Graphs of elementary and special functions: handbook
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
New York
Begell House
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | VIII, 766 S. graph. Darst. |
| ISBN: | 1567001564 |
Internformat
MARC
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| 245 | 1 | 0 | |a Graphs of elementary and special functions |b handbook |c N. O. Virchenko ; I. I. Lyashko |
| 264 | 1 | |a New York |b Begell House |c 2001 | |
| 300 | |a VIII, 766 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804129007834234880 |
|---|---|
| adam_text | GRAPHS OF ELEMENTARY AND SPECIAL FUNCTIONS HANDBOOK N.O. VIRCHENKO I.I.
LYASHKO BEGELL HOUSE, INC. PUBLISHERS NEW YORK CONTENTS PART I. PLOTS OF
GRAPHS WITH ELEMENTARY METHODS CHAPTER 1. BASIC NOTIONS OF NUMBERS,
VARIABLES AND FUNCTIONS 1.1. NUMBERS. VARIABLES. FUNCTIONS 3 1.1.1. REAL
NUMBERS 3 1.1.2. CONSTANTS AND VARIABLES 7 1.1.3. CONCEPT OF A FUNCTION
7 1.1.4. METHODS OF DEFINING A FUNCTION 8 1.2. CLASSIFICATION OF
FUNCTIONS 13 1.2.1. COMPOSITION OF FUNCTIONS 13 1.2.2. INVERSE FUNCTIONS
14 1.2.3. ELEMENTARY FUNCTIONS 15 1.2.4. SINGLE-VALUED AND MULTIVALUED
FUNCTIONS 17 1.2.5. BOUNDED AND UNBOUNDED FUNCTIONS 17 1.2.6. MONOTONE
FUNCTIONS 18 1.2.7. EVEN AND ODD FUNCTIONS 19 1.2.8. PERIODIC FUNCTIONS
20 1.3. LIMIT OF A FUNCTION. CONTINUITY OF A FUNCTION 24 1.3.1. LIMIT OF
A NUMBER SEQUENCE 24 1.3.2. LIMIT OF A FUNCTION 24 1.3.3. CONTINUITY OF
A FUNCTION 28 CHAPTER 2. ANALYSIS OF FUNCTIONS FOR CONSTRUCTING GRAPHS
2.1. COORDINATE SYSTEMS 31 2.1.1. CARTESIAN COORDINATE SYSTEM 31 2.1.2.
POLAR COORDINATE SYSTEM 32 2.1.3. TRANSFORMATIONS OF THE CARTESIAN
COORDINATE SYSTEM 34 2.2., ANALYSIS OF FUNCTIONS IN THE CARTESIAN
COORDINATE SYSTEM 37 2.2.1. DOMAIN OF A FUNCTION 37 2.2.2. RANGE OF A
FUNCTION. GRAPH OF A BOUNDED FUNCTION 38 2.2.3. EVEN AND ODD FUNCTIONS.
PROPERTIES OF GRAPHS 38 2.2.4. TYPES OF SYMMETRY ? -,._ 39 2.2.5. GRAPH
OF THE INVERSE FUNCTION 41 2:2.6. PERIODICITY OF A FUNCTION .42 2.2.7.
