Polynomials, power series, and calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.Y.
Van Nostrand
1968
|
| Schriftenreihe: | The university series in undergraduate mathematics.
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 158 S. |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804119378540625920 |
|---|---|
| adam_text | Contents
Exercises follow each of the sections listed.
1. BACKGROUND MATERIAL 1
Order and Absolute Values 1
Functions and Function Notation 3
Sequences 5
Some Polynomial Algebra 8
2. POLYNOMIALS 15
Polynomial Functions 15
Arithmetic Sequences and Polynomial Functions 20
The Algebra of Residues 23
Composition, Inverses, and the Extraction of Roots in Rn[x] 28
3. FUNCTIONS HAVING POLYNOMIAL
APPROXIMATIONS 33
Orders of Magnitude 33
Approximation by Polynomials 37
Continuous Functions 44
Derivatives 49
4. APPLICATIONS OF THE DERIVATIVE AND
ANTIDERIVATIVE 55
Tangents: Maxima and Minima 55
Some Useful Theorems 60
Applications of the Antiderivative 65
Applications of the Derivative 71
Higher Derivatives; Taylor s Theorem 75
5. INFINITE SEQUENCES AND INFINITE SERIES 80
Convergence of Infinite Sequences 80
vii
viii CONTENTS
Cauchy Sequences 84
Infinite Series 87
Algebra of Power Series 92
6. FUNCTIONS DEFINED BY POWER SERIES 98
Interval of Convergence 98
Analytic Functions 103
The Method of Undetermined Coefficients 109
7. SERIES EXPANSIONS OF THE ELEMENTARY
FUNCTIONS 114
The Exponential Functions 114
Logarithms; the Binomial Theorem 118
Trigonometric Functions 123
Inverse Trigonometric Functions 129
Angle Measure and the Trigonometric Functions of Angles 133
Curvature and the Osculating Circle 138
APPENDICES A. Some Peculiarities of Infinite Series 143
B. Other Notations for the Derivative and
Differential 145
C. The Riemann Integral 147
ANSWERS TO SELECTED EXERCISES 149
INDEX 155
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:25:15Z |
| institution | BVB |
| language | English |
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| physical | VIII, 158 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
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| publisher | Van Nostrand |
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| series2 | The university series in undergraduate mathematics. |
| spelling | Levi, Howard Verfasser aut Polynomials, power series, and calculus Princeton, N.Y. Van Nostrand 1968 VIII, 158 S. txt rdacontent n rdamedia nc rdacarrier The university series in undergraduate mathematics. Functions Polynom (DE-588)4046711-9 gnd rswk-swf Potenzreihe (DE-588)4138577-9 gnd rswk-swf Potenzreihe (DE-588)4138577-9 s DE-604 Polynom (DE-588)4046711-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003229612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levi, Howard Polynomials, power series, and calculus Functions Polynom (DE-588)4046711-9 gnd Potenzreihe (DE-588)4138577-9 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4138577-9 |
| title | Polynomials, power series, and calculus |
| title_auth | Polynomials, power series, and calculus |
| title_exact_search | Polynomials, power series, and calculus |
| title_full | Polynomials, power series, and calculus |
| title_fullStr | Polynomials, power series, and calculus |
| title_full_unstemmed | Polynomials, power series, and calculus |
| title_short | Polynomials, power series, and calculus |
| title_sort | polynomials power series and calculus |
| topic | Functions Polynom (DE-588)4046711-9 gnd Potenzreihe (DE-588)4138577-9 gnd |
| topic_facet | Functions Polynom Potenzreihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003229612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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