Higher math for beginners: mostly physicists and engineers
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Moskva
Mir
1987
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 560 S. |
Internformat
MARC
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| 100 | 1 | |a Zel'dovič, Jakov B. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Vysšaja matematika dlja načinajuščich fizikov i technikov |
| 245 | 1 | 0 | |a Higher math for beginners |b mostly physicists and engineers |c Ya. B. Zeldovich and I. M. Yaglom |
| 264 | 1 | |a Moskva |b Mir |c 1987 | |
| 300 | |a 560 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | FOR BEGINNERS (MOSTLY PHYSICISTS AND ENGINEERS} MIR PUBLISHERS MOSCOW
CONTENTS PART 1. ELEMENTS OF HIGHER MATHEMATICS CHAPTER 1. FUNCTIONS AND
GRAPHS 23 1.1 THE FUNCTIONAL RELATIONSHIP 23 1.2 COORDINATES. DISTANCES
AND ANGLES EXPRESSED IN TERMS OF COORDINATES 26 1.3 GRAPHICAL
REPRESENTATION OF FUNCTIONS. THE EQUATION OF THE STRAIGHT LINE 30 1.4
INVERSE PROPORTIONALITY AND THE HYPERBOLA. THE PARABOLA 34 1.5
HIGHER-ORDER PARABOLAS AND HYPERBOLAS. THE SEMICUBICAL PARABOLA 42 1.6
THE INVERSE OF A FUNCTION. GRAPHS OF INVERSE FUNCTIONS 47 1.7
TRANSFORMING GRAPHS OF FUNCTIONS 50 1.8 PARAMETRIC REPRESENTATION OF A
CURVE 59 1.9* SOME ADDITIONAL TOPICS FROM ANALYTIC GEOMETRY 61 CHAPTER
2. WHAT IS A DERIVATIVE? 67 2.1 MOTION, DISTANCE, AND VELOCITY 67 2.2*
SPECIFIC HEAT CAPACITY OF AN OBJECT. THERMAL EXPANSION 70 2.3 THE
DERIVATIVE OF A FUNCTION. SIMPLE EXAMPLES OF CALCULATING DERIVATIVES 72
2.4 PROPERTIES OF DERIVATIVES. APPROXIMATING THE VALUES OF A FUNCTION BY
MEANS OF A DERIVATIVE 75 2.5 A TANGENT TO A CURVE 80 2.6 INCREASE AND
DECREASE OF FUNCTIONS. MAXIMA AND MINIMA 85 2.7 THE SECOND DERIVATIVE OF
A FUNCTION. CONVEXITY AND CONCAVITY OF A CURVE. POINTS OF INFLECTION 89
CHAPTER 3. WHAT IS AN INTEGRAL? 92 3.1 DETERMINING DISTANCE FROM THE
RATE OF MOTION. THE AREA ROUNDED BY A CURVE 92 3.2 THE DEFINITE INTEGRAL
96 3.3 THE RELATIONSHIP BETWEEN THE INTEGRAL AND THE DERIVATIVE 101 3.4
THE INDEFINITE INTEGRAL 104 3.5 PROPERTIES OF INTEGRALS 109 3.6 EXAMPLES
AND APPLICATIONS 112 CHAPTER 4. CALCULATION OF DERIVATIVES 127 4.1 THE
DIFFERENTIAL 127 4.2 DERIVATIVES OF A SUM AND OF A PRODUCT OF FUNCTIONS
132 4.3 THE COMPOSITE FUNCTION. THE DERIVATIVE OF THE FRACTION OF TWO
FUNCTIONS 134 4.4 THE INVERSE FUNCTION. PARAMETRIC REPRESENTATION OF A
FUNCTION 135 4.5 THE POWER FUNCTION 138 4.6 DERIVATIVES OF ALGEBRAIC
FUNCTIONS 139 4.7 THE EXPONENTIAL FUNCTION 140 4.8 THE NUMBER E 142 4.9
LOGARITHMS 145 20 CONTENTS 4.10 TRIGONOMETRIE FUNCTIONS 148 4.11 INVERSE
TRIGONOMETRIE FUNCTIONS 151 4.12 DIFIERENTIATING FUNCTIONS DEPENDENT ON
A PARAMETER AND FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DERIVATIVES 153
4.13 THE DERIVATIVE OF AN IMPLICIT FUNCTION 158 GHAPTER 5. INTEGRATION
TECHNIQUES 162 5.1 STATEMENT OF THE PROBLEM 162 5.2 ELEMENTARY INTEGRALS
162 5.3 GENERAL PROPERTIES OF INTEGRALS 164 5.4 INTEGRATION BY PARTS 166
5.5 CHANGE OF VARIABLES IN INTEGRATION 168 5.6 CHANGE OF VARIABLE IN A
DEFINITE INTEGRAL 170 5.7 INTEGRATING FUNCTIONS DEPENDENT ON A PARAMETER
173 CHAPTER 6. SERIES. SIMPLE DIFFERENTIAL EQUATIONS 177 6.1 A SERIES
REPRESENTATION OF A FUNCTION 177 6.2 COMPUTING THE VALUES OF FUNCTIONS
BY MEANS OF SERIES 184 6.3 CASES WHERE SERIES EXPANSIONS CANNOT BE
APPLIED. THE GEOMETRIE PROGRES- SION 187 6.4 THE BINOMIAL THEOREM FOR
INTEGRAL AND FRACTIONAL EXPONENTS 192 6.5 THE ORDER OF INCREASE AND
DECREASE OF FUNCTIONS. L HOSPITAL S RULE 194 6.6 FIRST-ORDER
DIFFERENTIAL EQUATIONS. THE CASE OF VARIABLES SEPARABLE 198 6.7* THE
DIFFERENTIAL EQUATION FOR WATER FLOW FROM A VESSEL 202 CHAPTER 7.
