Continuing the Science for Everyone Series we now come to Differential Equations in Applications by V. V. Amel'kinFrom the back cover:This book is an easy-reading introduction to ordinary differential equations and their use in the study of real phenomena and processes. Problems taken from various fields of knowledge illustrate the tools used in setting up differential equations and the methods employed in their qualitative investigation. The book should be useful to  high-school students, teachers of science courses, college students, and specialists of, non-mathematical professions who use mathematics in their work.The book discusses many interesting problems and has 2 chapters. The first one is dedicated to constructing the differential models and finding their solutions. The second chapter is more interesting, it shows you the way to deal with differential equations qualitatively.The book was translated from the Russian by Eugene Yankovsky and was first published by Mir in 1990. This I think was one of the last books published by Mir, as after that the USSR came apart and so did all these wonderful state run publishers.Update: New link has been posted, earlier link was missing pages 180-181. Thanks Khalid for reporting this.ContentsChapter 1. Construction of Differential Models and Their Solutions 111.1 Whose Coffee Was Hotter? 111.2 Steady-State Heat Flow 141.3 An Incident in a National Park 181.4 Liquid Flow Out of Vessels. The Water Clock 261.5 Effectiveness of Advertising 301.6 Supply and Demand 321.7 Chemical Reactions 341.8 Differential Models in Ecology 381.9 A Problem from the Mathematical Theory of Epidemics 441.10 The Pursuit Curve 511.11 Combat Models 551.12 Why Are Pendulum Clocks Inaccurate? 691.13 The Cycloidal Clock 731.14 The Brachistochrone Problem 811.15 The Arithmetic Mean, the Geometric Mean, and the Associated Differential Equation 881.16 On the Flight of an Object Thrown at an Angle to the Horizon 931.17 Weightlessness 961.18 Kepler’s Laws of Planetary Motion 1001.19 Beam Deflection 1121.20 Transportation of Logs 119Chapter 2. Qualitative Methods of Studying Differential Models 1362.1 Curves of Constant Direction of Magnetic Needle 1362.2 Why Must an Engineer Know Existence and Uniqueness Theorems? 1432.3 A Dynamical Interpretation of Second-Order Differential Equations  1552.4 Conservative Systems in Mechanics 1622.5 Stability of Equilibrium Points and of Periodic Motion 1762.6 Lyapunov Functions 1842.7 Simple States of Equilibrium  1892.8 Motion of a Unit—Mass Object Under the Action of Linear Springs in a Medium with Linear Drag 1952.9 Adiabatic Flow of a Perfect Gas Through a Nozzle of Varying Cross Section  2032.10 Higher-Order Points of Equilibrium  2112.11 Inversion with Respect to a Circle and Homogeneous Coordinates 2182.12 Flow of a Perfect Gas Through a Rotating Tube of Uniform Cross Section 2232.13 Isolated Closed Trajectories 2362.14 Periodic Modes in Electric Circuits 2502.15 Curves Without Contact 2602.16 The Topographical System of Curves. The Contact Curve 2632.17 The Divergence of a Vector Field and Limit Cycles 270Selected Readings 274Appendices 275Appendix 1. Derivatives of Elementary Functions  275Appendix 2. Basic Integrals 278