ZEROES AND SIGNS OF FUNCTIONS 45 2.2.8. MONOTONICITY OF FUNCTIONS 46
2.2.9. CONVEXITY OF FUNCTIONS 47 2.2.10. CHARACTERISTIC POINTS OF GRAPH
50 III CONTENTS CHAPTER 3. GRAPHS OF PRINCIPAL ELEMENTARY FUNCTIONS 3.1.
POWER FUNCTION 57 3.2. EXPONENTIAL FUNCTION 75 3.3. LOGARITHMIC FUNCTION
75 3.4. TRIGONOMETRIC FUNCTIONS 76 3.5. INVERSE TRIGONOMETRIC FUNCTIONS
80 CHAPTER 4. METHODS FOR PLOTTING GRAPHS BY USING ARITHMETIC
TRANSFORMATIONS. TRANSFORMATIONS OF GRAPHS IN THE CARTESIAN COORDINATE
SYSTEM 4.1. ARITHMETIC TRANSFORMATIONS OF GRAPHS 85 4.1.1. ADDITION AND
SUBTRACTION OF GRAPHS 85 4.1.2. MULTIPLICATION AND DIVISION OF GRAPHS 93
4.2. PLOTTING GRAPHS BY USING SIMPLEST TRANSFORMATIONS 107 4.2.1.
TRANSFORMATIONS THAT DO NOT CHANGE THE SCALE 107 4.2.2. TRANSFORMATIONS
THAT CHANGE THE SCALE 109 4.2.3. PLOTTING GRAPHS OF FUNCTIONS THE
ANALYTIC EXPRESSION OF WHICH CONTAINS THE ABSOLUTE VALUE SIGN 117
CHAPTER 5. PLOTTING OF GRAPHS OF ELEMENTARY FUNCTIONS 5.1. PLOTS OF
COMPOSITIONS OF FUNCTIONS 144 5.1.1. PLOTTING THE GRAPHS OF FUNCTIONS Y
= (/[X)) R , WHERE R E Q. 148 5.1.2. PLOTTING THE GRAPH OF THE FUNCTION
= I/FIX) FROM THE GRAPH OF Y =/X). . 150
5.1.3.PLOTTINGTLIEGRAPHSOFTHEFUNCTION - V = A^ X) ,WHEREA|A-L| 0 151
5.1.4. PLOTTINGTHE GRAPHS OF THE FUNCTION^ = OG A J{X), WHERE A A- L| 0
. . . . 152 5.1.5. PLOTTING THE GRAPHS OF THE FUNCTIONS Y = SIN/(X),Y =
COSFFX) 155 5.1.6. PLOTTING THE GRAPHS OF FUNCTIONS = TAN - /(X),Y =
COT^X) 171 5.1.7. PLOTTING THE GRAPHS OF THE FUNCTIONS Y =
SACSIAJ[X),MCCOSJ{X) 180 5.1.8. PLOTTINGTHE GRAPHS OF THE FUNCTIONS =
ARCTANXX), = ARCCOT./(JF) .... 182 5.2. GRAPHS OF ALGEBRAIC FUNCTIONS
191 5.2.1. GRAPHS OF INTEGER FUNCTIONS 191 5.2.2. GRAPHS OF FRACTIONAL
RATIONAL FUNCTIONS 207 5.2.3. GRAPHS OF IRRATIONAL FUNCTIONS 214 5.3.
GRAPHS OF TRANSCENDENTAL FUNCTIONS 228 5.3.1. HYPERBOLIC FUNCTIONS 228
5.3.2. INVERSE HYPERBOLIC FUNCTIONS 235 CHAPTER 6. PLOTS OF
PARAMETRICALLY DEFINED CURVES 6.1. A STUDY OF PARAMETRICALLY DEFINED
FUNCTIONS 241 6.2. THE METHOD OF ELIMINATING THE PARAMETER/ 244 6.3.
METHODS FOR FINDING POINTS OF INTERSECTION OF THE CURVE X = AND THE
STRAIGHT LINE Y = KX 244 IV CONTENTS CHAPTER 7. PLOTS OF GRAPHS IN POLAR
COORDINATES 7.1. FUNCTIONS IN POLAR COORDINATES 259 7.2. PLOTS OF GRAPHS
IN POLAR COORDINATES 263 7.2.1. PLOTS OF THE CURVES P = A, P = ASIN CP,
P = ACOS 9, P = ACOS (CP * CP 0 ) ... 264 7.2.2. PLOTS OF THE GRAPHS OF
CURVES P = ASIN MP, P = ACOS MP (N E N, N 1) . . 267 7.2.3. PLOTS OF
THE GRAPHS OF CURVES P = A(L SIN CP), P = A(L COS 9) 272 7.2.4.
