978-0-534-21798-3 / 9780534217983

Calculus (Mathematics)


Publisher:Brooks/Cole Pub Co



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About the book:

CONTENTS: Review and Preview 1 Limits and Rates of Change 2 Derivatives 3 The Mean Value Theorem and Curve Sketching 4 Integrals 5 Applications of Integration 6 Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 7 Techniques of Integration 8 Further Applications of Integration 9 Parametric Equations and Polar Coordinates 10 Infinite Sequences and Series 11 Three-Dimensional Analytic Geometry and Vectors 12 Partial Derivatives 13 Multiple Integrals 14 Vector Calculus 15 Differential Equations; Appendixes; Index. EXCERPT: PREFACE - 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 two editions, I aim to convey to the student a sense of the utility of calculus and to 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. The emphasis is on understanding. Enough mathematical detail is presented so that the treatment is precise, but without allowing formalism to become obtrusive. The instructor can follow an appropriate course between intuition and rigor by choosing to include or exclude optional sections and proofs. Section 1.4, for example, on the precise definition of the limit is an optional section. Although a majority of theorems are proved in the text, some of the more difficult proofs are given in Appendix F . . .

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