Multivariable Calculus With Matrices

Contemporary calculus instructors and students face traditional challenges as well as new ones that result from changes in the role and practice of mathematics by scientists and engineers in the world at large. As a consequence, this sixth edition of our calculus textbook is its most extensive revision since the first edition appeared in 1982. Two entire chapters of the fifth edition have been replaced in the table of contents by two new ones; most of the remaining chapters have been extensively rewritten. Nearly 160 of the book's over 800 worked examples are new for this edition and the 1850 figures in the text include 250 new computer-generated graphics. Almost 800 of its 7250 problems are new, and these are augmented by over 330 new conceptual discussion questions that now precede the problem sets. Moreover, almost 1100 new true/false questions are included in the Study Guides on the new CD-ROM that accompanies this edition. In summary, almost 2200 of these 8650-plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement. PRINCIPAL NEW FEATURES The current revision of the text features Early transcendentalsfully integrated in Semester I. Differential equationsand applications in Semester II. Linear systems and matricesin Semester III. Complete coverage of the calculus of transcendental functions is now fully integrated in Chapters 1 through 6--with the result that the Chapter 7 and 8 titles in the 5th edition table of contents do pot appear in this 6th edition. A new chapter on differential equations (Chapter 8) now appears immediately after Chapter 7 on techniques of integration. It includes both direction fields and Eider's method together with the more elementary symbolic methods (which exploit techniques from Chapter 7) and interesting applications of both first- and second-order equations. Chapter 10 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of second-semester calculus on elementary differential equations. Linear systems and matrices, ending with an elementary treatment of eigenvalues and eigenvectors, are now introduced in Chapter 11. The subsequent coverage of multivariable calculus now integrates matrix methods and terminology with the traditional notation and approach--including (for instance) introduction and extensive application of the chain rule in matrix-product form. NEW LEARNING RESOURCES Conceptual Discussion Questions.The set of problems that concludes each section is now preceded by a briefConcepts: Questions and Discussionset consisting of several open-ended conceptual questions that can be used for either individual study or classroom discussion. The Text CD-ROM.The content of the new CD-ROM that accompanies this text is fully integrated with the textbook material, and is designed specifically for use hand-in-hand with study of the book itself. This CD-ROM features the following resources to support learning and teaching: Interactive True/False Study Guidesthat reinforce and encourage student reading of the text. Ten author-written questions for each section carefully guide students through the section, and students can request individual hints suggesting where in the section to look for needed information. Live Examplesfeature dynamic multimedia and computer algebra presentations--many accompanied by audio explanations--which enhance student intuition and understanding. These interactive examples expand upon many of the textbook's principal examples; students can change input data and conditions and then observe the resulting changes in step-by-step solutions and accompanying graphs and figures.Walkthrough videosdemonstrate howEdwards, C. Henry is the author of 'Multivariable Calculus With Matrices' with ISBN 9780130648181 and ISBN 0130648183.