Differential Equations in Applications 5030005218

Table of contents :
Front Cover
Contents
Preface
Chapter 1. Construction of Differential Models and Their Solutions
1.1 Whose Coffee was hotter?
1.2 Steady-State Heat Flow
1.3 An Incident in a National Park
1.4 Liquid Flow Out of Vessels. The Water Clock
1.5 Effectiveness of Advertising
1.6 Supply and Demand
1.7 Chemical Reactions
1.8 Differential Models in Ecology
1.9 A Problem from the Mathematical Theory of Epidemics
1.10 The Pursuit Curve
1.11 Combat Models
1.12 Why Are Pendulum Clocks Inaccurate
1.13 The Cycloidal Clock
1.14 The Bracbistochrone Problem
1.15 The Arithmetic Mean, the, the Geometric Mean, and the Associated Differential Equation
1.16 On the Flight of an Object Thrown at an Angle to the Horizon
1.17 Weightlessness
1.18 Kepler's Laws of Planetary Motion
1.19 Beam Deflection
1.20 Transportation of Logs
Chapter 2. Qualitative Methods of Studying Differential Models
2.1 Curves of Constant Direction of Magnetic Needle
2.2 Why Must an Engineer Know Existence of Uniqueness Theorems?
2.3 A Dynamical Interpretation of Second Order Differential Equations
2.4 Conservative Systems in Mechanics
2.5 Stability of Equilibriwn Points and of Periodic Motion
2.6 Lyapunov Functions
2.7 Simple States of Equilibrium
2.8 Motion of a Unit-Mass Object Under the Action of Linear Springs in a Medium with Linear Drag
2.9 Adiabatic Flow of a Perfect Gas Through a Nozzle of varying cross section
2.10 Higher-Order Points of Equilibrium
2.11 Inversion with Respect to a circle and Homogeneous Coordinates
2.12 Flow of a Perfect Gas Through a Rotating Tube of Uniform Cross Section
2.13 Isolated Closed Trajectories
2.14 Periodic Modes in Electric Circuits
2.15 Curves Without Contact
2.16 The Topographical System of Curves. The contact Curve
2.17 The Divergence of a Vector Field and Limit Cycles
Selected Readings
Appendices
Appendix 1. Derivateves of Elementary Functions
Appendix 2. Basic Integrals
Back Cover

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