INVESTIGATION OF FUNCTIONS. SOME PROBLEMS FROM GEOMETRY 214 7.1 SMOOTH
MAXIMA AND MINIMA 214 7.2 OTHER TYPES OF MAXIMA AND MINIMA. SALIENT
POINTS AND DISCONTINUITIES. THE LEFT AND RIGHT DERIVATIVES OF A FUNCTION
221 7.3 INVESTIGATING MAXIMA AND MINIMA OF FUNCTIONS DEPENDENT ON A
PARAMETER 227 7.4* CONVEX FUNCTIONS AND ALGEBRAIC INEQUALITIES 234 7.5
COMPUTING AREAS 241 7.6* ESTIMATING SUMS AND PRODUCTS 245 7.7* MORE ON
NATURAL LOGARITHMS 250 7.8 AVERAGE, OR MEAN, VALUES 253 7.9 ARE LENGTH
260 7.10 CURVATURE AND THE OSCULATING CIRCLE 265 7.11 SOLID GEOMETRY
APPLICATIONS OF INTEGRAL CALCULUS 271 7.12 CURVE SKETCHING 275 PART 2.
HIGHER MATH APPLIED TO PROBLEMS OF PHYSICS AND ENGINEERING CHAPTER 8.
RADIOACTIVE DECAY AND NUCLEAR FISSION 281 8.1 THE BASIC CHARACTERISTICS
OF RADIOACTIVE DECAY 281 8.2 MEASURING THE MEAN LIFETIME OF RADIOACTIVE
ATOMS 283 8.3 SERIES DISINTEGRATION (RADIOACTIVE FAMILY) 289 8.4
INVESTIGATING THE SOLUTION FOR A RADIOACTIVE FAMILY (SERIES) 291 8.5 THE
CHAIN REACTION IN THE FISSION OF URANIUM 294 8.6 MULTIPLICATION OF
NEUTRONS IN A LARGE SYSTEM 295 8.7 ESCAPE OF NEUTRONS 297 . . 8.8
CRITICAL MASS 298 8.9 SUBCRITICAL AND SUPERCRITICAL MASS FOR A CONSTANT
SOURCE OF NEUTRONS 299 8.10 THE CRITICAL MASS 301 CHAPTER 9. MECHANICS
303 9.1 FORCE, WORK, AND POWER 303 9.2 ENERGY 308 9.3 EQUILIBRIUM AND
STABILITY 312 9.4 NEWTON S SECOND LAW 316 21 9.5 IMPULSE 317 9.6 KINETIC
ENERGY 320 9.7 INERTIAL AND NONINERTIAL REFERENCE FRAMES 321 9.8*
THEJGALILEAN TRANSFORMATIONS. ENERGY IN A MOVING REFERENCE FRAME 324
9.9* THE PATH OF A PROJECTILE. THE SAFETY PARABOLA 327 9.10 THE MOTION
OF A BODY IN OUTER SPACE 331-,V * * 9.11 JET PROPULSION AND
TSIOLKOVSKY S FORMULA 334 9.12 THE MASS, CENTER OF GRAVITY, AND MOMENT
OF INERTIA OF A ROD 337 9.13*CENTERS OF GRAVITY OF A STRING AND OF A
PLATE 342 9.14 THE MOTION OF A BODY IN A MEDIUM THAT RESISTS THIS MOTION
WITH A FORCE DEPENDENT SOLELY ON THE VELOCITY 346 9.15*THE MOTION OF A
BODY IN A FLUID 350 CHAPTER 10. OSCILLATIONS 354 10.1 MOTION UNDER THE
ACTION OF AN ELASTIC FORCE 354 10.2 THE CASE OF A FORCE PROPORTIONAL TO
DEVIATION. HARMONIE OSCILLATIONS 357 10.3 PENDULUMS 360 10.4 OSCILLATION
ENERGY. DAMPED OSCILLATIONS 363 10.5 FORCED OSCILLATIONS AND RESONANCE
366 10.6 ON EXACT AND APPROXIMATE SOLUTIONS OF PHYSICAL PROBLEMS 368
10.7 COMBINING OSCILLATIONS. BEATS 372 10.8 THE VIBRATIONS OF A STRING
375 10.9 HARMONIE ANALYSIS. FOURIER SERIES 380 CHAPTER 11. THE THERMAL
MOTION OF MOLECULES. THE DISTRI- BUTION OF AIR DENSITY IN THE ATMOSPHERE
387 11.1 THE CONDITION FOR EQUILIBRIUM IN THE ATMOSPHERE 387 11.2 THE
RELATIONSHIP BETWEEN DENSITY AND PRESSURE 388 11.3 DENSITY DISTRIBUTION
389 11.4 THE MOLECULAR KINETIC THEORY OF DENSITY DISTRIBUTION 391 11.5