PLOTS OF GRAPHS OF CURVES P = A(L SIN MP), P = A(L COS MP) (N E N, N
1) 274 7.2.5. PLOTS OF THE GRAPHS OF CURVES P = ATANCP,P = ACOTCP 281
7.2.6. PLOTS OF THE GRAPHS OF CURVES P = OTAN MP, P = ACOT MP (N E N, N
1) . . 283 7.2.7. PLOTS OF THE GRAPHS OF CURVES P = A(L TAN 9), P =
A(L COT 9) 284 7.2.8. PLOTS OF THE GRAPHS OF CURVES P = A(L TAN MP),
P = A(L COT MP) (N E N, N 1) . 284 7.2.9.PLOTSOFTHEGRAPHSOFCURVESP =
6ASIN9, P = BACOSQ (B*A) ... 28 8 7.2.10. PLOTS OF THE GRAPHS OF
CURVES P = B ASIN NQ , P = B ACOS MP (/7EN,6*A,W L) 288 7.2.11.PLOTS
OF THE GRAPHS OF CURVES P = B ATANMP, P = B ACOTMP (6*A,NEN,WKL) 288 1
1 7.2.12. PLOTS OF THE GRAPHS OF CURVES P = A SIN /19, P = ACOS MP(/J E
N) .... 306 7.2.13. PLOTS OF THE GRAPHS OF CURVES P = A SIN 3 9, P = A
COS 3 N9 (/? E N) . . . . 306 7.2.14. PLOTS OF THE GRAPHS OF CURVES P =
A TAN 2 9, P = A COT 2 9 ( E N, N 1). 306 7.2.15. PLOTS OF CURVES P
= OTAN 3 MP, P = ACO^MP (N E N, N 1) 306 PLOTS OF CURVES P = A SIN^ 9,
P = A COS^ 9, P = ATAN^ 9, P = A COT^ 9, P ( ^ 9 ) , P = A(L COS^9), P
= A( A P = A(L COT ^ 9), P = A SIN ^ 9, P = A COS 9, P = A TAN ^ 9,
P = OC OT 9(P,A,EN) 311 7.2.16. PLOTS OF CURVES P = A/SIN* MP, P =
A/COS FC 779 (,& E N) 311 7.3. TRANSFORMATIONS OF GRAPHS IN POLAR
COORDINATES 338 CHAPTER 8. PLOTS OF IMPLICITLY DEFINED FUNCTIONS 8.1.
IMPLICITLY DEFINED FUNCTIONS 348 8.2. PLOTTING THE GRAPHS OF IMPLICITLY
DEFINED FUNCTIONS 350 8.2.1. PLOTTING THE GRAPHS BY TRANSFORMING AN
IMPLICITLY DEFINED FUNCTION INTO AN EXPLICIT FUNCTION 350 8.2.2.
PLOTTING THE GRAPHS BY USING THE METHOD OF LINEAR RELATION 351 8.2.3.
PLOTTING OF GRAPHS BY USING THE METHOD OF CELLS 353 8.3. CURVES
DEFINED BY SECOND-DEGREE ALGEBRAIC EQUATION 363 CONTENTS 8.4. CURVES
DEFINED BY A THIRD-DEGREE POLYNOMIAL 373 8.4.1. HYPERBOLIC HYPERBOLA 373
8.4.2. DEFECTIVE HYPERBOLA 383 8.4.3. PARABOLIC HYPERBOLA 391 8.4.4.
HYPERBOLISMS OF CONIC SECTIONS 394 8.4.5. TRIDENT (HYPERBOLA PARABOLISM)
400 8.4.6. PROLATE PARABOLA 400 8.4.7. CUBIC PARABOLA 403 8.5 GRAPHS OF
IMPLICITLY DEFINED FUNCTIONS CONTAINING THE ABSOLUTE VALUE SIGN . . .
403 8.6. EXAMPLES OF IMPLICITLY DEFINED FUNCTIONS FOR WHICH IT IS
CONVENIENT TO PLOT THE GRAPHS IN POLAR COORDINATES 412 CHAPTER 9. PLOTS
OF MORE COMPLICATED FUNCTIONS 9.1. FUNCTIONS DEFINED BY SEVERAL
ANALYTICAL EXPRESSIONS 414 9.2. FUNCTION^ = SIGN/JOE),.* =./LSIGN*) 414
9.3. PLOTS OF FUNCTIONS DEFINED BY A RECURRENCE RELATION 420 9.4. PLOTS
OF FUNCTIONS DEFINED IN TERMS OF LIMITS 424 9.5. PLOTS OF FUNCTIONS
Y=LF(X)] 425 9.6. PLOTS OF FUNCTIONS Y=/(M) 430 9.7. PLOTS OF FUNCTIONS
.Y = {/(*)} 430 9.8 PLOTS OF FUNCTIONS Y =/({*}) 442 PART II. PLOTS OF
GRAPHS WITH THE USE OF CALCULUS. GRAPHS OF SPECIAL FUNCTIONS CHAPTER 1.
DERIVATIVES AND DIFFERENTIALS. THEIR APPLICATIONS TO PLOTTING OF GRAPHS
1.1. DERIVATIVEOF AFUNCTIONOF ONE VARIABLE. PROPERTIES 447 1.2.
DIFFERENTIAL OF A FUNCTION OF ONE VARIABLE 449 1.3. FUNDAMENTAL THEOREMS
OF CALCULUS 450 1.4. STUDY OF FUNCTIONS BY USING DERIVATIVES 454 1.4.1.
