Amelkin V.V. Differential Equations In Applications

Translated from the Russian by E.Yankovsky. — Moscow: Mir Publishers, 1980. — 280 p. — (Science For Everyone).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.
Оригинальное издание: Амелькин В.В. Дифференциальные уравнения в приложениях /file/2416068/Construction of Differential Models and Their Solutions
Whose Coffee Was Hotter?
Steady-State Heat Flow
An Incident in a National Park
Liquid Flow Out of Vessels. The Water Clock
Effectiveness of Advertising
Supply and Demand
Chemical Reactions
Differential Models in Ecology
A Problem from the Mathematical Theory of Epidemics
The Pursuit Curve
Combat Models
Why Are Pendulum Clocks Inaccurate?
The Cycloidal Clock
The Brachistochrone Problem
The Arithmetic Mean, the Geometric Mean, and the Associated Differential Equation
On the Flight of an Object Thrown at an Angle to the Horizon
Weightlessness
Kepler’s Laws of Planetary Motion
Beam Deflection
Transportation of LogsQualitative Methods of Studying Differential Models
Curves of Constant Direction of Magnetic Needle
Why Must an Engineer Know Existence and Uniqueness Theorems?
A Dynamical Interpretation of Second-Order Differential Equations
Conservative Systems in Mechanics
Stability of Equilibrium Points and of Periodic Motion
Lyapunov Functions
Simple States of Equilibrium
Motion of a Unit—Mass Object Under the Action of Linear Springs in a Medium with Linear Drag
Adiabatic Flow of a Perfect Gas Through a Nozzle of Varying Cross Section
Higher-Order Points of Equilibrium
Inversion with Respect to a Circle and Homogeneous Coordinates
Flow of a Perfect Gas Through a Rotating Tube of Uniform Cross Section
Isolated Closed Trajectories
Periodic Modes in Electric Circuits
Curves Without Contact
The Topographical System of Curves. The Contact Curve
The Divergence of a Vector Field and Limit CyclesSelected Readings
Appendices
Appendix. Derivatives of Elementary Functions
Appendix. Basic Integrals