Hot molecules, cold electrons: from the mathematics of heat to the development of the trans-Atlantic telegraph cable
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
[2020]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 212 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9780691191720 9780691207858 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
FOREWORD
BY
JUDITH V
GRABINER
XI
1. MATHEMATICS
AND
PHYSICS
1.1
INTRODUCTION
1
1.2
FOURIER
AND
THE
ANALYTICAL
THEORY
OF
HEAT
2
1.3
A
FIRST
PEEK
INTO
FOURIER S
MATHEMATICAL MIND
5
2.
FOURIER S
MATHEMATICS
2.1
FOURIER
SERIES
18
2.2
FOURIER
TRANSFORMS
43
2.3
FOURIER
TRANSFORMS
AND
DIRICHLET S DISCONTINUOUS
INTEGRAL
48
3.
THE HEAT EQUATION
3.1
DERIVING
THE
HEAT EQUATION
IN
AN
INFINITE MASS
57
3.2
DERIVING
THE
HEAT EQUATION
IN
A
SPHERE
63
3.3
DERIVING
THE
HEAT EQUATION
IN
A
VERY LONG,
RADIATING
WIRE 71
4.
SOLVING
THE
HEAT EQUATION
4.1
THE CASE
OF A
SEMI-INFINITE
MASS
WITH A
FINITE
THICKNESS
79
4.2
THE
CASE
OF A
COOLING
SPHERE
89
4.3
THE CASE
OF
A
SEMI-INFINITE
MASS
WITH
INFINITE
THICKNESS 94
4.4
THE CASE
OF
A
CIRCULAR
RING
102
4.5
THE CASE
OF
AN
INSULATED
SPHERE
109
$
BIIOTHEK
DEUTSCHES
MUSEUM
T?
HLUENCHE A
X
CONTENTS
5. WILLIAM
THOMSON
AND
THE
INFINITELY
LONG TELEGRAPH
CABLE
EQUATION
5.1
THE
ORIGIN
OF
THE
ATLANTIC CABLE
PROJECT
5.2
SOME
ELECTRICAL
PHYSICS
FOR
MATHEMATICIANS
5.3
DERIVATION
OF
THE
HEAT
EQUATION
AS
THE
ATLANTIC
CABLE
EQUATION
5.4 SOLVING
THE
ATLANTIC CABLE
EQUATION
6. EPILOGUE
6.1
WHAT CAME
AFTER
THE
1866
CABLE
6.2
THE CABLE
EQUATION,
DUHAMEL S
INTEGRAL,
AND
ELECTRONIC COMPUTATION
APPENDIX:
HOW
TO
DIFFERENTIATE
AN
INTEGRAL
ACKNOWLEDGMENTS
NOTES
INDEX
ALSO
BY
PAUL J. NAHIN
115
118
131
136
142
157
183
191
195
207
213
|
| adam_txt |
CONTENTS
FOREWORD
BY
JUDITH V
GRABINER
XI
1. MATHEMATICS
AND
PHYSICS
1.1
INTRODUCTION
1
1.2
FOURIER
AND
THE
ANALYTICAL
THEORY
OF
HEAT
2
1.3
A
FIRST
PEEK
INTO
FOURIER'S
MATHEMATICAL MIND
5
2.
FOURIER'S
MATHEMATICS
2.1
FOURIER
SERIES
18
2.2
FOURIER
TRANSFORMS
43
2.3
FOURIER
TRANSFORMS
AND
DIRICHLET'S DISCONTINUOUS
INTEGRAL
48
3.
THE HEAT EQUATION
3.1
DERIVING
THE
HEAT EQUATION
IN
AN
INFINITE MASS
57
3.2
DERIVING
THE
HEAT EQUATION
IN
A
SPHERE
63
3.3
DERIVING
THE
HEAT EQUATION
IN
A
VERY LONG,
RADIATING
WIRE 71
4.
