tailieunhanh - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 2

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 2. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Preface xi course. Sections on algebra the theoretical basis of calculus including Rolle s Theorem and the Mean Value Theorem induction conics l Hopital s Rule for using derivatives to evaluate limits of an indeterminate form and Newton s method of using derivatives to approximate roots constitute Appendices A C D E F and G respectively. Certain appendices can be transported directly into the course. Others can be used as the basis of independent student projects. This book is a preliminary edition and should be viewed as a work in progress. The exposition and choice and sequencing of topics have evolved over the years and will I expect continue to evolve. I welcome instructors and students comments and suggestions on this edition. I can be contacted at the addresses given below. Robin Gottlieb Department of Mathematics 1 Oxford Street Cambridge MA 02138 gottlieb@ Acknowledgments A work in progress incurs many debts. I truly appreciate the good humor that participants have shown while working with an evolving course and text. For its progress to this point I d like to thank all my students and all my fellow instructors and course assistants for their feedback cooperation help and enthusiasm. They include Kevin Oden Eric Brussel Eric Towne Joseph Harris Andrew Engelward Esther Silberstein Ann Ryu Peter Gilchrist Tamara Lefcourt Luke Hunsberger Otto Bretscher Matthew Leerberg Jason Sunderson Jeanie Yoon Dakota Pippins Ambrose Huang and Barbara Damianic. Special thanks to Eric Towne without whose help writing course notes in the academic year 1996-1997 this text would not exist. Special thanks also to Eric Brussel whose support for the project has been invaluable and Peter Gilchrist whose help this past summer was instrumental in getting this preliminary edition ready. Thanks to Matt Leingang and Oliver Knill for technical assistance to Janine Clookey and Esther Silberstein for start-up assistance and to everyone in the Harvard Mathematics department .