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Mathematical Methods for Scientists and Engineers
Linear and Nonlinear Systems
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Part I of this text/reference presents techniques for linear systems with emphasis on asymptotic methods. The development in Part II employs the methods given in the first part and focuses attention on weakly nonlinear oscillatory systems and nonlinear difference equations. The stress is on practical methods, rather than on proof of theorems, and each method is illustrated by examples of applications in the sciences. Presents some numerical and graphical solutions generated by Lotus 1-2-3 and Math CAD.LINEAR SYSTEMS.Matrix Theory.The Gamma and Related Functions.Elements of Asymptotics.Evaluati...
Part I of this text/reference presents techniques for linear systems with emphasis on asymptotic methods. The development in Part II employs the methods given in the first part and focuses attention on weakly nonlinear oscillatory systems and nonlinear difference equations. The stress is on practical methods, rather than on proof of theorems, and each method is illustrated by examples of applications in the sciences. Presents some numerical and graphical solutions generated by Lotus 1-2-3 and Math CAD.
LINEAR SYSTEMS.
Matrix Theory.
The Gamma and Related Functions.
Elements of Asymptotics.
Evaluation of Sums: The Euler-MacLaurin Sum Expansion.
Evaluation of Integrals: The Laplace Method.
Differential Equations.
NONLINEAR SYSTEMS.
The Simple Harmonic Oscillator and the Logistic Equation.
Aspects of Harmonic Motion and the Concept of Secular Terms.
Equilibrium Points and the Phase Plane.
Conservative Systems.
Nonconservative Systems.
The Method of Averaging (MOA).
The Method of Multiple Times Scales (MMTS).
Higher-Order Calculations.
Error Analysis.
One-Dimensional Iterative Maps and the Onset of Chaos.
Appendix.
Index.
LINEAR SYSTEMS.
Matrix Theory.
The Gamma and Related Functions.
Elements of Asymptotics.
Evaluation of Sums: The Euler-MacLaurin Sum Expansion.
Evaluation of Integrals: The Laplace Method.
Differential Equations.
NONLINEAR SYSTEMS.
The Simple Harmonic Oscillator and the Logistic Equation.
Aspects of Harmonic Motion and the Concept of Secular Terms.
Equilibrium Points and the Phase Plane.
Conservative Systems.
Nonconservative Systems.
The Method of Averaging (MOA).
The Method of Multiple Times Scales (MMTS).
Higher-Order Calculations.
Error Analysis.
One-Dimensional Iterative Maps and the Onset of Chaos.
Appendix.
Index.