Power Series from a Computational Point of View
Springer-Verlag New York Inc.
978-0-387-96516-1 (ISBN)
To other scientists the rationale for the vi computational point of view might be the need for ef- cient accurate calculation; to mathematicians it is the motivation for learning theorems and the practice with inequalities, ~'s, o's, and N's.
1. Taylor Polynomials.- 1. Taylor Polynomials.- 2. Exponentials, Sines, and Cosines.- 3. The Geometric Sum.- 4. Combinations of Taylor Polynomials.- 5. Complex Taylor Polynomials.- Problems.- 2. Sequences and Series.- 1. Sequences of Real Numbers.- 2. Sequences of Complex Numbers and Vectors.- 3. Series of Real and Complex Numbers.- 4. Picard’s Theorem on Differential Equations.- 5. Power Series.- 6. Analytic Functions.- 7. Preview.- Problems.- 3. Power Series and Complex Differentiability.- 1. Paths in the Complex Plane C.- 2. Path Integrals.- 3. Cauchy’s Integral Theorem.- 4. Cauchy’s Integral Formula and Inequalities.- Problems.- 4. Local Analytic Functions.- 1. Logarithms.- 2. Local Solutions to Analytic Equations.- 3. Analytic Linear Differential Equations.- Problems.- 5. Analytic Continuation.- 1. Analytic Continuation Along Paths.- 2. The Monodromy Theorem.- 3. Cauchy’s Integral Formula and Theorem.- Problems.
Erscheint lt. Verlag | 4.5.1987 |
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Reihe/Serie | Universitext |
Zusatzinfo | VIII, 132 p. |
Verlagsort | New York, NY |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 0-387-96516-5 / 0387965165 |
ISBN-13 | 978-0-387-96516-1 / 9780387965161 |
Zustand | Neuware |
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