Differential Equations in Applications

Front Cover......Page 1
Back Cover......Page 2
Title Page......Page 5
© English translation, Eugene Yankovsky, 1990......Page 6
Contents......Page 7
Preface......Page 9
1.1 Whose Coffee Was Hotter?......Page 13
1.2 Steady-State Heat Flow......Page 16
1.3 An Incident in a National Park......Page 20
1.4 Liquid Flow Out of Vessels. The Water Clock......Page 28
1.5 Effectiveness of Advertising......Page 32
1.6 Supply and Demand......Page 34
1.7 Chemical Reactions......Page 36
1.8 Differential Models in Ecology......Page 40
1.9 A Problem from the Mathematical Theory of Epidemics......Page 46
1.10 The Pursuit Curve......Page 53
1.11 Combat Models......Page 57
1.12 Why Are Pendulum Clocks Inaccurate?......Page 71
1.13 The Cycloidal Clock......Page 75
1.14 The Brachistochrone Problem......Page 83
1.15 The Arithmetic Mean, the Geometric Mean, and the Associated Differential Equation......Page 90
1.16 On the Flight of an Object Thrown at an Angle to the Horizon......Page 95
1.17 Weightlessness......Page 98
1.18 Kepler\'s Laws of PlanetaryMotion......Page 102
1.19 Beam Deflection......Page 114
1.20 Transportation of Logs......Page 121
2.1 Curves of Constant Direction of Magnetic Needle......Page 138
2.2 Why Must an Engineer Know Existence and Uniqueness Theorems?......Page 145
2.3 A Dynamical Interpretation of Second-Order Differential Equations......Page 157
2.4 Conservative Systems in Mechanics......Page 164
2.5 Stability of Equilibrium Points and of Periodic Motion......Page 178
2.6 Lyapunov Functions......Page 186
2.7 Simple States of Equilibrium......Page 191
2.8 Motion of a Unit-Mass Object Under the Action of Linear Springs in a Medium with Linear Drag......Page 197
2.9 Adiabatic Flow of a Perfect Gas Through a Nozzle of Varying Cross Section......Page 205
2.10 Higher-Order Points of Equilibrium......Page 213
2.11 Inversion with Respect to a Circle and Homogeneous Coordinates......Page 220
2.12 Flow of a Perfect Gas Through a Rotating Tube of Uniform Cross Section......Page 225
2.13 Isolated Closed Trajectories......Page 238
2.14 Periodic Modes in Electric Circuits......Page 252
2.15 Curves Without Contact......Page 262
2.16 The Topographical System of Curves. The Contact Curve......Page 265
2.17 The Divergence of a Vector Field and Limit Cycles......Page 272
Selected Readings......Page 276
Appendix 1. Derivatives of Elementary Functions......Page 277
Appendix 2. Basic Integrals......Page 280