EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 10.1, Problem 3E
Interpretation Introduction

Interpretation:

To explain mathematically the result for xn+1 = exp(xn) using a cobweb or some other argument. Also, use the pocket calculator to explore the maps.

Concept Introduction:

  • ➢ Determine the fixed points for the given equation and its stability.

  • ➢ Plot the graph for the equation and compute numerical values.

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(b) Let I[y] be a functional of y(x) defined by [[y] = √(x²y' + 2xyy' + 2xy + y²) dr, subject to boundary conditions y(0) = 0, y(1) = 1. State the Euler-Lagrange equation for finding extreme values of I [y] for this prob- lem. Explain why the function y(x) = x is an extremal, and for this function, show that I = 2. Without doing further calculations, give the values of I for the functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
L sin 2x (1+ cos 3x) dx 59
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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY