500 Examples and Problems of Applied Differential Equations

Description

This book highlights an unprecedented number of real-life applications of differential equations together with the underlying theory and techniques. The problems and examples presented here touch on key topics in the discipline, including first order (linear and nonlinear) differential equations, second (and higher) order differential equations, first order differential systems, the Runge–Kutta method, and nonlinear boundary value problems. Applications include growth of bacterial colonies, commodity prices, suspension bridges, spreading rumors, modeling the shape of a tsunami, planetary motion, quantum mechanics, circulation of blood in blood vessels, price-demand-supply relations, predator-prey relations, and many more. Upper undergraduate and graduate students in Mathematics, Physics and Engineering will find this volume particularly useful, both for independent study and as supplementary reading. While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field. Front Matter ....Pages i-ix First-Order Linear Differential Equations (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 1-19 Some First-Order Nonlinear Differential Equations (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 21-45 Second- and Higher Order Differential Equations (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 47-84 Power Series Solutions (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 85-114 Systems of First-Order Differential Equations (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 115-161 Runge–Kutta Method (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 163-182 Stability Theory (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 183-220 Linear Boundary Value Problems (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 221-291 Nonlinear Boundary Value Problems (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages 293-378 Correction to: Systems of First-Order Differential Equations (Ravi P. Agarwal, Simona Hodis, Donal O’Regan)....Pages C1-C1 Back Matter ....Pages 379-388