Dr. Euler's fabulous formula: cures many mathematical ills
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 380 S. graph. Darst. |
| ISBN: | 0691118221 9780691118222 |
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| adam_text | DR. GUTERS JAVUTOUS FORMULA CURES MANY MATHEMATICAL ILLS PAUL J. JIANIN
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD TONTENTS WHAT THIS BOOK
IS ABOUT, WHAT YOU NEED TO KNOW TO READ IT, AND WHY YOU SHOULD READ IT
XIII 7 REJACE WHEN DID MATH BECOME SEXY? XVII INTRODUCTION 1 * CONCEPT
OF MATHEMATICAL BEAUTY * EQUATIONS, IDENTITIES, AND THEOREMS *
MATHEMATICAL UGLINESS * BEAUTY REDUX ( HAPTER I. COMPLEX - HUMVERS YAN
ASSORTMENT OF ESSAYS VEIIONA THE ETEMENTARU INVOTVINA COMPLEX NUMVERSJ
1.1 THE MYSTERY OF V^-T 13 1.2 THE CAYLEY-HAMILTON AND DE MOIVRE
THEOREMS 19 1.3 RAMANUJAN SUMS A SERIES 27 1.4 ROTATING VECTORS AND
NEGATIVE FREQUENCIES 33 1.5 THE CAUCHY-SCHWARZ INEQUALITY AND FALLING
ROCKS 38 1.6 REGULAR N-GONS AND PRIMES 43 1.7 FERMAT S LAST THEOREM, AND
FACTORING COMPLEX NUMBERS 53 1.8 DIRICHLET S DISCONTINUOUS INTEGRAL 63 (
ONTENT.S C HAPTER 2. VECTOR DRIPS SOME COMPLEX PLANE PROBLEMS IN WHICH
DIRECTION MATTERS) 2.1 THE GENERALIZED HARMONIC WALK 68 2.2 BIRDS FLYING
IN THE WIND 71 2.3 PARALLEL RACES 74 2.4 CAT-AND-MOUSE PURSUIT 84 2.5
SOLUTION TO THE RUNNING DOG PROBLEM 89 CHAPTER .3. WIE SRMTIONALITU OF
71 Y HIGHER MATH AT THE SOPHOMORE LEVEL) 3.1 THE IRRATIONALITY OF 7 T 92
3.2 THE R(X) = B(X)E X + A(X) EQUATION, D-OPERATORS, INVERSE OPERATORS,
AND OPERATOR COMMUTATIVITY 95 3.3 SOLVING FOR A(X) AND B(X) 102 3.4 THE
VALUE OF R(NI) 106 3.5 THE LAST STEP (AT LAST!) 112 CHAPTER 4. COURIER
BERIES (NAMED AFTER JOURIER KIT GULER WAS THERE FIRST KIT HE WAS, ALAS,
PARTIALH} WWM!) 4.1 FUNCTIONS, VIBRATING STRINGS, AND THE WAVE EQUATION
114 4.2 PERIODIC FUNCTIONS AND EULER S SUM 128 4.3 FOURIER S THEOREM FOR
PERIODIC FUNCTIONS AND PARSEVAL S THEOREM 139 4.4 DISCONTINUOUS
FUNCTIONS, THE GIBBS PHENOMENON, AND HENRY WILBRAHAM 163 4.5 DIRICHLET S
EVALUATION OF GAUSS S QUADRATIC SUM 173 4.6 HURWITZ AND THE
ISOPERIMETRIC INEQUALITY 181 CONTENTS CHAPTER 5. JOURIER STITEQRATS
(WHAT HAPPENS AS THE PERIOD OF A PERIODIC FUNCTION VECOMES INFINITE, AND
OTHER NEAT STUI 5.1 DIRAC S IMPULSE FUNCTION 188 5.2 FOURIER S
INTEGRAL THEOREM 200 5.3 RAYLEIGH S ENERGY FORMULA, CONVOLUTION, AND THE
AUTOCORRELATION FUNCTION 206 5.4 SOME CURIOUS SPECTRA 226 5.5 POISSON
SUMMATION 246 5.6 RECIPROCAL SPREADING AND THE UNCERTAINTY PRINCIPLE 253
5.7 HARDY AND SCHUSTER, AND THEIR OPTICAL INTEGRAL 263 CHAPTER 6.
ELECTRONICS AND J */ TECHNOLOQICAL APPLICATIONS OF COMPLEX NUMBERS THAT
GUTER, WHO WAS A PRACTICAL FELLOW HIMSELF, WOULD HAVE LOVED) 6.1 WHY
THIS CHAPTER IS IN THIS BOOK 275 6.2 LINEAR, TIME-INVARIANT SYSTEMS,
