Mathematical models : mechanical vibrations, population dynamics, and traffic flow : (an introduction to applied mathematics) / Richard Haberman.
Editor: Englewood Cliffs, N.J. : Prentice-Hall, c1977Descripción: xiii, 402 p. : il. ; 24 cmISBN: 0135617383Tema(s): Mathematics | Mathematical models | Vibration -- Mathematical models | Ecology -- Mathematical models | Traffic flow -- Mathematical modelsOtra clasificación: 00A69 (00A71 34-01 70-01 90-01)Mechanical Vibrations [1] 1. INTRODUCTION TO MATHEMATICAL MODELS IN THE PHYSICAL SCIENCES [3] 2. newton’s law [4] 3. newton’s law AS applied to a spring-mass system [6] 4. GRAVITY [9] 5. oscillation of a spring-mass system [12] 6. DIMENSIONS AND UNITS [16] 7. QUALITATIVE AND QUANTITATIVE BEHAVIOR OF A SPRING-MASS SYSTEM [18] 8. INITIAL VALUE PROBLEM [20] 9. A TWO-MASS OSCILLATOR [23] 10. FRICTION [29] 11. OSCILLATIONS OF A DAMPED SYSTEM [33] 12. UNDERDAMPED OSCILLATIONS [34] 13. OVERDAMPED AND CRITICALLY DAMPED OSCILLATIONS [40] 14. A PENDULUM [42] 15. HOW SMALL IS SMALL? [57] 16. A DIMENSIONLESS TIME VARIABLE [53] 17. NONLINEAR FRICTIONLESS SYSTEMS [54] 18. LINEARIZED STABILITY ANALYSIS OF AN EQUILIBRIUM SOLUTION [56] 19. CONSERVATION OF ENERGY [61] 20. ENERGY CURVES [67] 21. PHASE PLANE OF A LINEAR OSCILLATOR [70] 22. PHASE PLANE OF A NONLINEAR PENDULUM [76] 23. CAN A PENDULUM STOP? [82] 24. WHAT HAPPENS IF A PENDULUM IS PUSHED TOO HARD ? [84] 25. PERIOD OF A NONLINEAR PENDULUM [87] 26. NONLINEAR OSCILLATIONS WITH DAMPING [91] 27. EQUILIBRIUM POSITIONS AND LINEARIZED STABILITY [100] 28. NONLINEAR PENDULUM WITH DAMPING [104] 29. FURTHER READINGS IN MECHANICAL VIBRATIONS [114] Population Dynamics-Mathematical Ecology [117] 30. INTRODUCTION TO MATHEMATICAL MODELS IN BIOLOGY [119] 31. POPULATION MODELS [120] 32. A DISCRETE ONE-SPECIES MODEL [122] 33. CONSTANT COEFFICIENT FIRST—ORDER DIFFERENCE EQUATIONS [129] 34. EXPONENTIAL GROWTH [131] 35. DISCRETE ONE-SPECIES MODELS WITH AN AGE DISTRIBUTION [138] 36. STOCHASTIC BIRTH PROCESSES [143] 37. DENSITY-DEPENDENT GROWTH [151] 38. PHASE PLANE SOLUTION OF THE LOGISTIC EQUATION [155] 39. EXPLICIT SOLUTION OF THE LOGISTIC EQUATION [159] 40. GROWTH MODELS WITH TIME DELAYS [162] 41. LINEAR CONSTANT COEFFICIENT DIFFERENCE EQUATIONS [171] 42. DESTABILIZING INFLUENCE OF DELAYS [178] 43. INTRODUCTION TO TWO-SPECIES MODELS [185] 44. PHASE PLANE, EQUILIBRIUM, AND LINEARIZATION [187] 45. SYSTEM OF TWO CONSTANT COEFFICIENT FIRST-ORDER DIFFERENTIAL EQUATIONS [191] A. Method of Elimination, [192] B. Systems Method (using Matrix Theory), [193] 46. STABILITY OF TWO-SPECIES EQUILIBRIUM POPULATIONS [199] 47. PHASE PLANE OF LINEAR SYSTEMS [203] A. General Remarks, [203] B. Saddle Points, [205] C. Nodes, [212] D. Spirals, [216] E. Summary, [223] 48. PREDATOR-PREY MODELS [224] 49. DERIVATION OF THE LOTKA-VOLTERRA EQUATIONS [225] 50. QUALITATIVE SOLUTION OF THE LOTKA-VOLTERRA EQUATIONS [228] 51. AVERAGE POPULATIONS OF PREDATORS AND