附註:Includes bibliographical references (pages 607-608) and index.
Cover -- Preface -- Table of Contents -- Introduction -- Part I-Numbers and Functions, Sequences and Limits -- 1. Mathematical Modeling -- 2. Natural NUmbers Just Arent Enough -- 3. Infinity and Mathematical Induction -- 4. Rational Numbers -- 5. Functions -- 6. Polynomials -- 7. Functions, Functions and More Functions -- 8. LIpschitz Continuity -- 9. Sequences and Limits -- 10. Solving the Muddy Yard Model -- 11. Real Numbers -- 12. Functions of Real Numbers -- 13. The Bisection Algorithm -- 14. Inverse Functions -- 15. Fixed Points and Contraction Maps -- Part II-Differential and Integral Calculus -- 16. The Linearization of a Function at a Point -- 17. Analyzing the Behaviour of a Population Model -- 18. Interpretations of the Derivative -- 19. Differentiability on Intervals -- 20. Using Properties of the Derivative -- 21. The Mean Value Theorum -- 22. Derivative of Inverse Functions -- 23. Modeling with Differential Equations -- 24. Antidifferentiation -- 25. Integration -- 26. Properties of the Integral -- 27. Applications of the Integral -- 28. Rocket Propulsion and the Logarithm -- 29. Constant Relative Rate of Change and the Exponential -- 30. A Mass Spring System and the Trigonometric Functions -- 31. Fixed Point Iteration and Newton's Method -- Calculus Quagmires -- Part III-You Want Anaylsis? We've Got Your Analysis Right Here -- 32. Notions Of Continuity and Differentiability -- 33. Sequences of Functions -- 34. Relaxing Integration -- 35. Delicate Limits and Gross Behaviour -- 36. The Weierstrass Approximation Theorem -- 37. The Taylor Polynomial -- 38. Polynomial Interpolation -- 39. Nonlinear Differential Equations -- 40. The Picard Iteration -- 41. The Forward Euler Method -- A Conclusion or an Introduction? -- References.
摘要:"The book is well suited for an honors calculus sequence typically taken by first-year undergraduates planning to major in engineering, mathematics, and science and for an introductory course in rigorous real analysis offered to mathematics majors."--Jacket
