Utility of calculus

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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: EARLY TRANCENDENTALS, Sixth Edition, 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!...

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  • The art of teaching, Mark Van Doren said, is the art of assisting discovery. I have tried to write a book that assists students in discovering calculus—both for its practical power and its surprising beauty. In this edition, as in the first five editions, I aim to convey to the student a sense of the utility of calculus and develop technical competence, but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement.

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  • Edition, he has made hundreds of small improvements: new examples, additional steps in existing examples, updating of data in existing examples and exercises, new phrases and margin notes to clarify the exposition, references to other sources and web sites, redrawn art, and references to the TEC CD (Tools for Enriching Calculus). These refinements ensure that students and instructors have the best materials available. The number of pages in the book, however, remains unchanged from the 4th edition.

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  • Analyzing future distributed real-time systems, automotive and avionic systems, is requiring compositional hard real-time analysis techniques. Well known established techniques as SymTA/S and the real-time calculus are candidates solving the mentioned problem. However both techniques use quite simple event models. SymTA/S is based on discrete events the real-time calculus on continuous functions. Such simple models has been choosen because of the computational complexity of the considered mathematical operations required for real-time analysis.

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  • One of our objectives is to develop rigorously the concepts of limit, continuity, differen- tiability, and integrability, which you have seen in calculus. To do this requires a better understanding of the real numbers than is provided in calculus. The purpose of this section is to develop this understanding. Since the utility of the concepts introduced here will not become apparent until we are well into the study of limits and continuity, you should re- serve judgment on their value until they are applied. As this occurs, you should reread the applicable parts of this section.

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