Limits of mathematics -- Classification of nonlinearities -- Meaning of approximation solution -- Comparison among the Asymptotic, numerical, and exact solutions -- Methods of function approximation -- Approximate solution in time domain -- Limits of time series solution -- Steady state solution Lindstad-Poincare methods -- Averaging methods -- Multiple time scale methods -- Application of Lindstad-Poincare methods -- Application of Averaging methods -- Application of Multiple time scale methods -- Duffing equation -- Van der Pol equation -- Mathieu equation.

Approximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions. Covers practical model-prototype analysis and nondimensionalization of differential equations; Coverage includes approximate methods of responses of nonlinear differential equations; Discusses how to apply approximation methods to analysis, design, optimization, and control problems; Discusses how to implement approximation methods to new aspects of engineering and physics including nonlinear vibration and vehicle dynamics.