A primer of infinitesimal analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Univ. Press
1998
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 122 S. Ill., graph. Darst. |
| ISBN: | 0521624010 |
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Record in the Search Index
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| adam_text | A PRIMER OF INFINITESIMAL ANALYSIS JOHN L. BELL CAMBRIDGE UNIVERSITY
PRESS CONTENTS RREJACE ACKNOWLEDGEMENTS INTRODUCTION 1 BASIC FEATURES OF
SMOOTH WORLDS 2 BASIC DIFFERENTIAL CALCULUS 2.1 THE DERIVATIVE OF A
FUNCTION 2.2 STATIONARY POINTS OF FUNCTIONS 2.3 AREAS UNDER CURVES AND
THE CONSTANCY PRINCIPLE 2.4 THE SPECIAL FUNCTIONS 3 FIRST APPLICATIONS
OF THE DIFFERENTIAL CALCULUS 3.1 AREAS AND VOLUMES 3.2 VOLUMES OF
REVOLUTION 3.3 ARC LENGTH; SURFACES OF REVOLUTION; CURVATURE 4
APPLICATIONS TO PHYSICS 4.1 MOMENTS OF INERTIA 4.2 CENTRES OF MASS 4.3
PAPPUS THEOREMS 4.4 CENTRES OF PRESSURE 4.5 STRETCHING A SPRING 4.6
FLEXURE OF BEAMS 4.7 THE CATENARY, THE LOADED CHAIN, AND THE
BOLLARD-ROPE XI XIII 1 17 26 26 29 30 32 37 37 42 45 50 50 55 56 59 61
61 64 4.8 THE KEPLER-NEWTON AREAL LAW OF MOTION UNDER A CENTRAL FORCE 68
IX X CONTENTS 5 MULTIVARIABLE CALCULUS AND APPLICATIONS 70 5.1 PARTIAL
DERIVATIVES 70 5.2 STATIONARY VALUES OF FUNCTIONS . 73 5.3 THEORY OF
SURFACES - 76 5.4 THE HEAT EQUATION 80 5.5 THE BASIC EQUATIONS OF
HYDRODYNAMICS 81 5.6 THE CAUCHY-RIEMANN EQUATIONS FOR COMPLEX FUNCTIONS
84 6 THE DEFINITE INTEGRAL. HIGHER-ORDER INFINITESIMALS 87 6.1 THE
DEFINITE INTEGRAL 87 6.2 HIGHER-ORDER INFINITESIMALS AND TAYLOR S
THEOREM 90 6.3 THE THREE NATURAL MICRONEIGHBOURHOODS OF ZERO 93 7
SYNTHETIC DIFFERENTIAL GEOMETRY 94 7.1 TANGENT VECTORS AND TANGENT
SPACES 94 7.2 VECTOR FIELDS 96 7.3 DIFFERENTIALS AND DIRECTIONAL
DERIVATIVES 96 8 SMOOTH INFINITESIMAL ANALYSIS AS AN AXIOMATIC SYSTEM
100 8.1 NATURAL NUMBERS IN SMOOTH WORLDS 106 8.2 NONSTANDARD ANALYSIS
108 APPENDIX. MODELS FOR SMOOTH INFINITESIMAL ANALYSIS 111 NOTE ON
SOURCES AND FURTHER READING 117 REFERENCES 119 INDEX 121
|
| any_adam_object | 1 |
| author | Bell, John L. 1945- |
| author_GND | (DE-588)128411570 |
| author_facet | Bell, John L. 1945- |
| author_role | aut |
| author_sort | Bell, John L. 1945- |
| author_variant | j l b jl jlb |
| building | Verbundindex |
| bvnumber | BV011953317 |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)464155469 (DE-599)BVBBV011953317 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:05Z |
| institution | BVB |
| isbn | 0521624010 |
| language | English |
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| physical | XIII, 122 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Univ. Press |
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| spelling | Bell, John L. 1945- Verfasser (DE-588)128411570 aut A primer of infinitesimal analysis John L. Bell 1. publ. Cambridge Univ. Press 1998 XIII, 122 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bell, John L. 1945- A primer of infinitesimal analysis Infinitesimalrechnung (DE-588)4072798-1 gnd |
| subject_GND | (DE-588)4072798-1 |
| title | A primer of infinitesimal analysis |
| title_auth | A primer of infinitesimal analysis |
| title_exact_search | A primer of infinitesimal analysis |
| title_full | A primer of infinitesimal analysis John L. Bell |
| title_fullStr | A primer of infinitesimal analysis John L. Bell |
| title_full_unstemmed | A primer of infinitesimal analysis John L. Bell |
| title_short | A primer of infinitesimal analysis |
| title_sort | a primer of infinitesimal analysis |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd |
| topic_facet | Infinitesimalrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008081702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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