Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 10.1, Problem 1E
Interpretation Introduction

Interpretation:

To explain mathematically the result for xn+1 = 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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Problem 4 (10pt). Use Stokes' theorem to evaluate the line integral (zdx+xdy + ydz) where C is the triangle in the xy-plane with vertices (1,0,0), (0,1,0), and (1,2,0) with counterclockwise orientation when viewed from above.
Problem 3 (10pt). Let R be the portion of the plane x+y+z = 1 in the first octant (i.e, x,y,z > 0). Compute the surface integral xds.
Problem 5 (10pt). Let F = xyi - zj and R is the unit square in the xy-plane, {0 < x,y≤1,z=0}. Compute curlF ds = c curlF.NdS where N is the unit upward normal vector to R.
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