Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Acheson David — From calculus to chaos Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: From calculus to chaos Автор: Acheson David Аннотация: What is calculus really for? It helps tell us how - and why - things change with time. This is the purpose of dynamics, which lies at the heart of much of applied mathematics, science and engineering. Acheson explains why student mathematics is useful by exploring the most interesting ideas of calculus and dynamics from Newton to the present. Язык: Рубрика: Математика/Численные методы/Моделирование физических процессов/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997 Количество страниц: 269 Добавлена в каталог: 18.02.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель 17 Acceleration, centripetal      72 Acceleration, components in polar coordinates      75 Action, least      108 Action, stationary      110 Amplitude      55 Angular frequency      57 Angular velocity      70 147 Area under curve      11 Autonomous equations, defined      25 Autonomous equations, system of      33 64 154 156 166 174 Bernoulli, D.      61 173 Bifurcation      138 Bifurcation, imperfect      142 Bifurcation, subcritical      142 Bifurcation, supercritical      139 Binomial series      14 Blow-up      25 Boundary layer, idea      128 Boundary layer, separation      131 Boundary layer, viscous      129 Buckling of elastic strut      135 Calculus of several variables      94 106 Calculus of variations      110 Calculus, brief review      10 Catastrophe      140 145 Central force, deduced from orbit      91 Central force, equal-area rule      76 Central force, equations of motion      74 Centre of mass      84 Centripetal force      72 75 Chain rule      12 Chain rule for partial derivatives      106 Chaos      152 Chaos and forecasting      159 Chaos, conditions for      156 166 Chaos, from simple iteration      167 Chaos, period-doubling route to      163 Chaos, stretch-and-fold mechanism      161 circular motion      72 75 150 Close encounter      87 Coexistence of solutions      see “Multiple solution” comet      80 Complex variables      18 74 Conservation of energy      33 83 Convergence of numerical method      40 43 45 48 Convergence of series      15 Critical point      see “Equilibrium point” Cubic oscillator, forced      152 Damping      see “Friction” Degrees of freedom      59 Derivative      10 Derivative, partial      94 Diffusion equation      99 Dimensionless variables      see “Non-dimensionalization” Direction field      22 Divergence      121 160 Double-diffusive instability      105 Duffing equation, forced      164 e      16 Earth-moon system      90 Eccentricity of ellipse      72 Elastica      135 Electromagnetic waves      97 ellipse      71 79 82 Energy and Lagrange’s equations      108 113 Energy in central force motion      83 85 115 Energy, kinetic      33 83 Energy, potential      33 36 83 Epidemic      26 Equilibrium point      55 135 138 145 157 Euler buckling      135 143 Euler — Lagrange equation      111 Euler, L.      4 18 38 58 75 111 119 123 135 147 Euler’s (numerical) method      38 Euler’s (numerical) method, improved      50 Euler’s equations for rigid body      147 Exponential function      16 Finite-difference method      see “Numerical methods” Flow in phase space      121 160 161 Flow in teacup      130 Flow, down pipe      133 149 Flow, past circular cylinder      119 Focus, of ellipse      72 frequency      57 Frequency, natural      58 60 106 164 172 176 179 Friction      57 70 139 148 151 169 174 Galileo      3 General solution      29 Gravitation, inverse square law      73 78 Gyroscope      148 Hamilton’s principle      110 Heat equation      99 Homogeneous linear equations      29 Hysteresis      142 146 149 151 165 Imperfections      142 145 Improved Euler method      50 Improved Euler method, justification of      49 53 Incompressibility      121 Indian Rope Trick      182 Initial conditions, independence of      153 Initial conditions, sensitive dependence on      152 158 178 Instability of central force orbit      150 Instability of elastic strut      135 Instability of numerical method      102 Instability of pipe flow      133 149 Instability of spinning object      146 Instability of tippy-top      148 Instability, due to friction      148 Instability, due to gravity      135 143 Instability, due to spring      136 Instability, due to vibration      175 Instability, idea of      135 Integrating factors, method of      23 Integration      10 Integration by parts      12 Integration by substitution      12 Inverse square law      73 Inverted pendulum theorem      179 Jump phenomenon between an equilibrium and a periodic motion      151 Jump phenomenon between equilibria      141 143 146 Jump phenomenon between oscillations      165 Kepler’s rules of planetary motion      71 Lagrange, J.