SOLVING
THE
HEAT EQUATION
4.1
THE CASE
OF A
SEMI-INFINITE
MASS
WITH A
FINITE
THICKNESS
79
4.2
THE
CASE
OF A
COOLING
SPHERE
89
4.3
THE CASE
OF
A
SEMI-INFINITE
MASS
WITH
INFINITE
THICKNESS 94
4.4
THE CASE
OF
A
CIRCULAR
RING
102
4.5
THE CASE
OF
AN
INSULATED
SPHERE
109
$
BIIOTHEK
DEUTSCHES
MUSEUM
T?
HLUENCHE'A
X
CONTENTS
5. WILLIAM
THOMSON
AND
THE
INFINITELY
LONG TELEGRAPH
CABLE
EQUATION
5.1
THE
ORIGIN
OF
THE
ATLANTIC CABLE
PROJECT
5.2
SOME
ELECTRICAL
PHYSICS
FOR
MATHEMATICIANS
5.3
DERIVATION
OF
THE
HEAT
EQUATION
AS
THE
ATLANTIC
CABLE
EQUATION
5.4 SOLVING
THE
ATLANTIC CABLE
EQUATION
6. EPILOGUE
6.1
WHAT CAME
AFTER
THE
1866
CABLE
6.2
THE CABLE
EQUATION,
DUHAMEL'S
INTEGRAL,
AND
ELECTRONIC COMPUTATION
APPENDIX:
HOW
TO
DIFFERENTIATE
AN
INTEGRAL
ACKNOWLEDGMENTS
NOTES
INDEX
ALSO
BY
PAUL J. NAHIN
115
118
131
136
142
157
183
191
195
207
213 |
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| any_adam_object_boolean | 1 |
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| ctrlnum | (OCoLC)1153992259 (DE-599)BVBBV046620508 |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| era | Geschichte 1800-1900 gnd |
| era_facet | Geschichte 1800-1900 |
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| spelling | Nahin, Paul J. 1940- Verfasser (DE-588)136816614 aut Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable Paul J. Nahin Princeton ; Oxford Princeton University Press [2020] © 2020 212 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Geschichte 1800-1900 gnd rswk-swf Telegraf (DE-588)4184648-5 gnd rswk-swf Telefonleitung (DE-588)4154084-0 gnd rswk-swf Leitungsgleichungen (DE-588)4364518-5 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Atlantischer Ozean (DE-588)4003388-0 gnd rswk-swf Wärmeleitungsgleichung (DE-588)4188859-5 s Leitungsgleichungen (DE-588)4364518-5 s Telegraf (DE-588)4184648-5 s Telefonleitung (DE-588)4154084-0 s Atlantischer Ozean (DE-588)4003388-0 g Geschichte 1800-1900 z DE-604 Erscheint auch als Online-Ausgabe 978-0-691-19994-8 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032032240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nahin, Paul J. 1940- Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable Telegraf (DE-588)4184648-5 gnd Telefonleitung (DE-588)4154084-0 gnd Leitungsgleichungen (DE-588)4364518-5 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd |
| subject_GND | (DE-588)4184648-5 (DE-588)4154084-0 (DE-588)4364518-5 (DE-588)4188859-5 (DE-588)4003388-0 |
| title | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable |
| title_auth | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable |
| title_exact_search | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable |
| title_exact_search_txtP | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable |
| title_full | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable Paul J. Nahin |
| title_fullStr | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable Paul J. Nahin |
| title_full_unstemmed | Hot molecules, cold electrons from the mathematics of heat to the development of the trans-Atlantic telegraph cable Paul J. Nahin |
| title_short | Hot molecules, cold electrons |
| title_sort | hot molecules cold electrons from the mathematics of heat to the development of the trans atlantic telegraph cable |
| title_sub | from the mathematics of heat to the development of the trans-Atlantic telegraph cable |
| topic | Telegraf (DE-588)4184648-5 gnd Telefonleitung (DE-588)4154084-0 gnd Leitungsgleichungen (DE-588)4364518-5 gnd Wärmeleitungsgleichung (DE-588)4188859-5 gnd |
| topic_facet | Telegraf Telefonleitung Leitungsgleichungen Wärmeleitungsgleichung Atlantischer Ozean |
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