THE BROWNIAN MOVEMENT AND KINETIC-ENERGY DISTRIBUTION OF MOLECULES 393
11.6 RATES OF CHEMICAL REACTIONS 395 11.7 EVAPORATION. THE EMISSION
CURRENT OF A CATHODE 396 CHAPTER 12. ABSORPTION AND EMISSION OF LIGHT.
LASERS 399 12.1 ABSORPTION OF LIGHT: STATEMENT OF THE PROBLEM AND A
ROUGH ESTIMATE 399 12.2 THE ABSORPTION EQUATION AND ITS SOLUTION 400
12.3 THE RELATIONSHIP BETWEEN EXACT AND APPROXIMATE ABSORPTION CALCULA-
TIONS 400 12.4 THE EFFECTIVE CROSS SECTION 402 12.5 ATTENUATION OF A
CHARGED-PARTICLE FLUX OF ALPHA AND BETA RAYS 403 12.6* ABSORPTION AND
EMISSION OF LIGHT BY A HOT GAS 405 12.7* RADIATION IN THERMODYNAMIC
EQUILIBRIUM 407 12.8* EMISSION PROBABILITY AND THE CONDITIONS FOR
THERMODYNAMIC EQUILIBRIUM 410 12.9* LASERS 414 CHAPTER 13. ELECTRIC
CIRCUITS AND OSCILLATORY PHENOMENA IN THEM 418 13.1 BASIC CONCEPTS AND
UNITS OF MEASUREMENT 418 13.2 DISCHARGE OF A CAPACITOR THROUGH A
RESISTOR 423 13.3 OSCILLATIONS IN A CAPACITANCE CIRCUIT WITH SPARK GAP
425 13.4 THE ENERGY OF A CAPACITOR 428 13.5 INDUCTANCE CIRCUIT 431 13.6
BREAKING AN INDUCTANCE CIRCUIT 433 13.7 THE ENERGY OF INDUCTANCE 435
13.8 THE OSCILLATORY CIRCUIT 439 13.9 DAMPED OSCILLATIONS 441 13.10*THE
CASE OF A LARGE RESISTANCE 443 13.11 ALTERNATING CURRENT 444 13.12
AVERAGE QUANTITIES. POWER AND PHASE SHIFT 447 13.13 AN
ALTERNATING-CURRENT OSCILLATORY CIRCUIT. SERIES RESONANCE 449 13.14
INDUCTANCE AND CAPACITANCE IN PARALLEL. PARALLEL RESONANCE 451 22
CONTENTS 13.15 GENERAL PROPERTIES OF RESONANCE IN A LINEAR SYSTEM 452
13.16*DISPLACEMENT CURRENT AND THE ELECTROMAGNETIC THEORY OF LIGHT 453
13.17*NONLINEAR RESISTANCE AND THE TUNNEL DIODE 454 PART 3. SOME
ADDITIONAL TOPICS CHAPTER 14. COMPLEX NUMBERS 458 14.1 BASIC PROPERTIES
OF COMPLEX NUMBERS 458 14.2 RAISING A NUMBER TO AN IMAGINARY POWER AND
THE NUMBER E 463 14.3 TRIGONOMETRIE FUNCTIONS AND THE LOGARITHM 466
14.4* TRIGONOMETRIE FUNCTIONS OF A PURELY IMAGINARY INDEPENDENT
VARIABLE. HYPERBOLIC FUNCTIONS 469 CHAPTER 15. FUNCTIONS THE PHYSICIST
NEEDS 475 15.1 ANALYTIC FUNCTIONS OF A REAL VARIABLE 475 15.2 THE
DERIVATIVE |OF A FUNCTION OF A COMPLEX VARIABLE 478 CHAPTER 16. DIRAC S
REMARKABLE DELTA FUNCTION 486 16.1 VARIOUS WAYS OF DEFMING A FUNCTION
486 16.2 DIRAC AND HIS FUNCTION 487 16.3 DISCONTINUOUS FUNCTIONS AND
THEIR DERIVATIVES 489 16.4 REPRESENTING THE |DELTA FUNCTION BY FORMULAS
493 CHAPTER 17. APPLYING FUNCTIONS OF A COMPLEX VARIABLE AND THE DELTA
FUNCTION 496 17.1 COMPLEX NUMBERS AND MECHANICAL OSCILLATIONS 496 17.2
INTEGRALS IN THE COMPLEX PLANE 500 17.3 ANALYTIC FUNCTIONS OF A COMPLEX
VARIABLE AND LIQUID FLOW 507 17.4 APPLICATION OF THE DELTA FUNCTION 512
CONCLUSION. WHAT NEXT? 516 SELECTED READINGS 530 APPENDICES 532 1.
DERIVATIVES 532 2. INTEGRALS OF SOME FUNCTIONS 532 3. SERIES EXPANSIONS