CONVOLUTION (AGAIN), TRANSFER FUNCTIONS, AND CAUSALITY 275 6.3 THE
MODULATION THEOREM, SYNCHRONOUS RADIO RECEIVERS, AND HOW TO MAKE A
SPEECH SCRAMBLER 289 6.4 THE SAMPLING THEOREM, AND MULTIPLYING BY
SAMPLING AND FILTERING 302 6.5 MORE NEAT TRICKS WITH FOURIER TRANSFORMS
AND FILTERS 305 6.6 SINGLE-SIDED TRANSFORMS, THE ANALYTIC SIGNAL, AND
SINGLE-SIDEBAND RADIO 309 ( ONTENTS BYUTER: DHE **MAN AND THE
MATHEMATICAL IHUSICIST 324 ^IOTES 347 ACHIOWLEDQMENTS 375 SNDEX 377
|
| adam_txt |
DR. GUTERS JAVUTOUS FORMULA CURES MANY MATHEMATICAL ILLS PAUL J. JIANIN
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD TONTENTS WHAT THIS BOOK
IS ABOUT, WHAT YOU NEED TO KNOW TO READ IT, AND WHY YOU SHOULD READ IT
XIII 7 REJACE "WHEN DID MATH BECOME SEXY?" XVII INTRODUCTION 1 * CONCEPT
OF MATHEMATICAL BEAUTY * EQUATIONS, IDENTITIES, AND THEOREMS *
MATHEMATICAL UGLINESS * BEAUTY REDUX ( HAPTER I. COMPLEX -'HUMVERS YAN
ASSORTMENT OF ESSAYS VEIIONA THE ETEMENTARU INVOTVINA COMPLEX NUMVERSJ
1.1 THE "MYSTERY" OF V^-T 13 1.2 THE CAYLEY-HAMILTON AND DE MOIVRE
THEOREMS 19 1.3 RAMANUJAN SUMS A SERIES 27 1.4 ROTATING VECTORS AND
NEGATIVE FREQUENCIES 33 1.5 THE CAUCHY-SCHWARZ INEQUALITY AND FALLING
ROCKS 38 1.6 REGULAR N-GONS AND PRIMES 43 1.7 FERMAT'S LAST THEOREM, AND
FACTORING COMPLEX NUMBERS 53 1.8 DIRICHLET'S DISCONTINUOUS INTEGRAL 63 (
ONTENT.S C HAPTER 2. VECTOR "DRIPS SOME COMPLEX PLANE PROBLEMS IN WHICH
DIRECTION MATTERS) 2.1 THE GENERALIZED HARMONIC WALK 68 2.2 BIRDS FLYING
IN THE WIND 71 2.3 PARALLEL RACES 74 2.4 CAT-AND-MOUSE PURSUIT 84 2.5
SOLUTION TO THE RUNNING DOG PROBLEM 89 CHAPTER .3. WIE SRMTIONALITU OF
71 Y HIGHER MATH AT THE SOPHOMORE LEVEL) 3.1 THE IRRATIONALITY OF 7 T 92
3.2 THE R(X) = B(X)E X + A(X) EQUATION, D-OPERATORS, INVERSE OPERATORS,
AND OPERATOR COMMUTATIVITY 95 3.3 SOLVING FOR A(X) AND B(X) 102 3.4 THE
VALUE OF R(NI) 106 3.5 THE LAST STEP (AT LAST!) 112 CHAPTER 4. COURIER
BERIES (NAMED AFTER JOURIER KIT GULER WAS THERE FIRST KIT HE WAS, ALAS,
PARTIALH} WWM!) 4.1 FUNCTIONS, VIBRATING STRINGS, AND THE WAVE EQUATION
114 4.2 PERIODIC FUNCTIONS AND EULER'S SUM 128 4.3 FOURIER'S THEOREM FOR
PERIODIC FUNCTIONS AND PARSEVAL'S THEOREM 139 4.4 DISCONTINUOUS
FUNCTIONS, THE GIBBS PHENOMENON, AND HENRY WILBRAHAM 163 4.5 DIRICHLET'S
EVALUATION OF GAUSS'S QUADRATIC SUM 173 4.6 HURWITZ AND THE
ISOPERIMETRIC INEQUALITY 181 CONTENTS CHAPTER 5. JOURIER STITEQRATS
(WHAT HAPPENS AS THE PERIOD OF A PERIODIC FUNCTION VECOMES INFINITE, AND
OTHER NEAT STUI 5.1 DIRAC'S IMPULSE "FUNCTION" 188 5.2 FOURIER'S
INTEGRAL THEOREM 200 5.3 RAYLEIGH'S ENERGY FORMULA, CONVOLUTION, AND THE
AUTOCORRELATION FUNCTION 206 5.4 SOME CURIOUS SPECTRA 226 5.5 POISSON
SUMMATION 246 5.6 RECIPROCAL SPREADING AND THE UNCERTAINTY PRINCIPLE 253
5.7 HARDY AND SCHUSTER, AND THEIR OPTICAL INTEGRAL 263 CHAPTER 6.
