微積分·第2卷(英文版)

The first edition was intended to be a synthesis of reform and traditional approaches to calculus instruction。In this second edition I continue to follow that path by empha- sizing conceptual understanding through visual，numerical，and algebraic approaches。The principal way in which this book differs from my more traditional calculus textbooks is that it is more streamlined。For instance，there is no complete chapter on techniques of integration；I don』t prove as many theorems（see the discussion on rigor on page xi）；and the material on transcendental functions and on parametric equations is interwoven throughout the book instead of being treated in separate chapters。Instruc- tors who prefer fuller coverage of traditional calculus topics should look at my books Calculus，Fourth Edition and Calculus: Early Transcendentals，Fourth Edition。 Changes in the Second Edition~The data in examples and exercises have been updated to be more timely。~ Several new examples have been added。For instance，I added the new Example 1 in Section 5.4（page 381）because students have a tough time grasping the idea of a function defined by an integral with a variable limit of integration。I think it helps to look at Examples 1 and 2 before considering the Fundamental Theorem of Calculus。