-L.      114 Lagrange’s equations of motion      114 118 Laws of motion      5 54 59 75 93 114 123 Least action, principle of      108 Leibniz, G. W.      12 Light, reflection of      108 Light, refraction of      117 Light, velocity of      97 Limit cycle      154 Linear differential equations      23 29 linear oscillator      30 46 55 65 Linear stability theory      136 Linearization of equations      55 137 Lorenz equations      158 Matchbox, spinning      146 Mathieu’s equation      175 Maxima and minima      19 110 Minimal surface      112 117 Mode of oscillation      see “Frequency natural” Moments of inertia      147 Mullin, T.      180 193 Multiple solutions, a periodic oscillation and a chaotic oscillation      164 Multiple solutions, an equilibrium and a periodic oscillation      151 169 184 Multiple solutions, different equilibria      138 141 145 Multiple solutions, different periodic oscillations      165 167 186 Natural frequency      see “Frequency natural” Navier — Stokes equations      123 Newton, Sir Isaac      1 2 15 38 77 No-slip condition      124 Non-autonomous equations      33 34 43 152 157 164 174 Non-dimensionalization      47 66 81 86 101 137 144 174 Non-uniqueness      see Multiple solutions Nonlinear differential equations, defined      23 (see also “Linear differential equations”) Nonlinear differential equations, examples of      25 43 66 81 113 123 177 Numerical methods for ordinary differential equations      37 Numerical methods for partial differential equations      100 Orbit, planetary      71 73 Oscillations of string      106 Oscillations, chaotic      152 Oscillations, coupled      61 Oscillations, damped      57 Oscillations, forced      58 Oscillations, multiple modes      60 Oscillations, nonlinear      64 Oscillations, relaxation      154 Oscillations, resonant      58 165 Oscillations, self-excited      154 Partial derivatives      94 105 Partial differential equations      94 99 104 123 Particle motion, equations of      5 Particular integral      31 Pattern formation, biological      104 Pendulum with spring      136 Pendulum with vibrated pivot      168 173 177 179 Pendulum, and planetary motion      171 Pendulum, chaotic      176 Pendulum, coupled pair      63 Pendulum, double      60 171 177 Pendulum, inverted, dancing oscillation      170 186 Pendulum, inverted, double      186 Pendulum, inverted, simple      168 Pendulum, inverted, theorem      179 Pendulum, inverted, triple      181 Pendulum, oscillations, free, large      66 Pendulum, oscillations, free, small      54 Pendulum, simple      54 66 118 Pendulum, torque-driven      151 Pendulum, triple      173 180 Pendulum, upside-down      see “Inverted” Pendulum, whirling      68 70 151 Pendumonium      176 Period of oscillation      55 57 Period of planetary orbit      81 Period-doubling      163 Phase paths      65 Phase space      33 Phase space, cylindrical      68 Phase space, flow in      121 Planetary orbit data      73 Poincare — Bendixon theorem      156 Poincare, H.      91 156 Polar coordinates      74 Prandtl, L.      130 Predictability      159 Projectile problem      2 Reaction-diffusion equations      104 Resonance      58 69 Reversibility      125 Reynolds number      124 Rossler equations      161 Rounding errors      42 45 Runge — Kutta method      51 Scaling      see “Non-dimensionalization” Sensitivity to initial conditions      152 158 178 Separable first-order equations      27 32 Series, convergence of      15 Series, Taylor      13 Simple harmonic oscillator      see “Linear oscillator” Soap film      112 117 Spermatazoa, swimming      126 Spin-down of cup of tea      130 Spinning top      148 Spring constant      56 136 Spring-mass system, instability of      136 143 Spring-mass system, oscillations of      55 60 118 Stability      see “Instability” Standing wave      105 State of system      65 Stationary point      19 Step size      see “Time step” Step-by-step methods      see “Numerical methods” Strange Attractor      160 Stretch-and-fold      161 Symmetry and conservation laws      116 System, first-order      31 34 46 Taylor series      13 Three-body problem      85 Three-body problem, restricted      89 Time step      39 Time step, halving, as a check      45 53 83 159 Time step, variable      51 83 87 Tippy-top      148 Turbulence      134 149 Two-body problem      84 van der Pol equation      154 Velocity, angular      147 Velocity, components in polar coordinates      75 78 Viscosity, coefficient of      123 Viscous flow, boundary layers      129 Viscous flow, equations of      123 Viscous flow, very viscous      125 Wave equation      94 Waves on string      93 96 Waves, standing      105 Waves, travelling      96 Wire trick, floppy      185 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020 | | О проекте