Introduction to analysis
著者
書誌事項
Introduction to analysis
Prentice Hall, 1999
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注記
Includes index
内容説明・目次
内容説明
Designed for a one-semester undergraduate analysis course, this new text is written in a conversational, accessible style offering a great deal of examples. It gradually ascends in difficulty to help the student avoid hitting a wall.
目次
1. Real Numbers and Monotone Sequences.
2. Estimations and Approximations.
3. The Limit of a Sequence.
4. The Error Term.
5. Limit Theorems for Sequences.
6. The Completeness Principle.
7. Infinite Series.
8. Power Series.
9. Functions of One Variable.
10. Local and Global Behavior.
11. Continuity and Limits of Functions.
12. The Intermediate Value Theorem.
13. Continuous Functions on Compact Intervals.
14. Differentiation: Local Properties.
15. Differentiation: Global Properties.
16. Linearization and Convexity.
17. Taylor Approximation.
18. Integrability.
19. The Riemann Integral.
20. Derivatives and Integrals.
21. Improper Integrals.
22. Sequences and Series of Functions.
23. Infinite Sets and the Lebesgue Integral.
24. Continuous Functions on the Plane.
25. Point-sets in the Plane.
26. Integrals with a Parameter.
27. Differentiating Improper Integrals.
Appendix.
A. Sets, Numbers, and Logic.
B. Quantifiers and Negation.
C. Picard's Method.
D. Applications to Differential Equations.
E. Existence and Uniqueness of ODE Solutions.
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