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Introductory Real Analysis, by Frank Dangello, Michael Seyfried
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This text for courses in real analysis or advanced calculus is designed specifically to present advanced calculus topics within a framework that will help students more effectively write and analyze proofs. The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.
- Sales Rank: #895120 in Books
- Published on: 2000
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 7.50" w x .50" l, 1.35 pounds
- Binding: Hardcover
- 304 pages
Review
1. Proofs, Sets, and Functions Proofs Sets Functions Mathematical Induction 2. The Structure of R Algebraic and Other Properties of R The Completeness Axiom The Rational Numbers Are Dense in R Cardinality 3. Sequences Convergence Limit Theorems Subsequences Monotone Sequences Bolzano-Weierstrass Theorems Cauchy Sequences Limits at Infinity Limit Superior and Limit Inferior 4. Continuity Continuous Functions Continuity and Sequences Limits of Functions Consequences of Continuity Uniform Continuity Discontinuities and Monotone Functions 5. Differentiation The Derivative Mean Value Theorems Taylor's Theorem L'Hopital's Rule 6. Riemann Integration Existence of the Riemann Integral Riemann Sums Properties of the Riemann Integral Families of Riemann Integrable Functions Fundamental Theorem of Calculus Improper Integrals 7. Infinite Series Convergence and Divergence Absolute and Conditional Convergence Regrouping and Rearranging Series Multiplication of Series 8. Sequences and Series of Functions Function Sequences Preservation Theorems Series of Functions Weierstrass Approximation Theorem 9. Power Series Convergence Taylor Series 10. The Riemann-Stieltjes Theorem Monotone Increasing Integrators Families of Intergrable Functions Riemann-Stieltjes Sums Functions of Bounded Variation Integrators of Bounded Variations 11. The Topology of R Open and Closed Sets Neighborhoods and Accumulation Points Compact Sets Connected Sets Continuous Functions Bibliography. Hints and Answers. Index
Most helpful customer reviews
1 of 1 people found the following review helpful.
Math!
By S.ell
I used this book for a core class in college. This book complemented the class well. I was able to follow the book after the lecture and could still complete the examples on my own.
0 of 0 people found the following review helpful.
Compact and effective
By Jurgen Xhafaj
Very compact and effective in delivering knowledge. The hints for homework exercisese at the end of the book help a lot in developing a solving strategy for several kinds of problems, without actualky showing you the full solution (which would beat the purpose of an exercise).
2 of 3 people found the following review helpful.
This book makes the concepts in real analysis easy to understand
By E.W.C.
This book makes the concepts in real analysis easy to understand. I like it better than the Ross book, although I think it covers less topics. (Sufficient for a 1 semester Real Analysis course though)
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