CONDITION FOR CONSTANCY 454 1.4.2. CONDITION FOR MONOTONICITY 454 1.4.3.
MAXIMA AND MINIMA OF A FUNCTION 455 1.4.4. DETERMINING EXTREMUMS OF A
FUNCTION BY USING THE SECOND DERIVATIVE . . 457 1.4.5. DETERMINING
EXTREMUMS OF A FUNCTION BY USING TAYLOR S FORMULA .... 457 1.4.6. THE
MAXIMAL AND MINIMAL VALUE OF A FUNCTION ON AN INTERVAL 458 1.4.7.
CONVEXITY AND CONCAVITY OF A CURVE. INFLECTION POINTS 458 1.5. GRAPH
PLOTTING WITH THE USE OF DERIVATIVES 460 1.6. PLOTTING THE GRAPH OF/
(X) AND/ (X) FROM THE GRAPH OF F(X) 460 1.7. GRAPHICAL DIFFERENTIATION
462 1.8. GRAPHICAL INTEGRATION 464 1.8.1. THE RULE OF
BERNOULLI-L HOSPITAL 466 1.9. APPROXIMATIONS FOR SOLUTIONS OF EQUATIONS
468 VI CONTENTS 1.9.1. THE CHORD METHOD 468 1.9.2. THE TANGENT METHOD
(NEWTON S METHOD) 469 CHAPTER 2. GRAPHS OF ALL TYPES OF FUNCTIONS 2.1.
GRAPHS OF FUNCTIONS Y=F(X) IN CARTESIAN COORDINATES 472 2.2. PLOTS OF
PARAMETRICALLY DEFINED FUNCTIONS 489 2.2.1. A STUDY OF PARAMETRICALLY
DEFINED FUNCTIONS BY USING DERIVATIVES .... 489 2.2.2. GRAPHS OF
PARAMETRICALLY DEFINED FUNCTIONS 516 2.3. GRAPHS OF IMPLICITLY DEFINED
FUNCTIONS 520 2.4. GRAPHS OF FUNCTIONS IN POLAR COORDINATES 527 CHAPTER
3. GRAPHS OF CERTAIN REMARKABLE CURVES 3.1. ALGEBRAIC CURVES 531 3.2.
CURVES OF DEGREE TWO 533 3.2.1. THE CIRCLE 533 3.2.2. THE ELLIPSE 536
3.2.3. THE HYPERBOLA 538 3.2.4. THE PARABOLA 541 3.3. CURVES OF DEGREE
THREE 543 3.3.1. FOLIUM OF DESCARTES 544 3.3.2. CISSOID OF DIODES 547
3.3.3. STROPHOID 550 3.3.4. OPHIURIDA ; 552 3.3.5. TRISECTRIX OF
MACLAURIN 553 3.3.6. CUBIC OF TSCHIRNHAUSEN 553 3.3.7. VERSIERAOF AGNESI
555 3.3.8. SEMICUBIC PARABOLA (PARABOLA OF NEIL). . . 556 3.4. CURVES OF
DEGREE FOUR 556 3.4.1. CONCHOID 558 3.4.2. THE LIMACON OF PASCAL 562
3.4.3. CYCLOIDAL CURVES 563 3.5. TRANSCENDENTAL CURVES 596 3.5.1. SPIRAL
OF ARCHIMEDES 596 3.5.2. ALGEBRAIC SPIRALS 598 3.5.3. CATENARY : 604
3.5.4. TRACTRIX -. 606 3.5.5. QUADRATRIXOFDINOSTRATUS 608 3.5.6.
COCHLEOID 610 3.5.7. EXPONENTIAL CURVES 610 3.5.8. CYCLOID 612 3.5.9.
CURVES OF STURM 615 3.5.10. INVOLUTE OF A CIRCLE 616 3.5.11. PURSUIT
CURVE 618 3.5.12. CURVES OF RIBAUCOUR 629 VII CONTENTS 3.5.13. CORNU S
SPIRAL 620 3.5.14. RADIAL CURVES 622 CHAPTER 4. GRAPHS OF SPECIAL
FUNCTIONS 4.1. FACTORIAL FUNCTION N . BERNOULLI NUMBERS AND POLYNOMIALS.
EULER NUMBERS AND POLYNOMIALS. BINOMIAL COEFFICIENTS. POCHHAMMER
POLYNOMIALS 624 4.2. GAMMA FUNCTION AND RELATED FUNCTIONS 635 4.2.1.
