Calculus: From Graphical, Numerical, and Symbolic Points of View (Calculus Reviews

This flexible series offers instructors a true balance of traditional and conceptual approaches to calculus for math, science, and engineering majors. The Second Edition continues to focus on conceptual understanding as its primary goal and combines a variety of approaches and viewpoints to help students achieve this understanding. In addition to providing a readable tone that appeals to students and supports independent work, the authors present a balance of traditional theorems and proofs along with conceptually driven examples and exercises featuring graphical, numerical, and symbolic points of view. In addition, the text offers a wealth of diverse, well-graded exercises, including some more challenging problems. Varied exercise sets feature Basic Exercises, which help reinforce a single concept, and Further Exercises, which provide more challenge, requiring the synthesis of several ideas, deeper or more sophisticated understanding of basic concepts, or better symbol manipulation skills. Guidelines on how to assign the exercises can be found in the Instructor's Resource Manual. Topics are presented first using graphs and then through symbols. Selective emphasis on proofs presents discussion of only those proofs that contribute significantly to the understanding of calculus concepts. Derivatives appear earlier in the text, first in Section 1.4. Chapter 1 now includes complete coverage of the graphical point of view, Chapter 2 introduces and interprets the symbolic point of view, and Chapter 3 presents the combinatorial rules for calculating derivatives (e.g., the product and quotient rules). Coverage of Differential Equations appears earlier and more frequently than in the first edition. Section 2.5 presents the basic idea (a few sections after introducing the ideas of derivative and antiderivative in symbolic form). Chapter-ending Interludes —brief project-oriented expositions with exercises designed for independent student work—address topics or questions that are 'optional' or out of the given chapter's main stream of development.