534 4. NUMERICAL TABLES 534 5. THE INTERNATIONAL SYSTEM, OR SI 536 6.
GREEK ALPHABET 536 HINTS, ANSWERS, AND SOLUTIONS 537 NAME INDEX 555
SUBJECT INDEX 557
|
| any_adam_object | 1 |
| author | Zel'dovič, Jakov B. Jaglom, Isaak M. 1921-1988 |
| author_GND | (DE-588)117713511 |
| author_facet | Zel'dovič, Jakov B. Jaglom, Isaak M. 1921-1988 |
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| building | Verbundindex |
| bvnumber | BV025156367 |
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| discipline | Chemie / Pharmazie |
| format | Book |
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| indexdate | 2024-07-09T22:28:04Z |
| institution | BVB |
| language | English |
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| physical | 560 S. |
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| spelling | Zel'dovič, Jakov B. Verfasser aut Vysšaja matematika dlja načinajuščich fizikov i technikov Higher math for beginners mostly physicists and engineers Ya. B. Zeldovich and I. M. Yaglom Moskva Mir 1987 560 S. txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf Chemiker (DE-588)4009836-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematik (DE-588)4037944-9 s Chemiker (DE-588)4009836-9 s DE-604 Jaglom, Isaak M. 1921-1988 Verfasser (DE-588)117713511 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019802031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zel'dovič, Jakov B. Jaglom, Isaak M. 1921-1988 Higher math for beginners mostly physicists and engineers Mathematik (DE-588)4037944-9 gnd Chemiker (DE-588)4009836-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4009836-9 (DE-588)4151278-9 |
| title | Higher math for beginners mostly physicists and engineers |
| title_alt | Vysšaja matematika dlja načinajuščich fizikov i technikov |
| title_auth | Higher math for beginners mostly physicists and engineers |
| title_exact_search | Higher math for beginners mostly physicists and engineers |
| title_full | Higher math for beginners mostly physicists and engineers Ya. B. Zeldovich and I. M. Yaglom |
| title_fullStr | Higher math for beginners mostly physicists and engineers Ya. B. Zeldovich and I. M. Yaglom |
| title_full_unstemmed | Higher math for beginners mostly physicists and engineers Ya. B. Zeldovich and I. M. Yaglom |
| title_short | Higher math for beginners |
| title_sort | higher math for beginners mostly physicists and engineers |
| title_sub | mostly physicists and engineers |
| topic | Mathematik (DE-588)4037944-9 gnd Chemiker (DE-588)4009836-9 gnd |
| topic_facet | Mathematik Chemiker Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019802031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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