ELECTRONICS AND \J */ TECHNOLOQICAL APPLICATIONS OF COMPLEX NUMBERS THAT
GUTER, WHO WAS A PRACTICAL FELLOW HIMSELF, WOULD HAVE LOVED) 6.1 WHY
THIS CHAPTER IS IN THIS BOOK 275 6.2 LINEAR, TIME-INVARIANT SYSTEMS,
CONVOLUTION (AGAIN), TRANSFER FUNCTIONS, AND CAUSALITY 275 6.3 THE
MODULATION THEOREM, SYNCHRONOUS RADIO RECEIVERS, AND HOW TO MAKE A
SPEECH SCRAMBLER 289 6.4 THE SAMPLING THEOREM, AND MULTIPLYING BY
SAMPLING AND FILTERING 302 6.5 MORE NEAT TRICKS WITH FOURIER TRANSFORMS
AND FILTERS 305 6.6 SINGLE-SIDED TRANSFORMS, THE ANALYTIC SIGNAL, AND
SINGLE-SIDEBAND RADIO 309 ( ONTENTS BYUTER: DHE **MAN AND THE
'MATHEMATICAL IHUSICIST 324 ^IOTES 347 ACHIOWLEDQMENTS 375 SNDEX 377 |
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| language | English |
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| spelling | Nahin, Paul J. 1940- Verfasser (DE-588)136816614 aut Dr. Euler's fabulous formula cures many mathematical ills Paul J. Nahin Doctor Euler's fabulous formula Princeton [u.a.] Princeton Univ. Press 2006 XX, 380 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Geschichte Mathematik Numbers, Complex Euler's numbers Mathematics History Eulersche Formel (DE-588)4359957-6 gnd rswk-swf Eulersche Formel (DE-588)4359957-6 s Geschichte z DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015748963&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nahin, Paul J. 1940- Dr. Euler's fabulous formula cures many mathematical ills Geschichte Mathematik Numbers, Complex Euler's numbers Mathematics History Eulersche Formel (DE-588)4359957-6 gnd |
| subject_GND | (DE-588)4359957-6 |
| title | Dr. Euler's fabulous formula cures many mathematical ills |
| title_alt | Doctor Euler's fabulous formula |
| title_auth | Dr. Euler's fabulous formula cures many mathematical ills |
| title_exact_search | Dr. Euler's fabulous formula cures many mathematical ills |
| title_exact_search_txtP | Dr. Euler's fabulous formula cures many mathematical ills |
| title_full | Dr. Euler's fabulous formula cures many mathematical ills Paul J. Nahin |
| title_fullStr | Dr. Euler's fabulous formula cures many mathematical ills Paul J. Nahin |
| title_full_unstemmed | Dr. Euler's fabulous formula cures many mathematical ills Paul J. Nahin |
| title_short | Dr. Euler's fabulous formula |
| title_sort | dr euler s fabulous formula cures many mathematical ills |
| title_sub | cures many mathematical ills |
| topic | Geschichte Mathematik Numbers, Complex Euler's numbers Mathematics History Eulersche Formel (DE-588)4359957-6 gnd |
| topic_facet | Geschichte Mathematik Numbers, Complex Euler's numbers Mathematics History Eulersche Formel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015748963&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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