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To the Reader | ||
Contents | ||
Ch. I | Derivatives | |
1 | First Derivative | 3 |
2 | The Mean Value Theorem | 12 |
3 | Derivatives of Higher Order | 20 |
4 | Convex Functions of a Real Variable | 23 |
Ch. II | Primitives and Integrals | |
1 | Primitives and Integrals | 51 |
2 | Integrals Over Non-Compact Intervals | 62 |
3 | Derivatives and Integrals of Functions Depending on a Parameter | 68 |
Ch. III | Elementary Functions | |
1 | Derivatives of the Exponential and Circular Functions | 91 |
2 | Expansions of the Exponential and Circular Functions, and of the Functions Associated with Them | 105 |
Ch. IV | Differential Equations | |
1 | Existence Theorems | 163 |
2 | Linear Differential Equations | 177 |
Ch. V | Local Study of Functions | |
1 | Comparison of Functions on a Filtered Set | 211 |
2 | Asymptotic Expansions | 220 |
3 | Asymptotic Expansions of Functions of a Real Variable | 227 |
4 | Application to Series with Positive Terms | 236 |
Ch. VI | Generalized Taylor Expansions. Euler-Maclaurin Summation Formula | |
1 | Generalized Taylor Expansions | 269 |
2 | Eulerian Expansions of the Trigonometric Functions and Bernoulli Numbers | 283 |
3 | Bounds for the Remainder in the Euler-Maclaurin Summation Formula | 288 |
Ch. VII | The Gamma Function | |
1 | The Gamma Function in the Real Domain | 305 |
2 | The Gamma Function in the Complex Domain | 315 |
Index of Notation | 333 | |
Index | 335 |
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