| Description |
1 online resource (443 p.) |
| Series |
Textbooks in Mathematics Ser |
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Textbooks in Mathematics Ser
|
| Contents |
880-01 2.1. Main Definitions and Basic Convergence Tests -- 2.2. Raabe and Logarithmic Tests -- 2.3. The Kummer, Bertrand, and Gauss Tests -- 2.4. More Sophisticated Tests Based on Monotonicity -- 2.5. On the Universal Test -- 2.6. Tests for General Series -- 2.7. Properties of Convergent Series -- 2.8. Infinite Products -- 2.9. Worked Examples -- 2.10. Exercises -- 3. Continuity -- 3.1. Definition of Continuity -- 3.2. Limits of Functions -- 3.3. Three Fundamental Theorems -- 3.4. From the Intermediate Value Theorem to Chaos -- 3.5. Monotone Functions -- 3.6. Worked Examples -- 3.7. Exercises |
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880-01/(S Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- 1. Sequences -- 1.1. Completeness Theorems for the Real Number System -- 1.2. Stolz-Cesàro Theorem -- 1.3. Worked Examples -- 1.3.1. ε - N definition -- 1.3.2. Cauchy criterion -- 1.3.3. The squeeze theorem -- 1.3.4. Monotone convergence theorem -- 1.3.5. Upper and lower limits -- 1.3.6. Stolz-Cesàro theorem -- 1.3.7. Fixed-point theorems -- 1.3.8. Recursions with closed forms -- 1.3.9. Limits involving the harmonic numbers -- 1.4. Exercises -- 2. Infinite Numerical Series |
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4. Differentiation -- 4.1. Derivatives -- 4.2. Fundamental Theorems of Differentiation -- 4.3. L'Hôpital's Rules -- 4.4. Convex Functions -- 4.5. Taylor's Theorem -- 4.6. Worked Examples -- 4.7. Exercises -- 5. Integration -- 5.1. The Riemann Integral -- 5.2. Classes of Integrable Functions -- 5.3. The Mean Value Theorem -- 5.4. The Fundamental Theorems of Calculus -- 5.5. Worked Examples -- 5.6. Exercises -- 6. Sequences and Series of Functions -- 6.1. Pointwise and Uniform Convergence -- 6.2. Importance of Uniform Convergence -- 6.3. Two Other Convergence Theorems -- 6.4. Power Series |
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6.5. Weierstrass's Approximation Theorem -- 6.6. Worked Examples -- 6.7. Exercises -- 7. Improper and Parametric Integration -- 7.1. Improper Integrals -- 7.2. Integrals with Parameters -- 7.3. The Gamma Function -- 7.4. Worked Examples -- 7.5. Exercises -- A. List of Problems from MAA -- Bibliography -- Index |
| Notes |
Description based upon print version of record |
| Form |
Electronic book
|
| ISBN |
9781000786590 |
|
1000786595 |
|
9781003304135 |
|
1003304133 |
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