Inside interesting integrals: (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions)
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2015
|
| Series: | Undergraduate lecture notes in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXIII, 412 S. Ill., graph. Darst. |
| ISBN: | 9781493912766 |
Staff View
MARC
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| 245 | 1 | 0 | |a Inside interesting integrals |b (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) |c Paul J. Nahin |
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Record in the Search Index
| _version_ | 1804152495623110656 |
|---|---|
| adam_text | Contents
Introduction
.......................................... 1
1.1
The Riemann Integral
............................... 1
1.2
An Example of Riemann Integration
.................... 5
1.3
The Lebesgue Integral
............................... 7
1.4
Interesting and Inside
............................. 10
1.5
Some Examples of Tricks
............................ 12
1.6
Singularities
...................................... 17
1.7
Dalzell s Integral
.................................. 22
1.8
Where Integrals Come From
.......................... 24
1.9
Last Words
....................................... 39
1.10
Challenge Problems
................................ 40
Easy Integrals
........................................ 43
2.1
Six Easy Warm-Ups
............................... 43
2.2
A New Trick
..................................... 48
2.3
Two Old Tricks, Plus a New One
...................... 55
2.4
Another Old Trick:
Euler
s
Log-Sine Integral
.............. 64
2.5
Challenge Problems
................................ 70
Feynman s Favorite Trick
............................... 73
3.1
Leibniz s Formula
................................. 73
3.2
An Amazing Integral
............................... 83
3.3
Frullani s Integral
.................................. 84
3.4
The Flip-Side of Feynman s Trick
...................... 88
3.5
Combining Two Tricks
.............................. 98
3.6
Uhler s Integral and Symbolic Integration
................ 102
3.7
The Probability Integral Revisited
...................... 105
3.8
Dini s Integral
.................................... 109
3.9
Feynman s Favorite Trick Solves a Physics Equation
........ 112
3.10
Challenge Problems
................................ 114
XXI
xxii Contents
4
Gamma and Beta Function Integrals
....................... 117
4.1
Euler s Gamma Function
............................. 117
4.2 Wallis
Integral and the Beta Function
................... 119
4.3
Double Integration Reversal
.......................... 130
4.4
The Gamma Function Meets Physics
.................... 141
4.5
Challenge Problems
................................ 145
5
Using Power Series to Evaluate Integrals
.................... 149
5.1
Catalan s Constant
................................. 149
5.2
Power Series for the Log Function
...................... 153
5.3
Zeta
Function Integrals
.............................. 161
5.4
Euler s Constant and Related Integrals
................... 167
5.5
Challenge Problems
................................ 183
6
Seven Not-So-Easy Integrals
.............................. 187
6.1
Bernoulli s Integral
................................. 187
6.2
Ahmed s Integral
.................................. 190
6.3
Coxeter s Integral
.................................. 194
6.4
The Hardy-Schuster Optical Integral
.................... 201
6.5
The Watson/van Peype Triple Integrals
.................. 206
6.6
Elliptic Integrals in a Physical Problem
.................. 212
6.7
Challenge Problems
................................ 219
7
Using /—
1
to Evaluate Integrals
.......................... 225
7.1
Euler s Formula
................................... 225
7.2
The Fresnel Integrals
............................... 227
7.3
ζ(3)
and More Log-Sine Integrals
...................... 231
7.4
ζ(2),
At Last!