PREYS [242] 52. MAN’S INFLUENCE ON PREDATOR-PREY ECOSYSTEMS [244] 53. LIMITATIONS OF THE LOTKA-VOLTERRA EQUATION [245] 54. TWO COMPETING SPECIES [247] 55. FURTHER READING IN MATHEMATICAL ECOLOGY [255] Traffic Flow [257] 56. INTRODUCTION TO TRAFFIC FLOW [259] 57. AUTOMOBILE VELOCITIES AND A VELOCITY FIELD [260] 58. TRAFFIC FLOW AND TRAFFIC DENSITY [265] 59. FLOW EQUALS DENSITY TIMES VELOCITY [273] 60. CONSERVATION OF THE NUMBER OF CARS [275] 61. A VELOCITY-DENSITY RELATIONSHIP [282] 62. EXPERIMENTAL OBSERVATIONS [286] 63. TRAFFIC FLOW [289] 64. STEADY-STATE CAR-FOLLOWING MODELS [293] 65. PARTIAL DIFFERENTIAL EQUATIONS [298] 66. LINEARIZATION [301] 67. A LINEAR PARTIAL DIFFERENTIAL EQUATION [303] 68. TRAFFIC DENSITY WAVES [309] 69. AN INTERPRETATION OF TRAFFIC WAVES [314] 70. A NEARLY UNIFORM TRAFFIC FLOW EXAMPLE [375] 71. NONUNIFORM TRAFFIC—THE METHOD OF CHARACTERISTICS [379] 72. AFTER A TRAFFIC LIGHT TURNS GREEN [323] 73. A LINEAR VELOCITY-DENSITY RELATIONSHIP [331] 74. AN EXAMPLE [339] 75. WAVE PROPAGATION OF AUTOMOBILE BRAKE LIGHTS [344] 76. CONGESTION AHEAD [345] 77. DISCONTINUOUS TRAFFIC [347] 78. UNIFORM TRAFFIC STOPPED BY A RED LIGHT [354] 79. A STATIONARY SHOCK WAVE [360] 80. THE EARLIEST SHOCK [363] 81. VALIDITY OF LINEARIZATION [370] 82. EFFECT OF A RED LIGHT OR AN ACCIDENT [372] 83. EXITS AND ENTRANCES [385] 84. CONSTANTLY ENTERING CARS [387] 85. A HIGHWAY ENTRANCE [389] 86. FURTHER READING IN TRAFFIC FLOW [394] INDEX [395]
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A69 H114 (Browse shelf) | Available | A-4927 |
Incluye referencias bibliográficas.
Mechanical Vibrations [1] --
1. INTRODUCTION TO MATHEMATICAL MODELS IN THE PHYSICAL SCIENCES [3] --
2. newton’s law [4] --
3. newton’s law AS applied to a spring-mass system [6] --
4. GRAVITY [9] --
5. oscillation of a spring-mass system [12] --
6. DIMENSIONS AND UNITS [16] --
7. QUALITATIVE AND QUANTITATIVE BEHAVIOR OF A SPRING-MASS SYSTEM [18] --
8. INITIAL VALUE PROBLEM [20] --
9. A TWO-MASS OSCILLATOR [23] --
10. FRICTION [29] --
11. OSCILLATIONS OF A DAMPED SYSTEM [33] --
12. UNDERDAMPED OSCILLATIONS [34] --
13. OVERDAMPED AND CRITICALLY DAMPED OSCILLATIONS [40] --
14. A PENDULUM [42] --
15. HOW SMALL IS SMALL? [57] --
16. A DIMENSIONLESS TIME VARIABLE [53] --
17. NONLINEAR FRICTIONLESS SYSTEMS [54] --
18. LINEARIZED STABILITY ANALYSIS OF AN EQUILIBRIUM SOLUTION [56] --
19. CONSERVATION OF ENERGY [61] --
20. ENERGY CURVES [67] --
21. PHASE PLANE OF A LINEAR OSCILLATOR [70] --
22. PHASE PLANE OF A NONLINEAR PENDULUM [76] --
23. CAN A PENDULUM STOP? [82] --
24. WHAT HAPPENS IF A PENDULUM IS PUSHED TOO HARD ? [84] --
25. PERIOD OF A NONLINEAR PENDULUM [87] --
26. NONLINEAR OSCILLATIONS WITH DAMPING [91] --
27. EQUILIBRIUM POSITIONS AND LINEARIZED STABILITY [100] --
28. NONLINEAR PENDULUM WITH DAMPING [104] --
29. FURTHER READINGS IN MECHANICAL VIBRATIONS [114] --
Population Dynamics-Mathematical Ecology [117] --
