Functions 14. Partial Derivatives 15. Multiple Integrals 16. Vector Calculus 17. Second-order Differential Equations Appendixes A: Coordinate Geometry and Lines B: Graphs of Second-Degree Equations C: Trigonometry D: Sigma Notation E: Proofs of Theorems F: The Logarithm Defined as an Integral G: Complex Numbers H: Answers to Odd-Numbered Exercises