Improper Riemann integrals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2014
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIV, 675 S. graph. Darst. |
| ISBN: | 9781466588073 |
Internformat
MARC
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| 100 | 1 | |a Roussos, Ioannis M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Improper Riemann integrals |c Ioannis Markos Roussos |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2014 | |
| 300 | |a XIV, 675 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Riemannsches Integral |0 (DE-588)4049996-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Riemannsches Integral |0 (DE-588)4049996-0 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026190384 | ||
Datensatz im Suchindex
| _version_ | 1804150650116767744 |
|---|---|
| adam_text | Contents
Acknowledgements
ix
Prologue
xi
1
Improper Riemann Integrals
1
1.1
Definitions and Examples
................. 1
1.1.1
Applications
.................... 15
1.2
Cauchy Principal Value
.................. 25
1.3
Some Criteria of Existence
................ 34
2
Real Analysis Techniques
63
2.1
Calculus Techniques
.................... 63
2.1.1
Applications
.................... 66
2.2
Integrals Dependent on Parameters
........... 75
2.3
Commuting Limits with Integrals and Derivatives
... 110
2.3.1
Commuting Limits and Integrals
......... 110
2.3.2
Commuting Limits and Derivatives
........ 128
2.4
Double Integral Technique
................ 134
2.5
Frullani Integrals
...................... 148
2.6
The Real Gamma and Beta Functions
.......... 166
2.6.1
The Gamma Function
............... 166
2.6.2
The Beta Function
................. 178
2.6.3
Applications
.................... 187
2.7
A Brief Overview of Laplace Transform
......... 217
2.7.1
Laplace Transform
................. 218
2.7.2
Inverse Laplace Transform
............. 240
2.7.3
Applications
.................... 242
3
Complex Analysis Techniques
253
3.1
Basics of Complex Variables
............... 253
3.1.1
Basic Definitions and Operations
......... 253
3.1.2
Representations and Roots of Complex Numbers
256
3.1.3
Square Roots without
De Moivre
......... 273
3.2
Power Series
—
a Quick Review
.............. 281
vii
viii Contents
3.3 Limits,
Continuity and Derivatives
............ 299
3.4
Line Integrals in the Complex Plane
........... 312
3.5
Cauchy-Goursat Theorem and Consequences
...... 323
3.5.1
Complex Preliminaries and Notation
....... 323
3.5.2
Cauchy-Goursat Theorem
............. 329
3.5.3
Complex Logarithm
................ 336
3.5.4
Complex Power Functions
............. 343
3.5.5
Properties of Complex Logarithms and Powers
. 348
3.5.6
Consequence
.................... 354
3.5.7
Cauchy Integral Formula
............. 359
3.5.8
Appendix
...................... 371
3.6
Roots, Singularities, Residues
............... 383
3.6.1
Definitions. Laurent Expansion and Examples
. . 383
3.6.2
Five Ways to Evaluate Residues
......... 396
3.7
Contour Integration and Integrals
............ 410
3.7.1
Residue Theorem and Examples
......... 410
3.7.2
Contour Integration and Improper Real Integrals
416
3.7.3
Infinite Isolated Singularities and Integrals
. . . 459
3.7.4
Infinite Isolated Singularities and Series
..... 477
3.7.5
Fourier Type Integrals
............... 503
3.7.6
Rules and Properties of the Fourier Transform
. 524
3.7.7
Applications
.................... 534
3.7.8
The Fourier Transform with Complex Argument
539
3.7.9
Improper Integrals and Logarithms
........ 559
3.7.10
Application to Inverse Laplace Transform
.... 572
3.8
Definite Integrals with Sines and Cosines
........ 592
3.8.1
Rational Functions of Sines and Cosines
..... 593
3.8.2
Other Techniques with Sines and Cosines
.... 598
3.8.3
Appendix
...................... 609
4
List of Non-elementary Integrals and Sums in Text
611
4.1
List of Non-elementary Integrals
............. 611
4.2
List of
Non-
element
ary
Sums
............... 646
Bibliography
661
Index
665
Improper Riemann Integrals gives readers the prerequisites and tools to
understand the convergence, principal value, and evaluation of the improper/
generalized Riemann integral. It also illustrates applications to science and
engineering problems.
The book contains the necessary background, theorems, and tools, along
with two lists of the most important integrals and sums computed in the text.
Numerous examples at various levels of difficulty illustrate the concepts and
theorems. The book uses powerful tools of real and complex analysis not
only to compute the examples and solve the problems but also to justify
that the computation methods are legitimate.
Features
•
Describes various methods from advanced calculus and real and
complex analysis for computing improper integrals
•
Provides the necessary theorems and results
•
Offers justification for many steps by using the tools of advanced
analysis
—
a feature often omitted from other books
•
Contains detailed examples that illustrate the tools for checking
convergence of improper integrals and evaluating their exact vaiue
when possible
•
Presents many of the same examples in different ways, highlighting
the interconnection among topics, how a problem can be viewed
in various contexts, and how different methods can solve the same
problem
•
Includes problems in every section, several projects and applications,
and an extensive bibliography at the back of the book
•
Lists all the major integrals and finite and infinite sums computed in
the text
Enriched with many examples, applications, and problems, this book helps
readers acquire a deeper understanding of the subject, preparing them for
further study. It shows how to solve the integrals without exclusively relying
on tables and computer packages.
KBG3bb
ISBN:
781466 588073
|
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| discipline | Mathematik |
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| isbn | 9781466588073 |
| language | English |
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| physical | XIV, 675 S. graph. Darst. |
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| spelling | Roussos, Ioannis M. Verfasser aut Improper Riemann integrals Ioannis Markos Roussos Boca Raton [u.a.] CRC Press 2014 XIV, 675 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Riemannsches Integral (DE-588)4049996-0 gnd rswk-swf Riemannsches Integral (DE-588)4049996-0 s DE-604 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=026190384&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=026190384&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Roussos, Ioannis M. Improper Riemann integrals Riemannsches Integral (DE-588)4049996-0 gnd |
| subject_GND | (DE-588)4049996-0 |
| title | Improper Riemann integrals |
| title_auth | Improper Riemann integrals |
| title_exact_search | Improper Riemann integrals |
| title_full | Improper Riemann integrals Ioannis Markos Roussos |
| title_fullStr | Improper Riemann integrals Ioannis Markos Roussos |
| title_full_unstemmed | Improper Riemann integrals Ioannis Markos Roussos |
| title_short | Improper Riemann integrals |
| title_sort | improper riemann integrals |
| topic | Riemannsches Integral (DE-588)4049996-0 gnd |
| topic_facet | Riemannsches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026190384&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=026190384&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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