..................................... 236
7.5
The Probability Integral Again
......................... 240
7.6
Beyond
Dirichleťs
Integral
........................... 241
7.7
Dirichlet Meets the Gamma Function
.................... 249
7.8
Fourier Transforms and Energy Integrals
................. 252
7.9
Weird Integrals from Radio Engineering
................ 257
7.10
Causality and Hubert Transform Integrals
................ 267
7.11
Challenge Problems
................................ 275
8
Contour Integration
.................................... 279
8.1
Prelude
......................................... 279
8.2
Line Integrals
..................................... 280
8.3
Functions of a Complex Variable
....................... 282
8.4
The Cauchy-Riemann Equations and Analytic Functions
..... 289
8.5
Green s Integral Theorem
............................ 292
8.6
Cauchy s First Integral Theorem
....................... 295
8.7
Cauchy s Second Integral Theorem
..................... 309
8.8
Singularities and the Residue Theorem
.................. 323
8.9
Integrals with Multi-valued Integrands
................... 331
8.10
Challenge Problems
................................ 339
Contents xxiii
9
Epilogue
............................................. 343
9.1 Riemann,
Prime Numbers, and the
Zeta
Function
........... 343
9.2
Deriving the Functional Equation for
ζ(β)
................. 352
9.3
Challenge Questions
................................ 365
Solutions to the Challenge Problems
........................... 369
Index
................................................... 409
Undergraduate Lecture Notes in Physics
PaulJ.Nahin
Inside Interesting Integrals
Whats the point of calculating definite integrals since you can t possibly do them all?
What makes doing the specific integrals in this book of value aren t the specific answers
well obtain, but rather the methods we ll use in obtaining those answers; methods you
can use for evaluating the integrals you will encounter in the future.
Ihis book is written in a light-hearted manner for students who have completed the
first year of college or high school AP calculus, and have just a bit of exposure to the
concept of a differentia] equation. Every result is fully derived. It you are fascinated by
definite integrals, then this is a book for you.
Definite integrals have fascinated mathematicians
ror
centuries, and in this book you ll
see how people like
Euler,
Cauchy, Riemann,
Frullarli, Dirichlet,
Lebesgue, Leibni/,
Dini,
Wallis, Eeynman,
and Hardy did battle with, and
eventuali}
solved, some very
interesting ones, indeed. All of the integrals discussed were chosen to illustrate a wide
variety of techniques ( clever tricks of the trade1), and many of them have historical
significance in physics, mathematics, and engineering.
Paul J. Nahin, with decades of experience in teaching these techniques to students at
Harvey
M
udd
Cołfege,
the Naval Postgraduate School, and the Universities of Virginia
and New Hampshire, is Professor Emeritus of Electrical Engineering at the University
of New Hampshire.
|
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| discipline | Mathematik |
| format | Book |
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| spelling | Nahin, Paul J. 1940- Verfasser (DE-588)136816614 aut Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) Paul J. Nahin New York [u.a.] Springer 2015 XXIII, 412 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate lecture notes in physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf (DE-588)4144384-6 Beispielsammlung gnd-content Integration Mathematik (DE-588)4072852-3 s DE-604 Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4939-1277-3 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499375&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499375&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nahin, Paul J. 1940- Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) Mathematische Physik (DE-588)4037952-8 gnd Integration Mathematik (DE-588)4072852-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4072852-3 (DE-588)4144384-6 |
| title | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) |
| title_auth | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) |
| title_exact_search | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) |
| title_full | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) Paul J. Nahin |
| title_fullStr | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) Paul J. Nahin |
| title_full_unstemmed | Inside interesting integrals (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) Paul J. Nahin |
| title_short | Inside interesting integrals |
| title_sort | inside interesting integrals with an introduction to contour integration a collection of sneaky tricks sly substitutions and numerous other stupendously clever awesomely wicked and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics engineering and mathematics plus 60 challenge problems with complete detailed solutions |
| title_sub | (with an introduction to contour integration) ; a collection of sneaky tricks, sly substitutions, and numerous other stupendously clever, awesomely wicked, and devilishly seductive maneuvers for computing nearly 200 perplexing definite integrals from physics, engineering, and mathematics (plus 60 challenge problems with complete, detailed solutions) |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Integration Mathematik (DE-588)4072852-3 gnd |
| topic_facet | Mathematische Physik Integration Mathematik Beispielsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499375&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027499375&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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