30. INTRODUCTION TO MATHEMATICAL MODELS IN BIOLOGY [119] --
31. POPULATION MODELS [120] --
32. A DISCRETE ONE-SPECIES MODEL [122] --
33. CONSTANT COEFFICIENT FIRST—ORDER DIFFERENCE EQUATIONS [129] --
34. EXPONENTIAL GROWTH [131] --
35. DISCRETE ONE-SPECIES MODELS WITH AN AGE DISTRIBUTION [138] --
36. STOCHASTIC BIRTH PROCESSES [143] --
37. DENSITY-DEPENDENT GROWTH [151] --
38. PHASE PLANE SOLUTION OF THE LOGISTIC EQUATION [155] --
39. EXPLICIT SOLUTION OF THE LOGISTIC EQUATION [159] --
40. GROWTH MODELS WITH TIME DELAYS [162] --
41. LINEAR CONSTANT COEFFICIENT DIFFERENCE EQUATIONS [171] --
42. DESTABILIZING INFLUENCE OF DELAYS [178] --
43. INTRODUCTION TO TWO-SPECIES MODELS [185] --
44. PHASE PLANE, EQUILIBRIUM, AND LINEARIZATION [187] --
45. SYSTEM OF TWO CONSTANT COEFFICIENT FIRST-ORDER DIFFERENTIAL EQUATIONS [191] --
A. Method of Elimination, [192] --
B. Systems Method (using Matrix Theory), [193] --
46. STABILITY OF TWO-SPECIES EQUILIBRIUM POPULATIONS [199] --
47. PHASE PLANE OF LINEAR SYSTEMS [203] --
A. General Remarks, [203] --
B. Saddle Points, [205] --
C. Nodes, [212] --
D. Spirals, [216] --
E. Summary, [223] --
48. PREDATOR-PREY MODELS [224] --
49. DERIVATION OF THE LOTKA-VOLTERRA EQUATIONS [225] --
50. QUALITATIVE SOLUTION OF THE LOTKA-VOLTERRA EQUATIONS [228] --
51. AVERAGE POPULATIONS OF PREDATORS AND PREYS [242] --
52. MAN’S INFLUENCE ON PREDATOR-PREY ECOSYSTEMS [244] --
53. LIMITATIONS OF THE LOTKA-VOLTERRA EQUATION [245] --
54. TWO COMPETING SPECIES [247] --
55. FURTHER READING IN MATHEMATICAL ECOLOGY [255] --
Traffic Flow [257] --
56. INTRODUCTION TO TRAFFIC FLOW [259] --
57. AUTOMOBILE VELOCITIES AND A VELOCITY FIELD [260] --
58. TRAFFIC FLOW AND TRAFFIC DENSITY [265] --
59. FLOW EQUALS DENSITY TIMES VELOCITY [273] --
60. CONSERVATION OF THE NUMBER OF CARS [275] --
61. A VELOCITY-DENSITY RELATIONSHIP [282] --
62. EXPERIMENTAL OBSERVATIONS [286] --
63. TRAFFIC FLOW [289] --
64. STEADY-STATE CAR-FOLLOWING MODELS [293] --
65. PARTIAL DIFFERENTIAL EQUATIONS [298] --
66. LINEARIZATION [301] --
67. A LINEAR PARTIAL DIFFERENTIAL EQUATION [303] --
68. TRAFFIC DENSITY WAVES [309] --
69. AN INTERPRETATION OF TRAFFIC WAVES [314] --
70. A NEARLY UNIFORM TRAFFIC FLOW EXAMPLE [375] --
71. NONUNIFORM TRAFFIC—THE METHOD OF CHARACTERISTICS [379] --
72. AFTER A TRAFFIC LIGHT TURNS GREEN [323] --
73. A LINEAR VELOCITY-DENSITY RELATIONSHIP [331] --
74. AN EXAMPLE [339] --
75. WAVE PROPAGATION OF AUTOMOBILE BRAKE LIGHTS [344] --
76. CONGESTION AHEAD [345] --
77. DISCONTINUOUS TRAFFIC [347] --
78. UNIFORM TRAFFIC STOPPED BY A RED LIGHT [354] --
79. A STATIONARY SHOCK WAVE [360] --
80. THE EARLIEST SHOCK [363] --
81. VALIDITY OF LINEARIZATION [370] --
82. EFFECT OF A RED LIGHT OR AN ACCIDENT [372] --
83. EXITS AND ENTRANCES [385] --
84. CONSTANTLY ENTERING CARS [387] --
85. A HIGHWAY ENTRANCE [389] --
86. FURTHER READING IN TRAFFIC FLOW [394] --
INDEX [395] --
MR, 55 #14066
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