GAMMA FUNCTION T(X) 635 4.2.2. BETA FUNCTION B(X,Y) (EULER INTEGRAL OF
THE FIRST KIND) 637 4.2.3. PSI FUNCTION (DIGAMMA FUNCTION V|/(X)) 638
4.2.4. THE FUNCTION G(X) (BATEMAN FUNCTION) 642 4.2.5. INCOMPLETE GAMMA
FUNCTIONS 642 4.3. INTEGRAL EXPONENTIAL AND RELATED FUNCTIONS 645 4.4.
INTEGRAL SINE AND COSINE FUNCTIONS 650 4.5. FRESNEL INTEGRALS 655 4.6.
PROBABILITY INTEGRAL AND RELATED FUNCTIONS 658 4.7. BESSEL FUNCTIONS 663
4.8. HYPERGEOMETRIC FUNCTIONS 692 4.9. ORTHOGONAL POLYNOMIALS 703 4.9.1.
GENERAL PROPERTIES OF ORTHOGONAL POLYNOMIALS 703 4.9.2. JACOBI
POLYNOMIALS/^ A P) (X) 704 4.9.3. JACOBI FUNCTIONS OF THE SECOND KIND
708 4.9.4. GEGENBAUER POLYNOMIALS (ULTRA-SPHERICAL POLYNOMIALS) 709
4.9.5. LEGENDRE POLYNOMIALS (SPHERICAL POLYNOMIALS) P N (X) 711 4.9.6.
LAGUERRE POLYNOMIALS L N (X) 714 4.9.7. HERMITE POLYNOMIALS H N (X)
718 4.9.8. CHEBYSHEV POLYNOMIALS 722 4.10. LEGENDRE FUNCTIONS 726 4.11.
ELLIPTIC INTEGRALS AND ELLIPTIC FUNCTIONS 731 4.12. MATHIEU FUNCTIONS
744 4.13. ZETA NUMBERS AND RELATED FUNCTIONS 750 4.14. HURWITZ FUNCTION
753 4.15. HEAVISIDE FUNCTION. DIRAC S DELTA FUNCTION 756 BIBLIOGRAPHY
760 INDEX 761 VIII
|
| any_adam_object | 1 |
| author | Virčenko, Nina A. 1930- Lijasko, Ivan I. |
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| ctrlnum | (OCoLC)248396693 (DE-599)BVBBV014137077 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV014137077 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:58:18Z |
| institution | BVB |
| isbn | 1567001564 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009686826 |
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| physical | VIII, 766 S. graph. Darst. |
| publishDate | 2001 |
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| publisher | Begell House |
| record_format | marc |
| spelling | Virčenko, Nina A. 1930- Verfasser (DE-588)161013988 aut Grafiki ėlementarnych i spetsial'nych funktsii Graphs of elementary and special functions handbook N. O. Virchenko ; I. I. Lyashko New York Begell House 2001 VIII, 766 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Functions Graphic methods Functions, Special Graphic methods Graph (DE-588)4021842-9 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Graph (DE-588)4021842-9 s Funktion Mathematik (DE-588)4071510-3 s DE-604 Lijasko, Ivan I. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009686826&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Virčenko, Nina A. 1930- Lijasko, Ivan I. Graphs of elementary and special functions handbook Functions Graphic methods Functions, Special Graphic methods Graph (DE-588)4021842-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4071510-3 |
| title | Graphs of elementary and special functions handbook |
| title_alt | Grafiki ėlementarnych i spetsial'nych funktsii |
| title_auth | Graphs of elementary and special functions handbook |
| title_exact_search | Graphs of elementary and special functions handbook |
| title_full | Graphs of elementary and special functions handbook N. O. Virchenko ; I. I. Lyashko |
| title_fullStr | Graphs of elementary and special functions handbook N. O. Virchenko ; I. I. Lyashko |
| title_full_unstemmed | Graphs of elementary and special functions handbook N. O. Virchenko ; I. I. Lyashko |
| title_short | Graphs of elementary and special functions |
| title_sort | graphs of elementary and special functions handbook |
| title_sub | handbook |
| topic | Functions Graphic methods Functions, Special Graphic methods Graph (DE-588)4021842-9 gnd Funktion Mathematik (DE-588)4071510-3 gnd |
| topic_facet | Functions Graphic methods Functions, Special Graphic methods Graph Funktion Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009686826&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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