Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 11.3, Problem 1E
Interpretation Introduction
Interpretation:
Construct the new kind of Cantor set by removing the middle half of each sub-interval instead of removing middle third
Find similarity dimension of the set.
Find the measure of the set.
Concept Introduction:
Fractals are the complex geometric shapes with fine structure at arbitrarily small scales.
Cantor set consist an infinite number of infinitesimal pieces separated by gaps of various sizes.
The dimension of the Cantor set is not an integer it is a fraction.
The similarity dimension d is defined as
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1) Answer the following questions by circling TRUE or FALSE (No explanation or
work required).
−1
0 01
i) If A
=
0
0
2 0, then its eigenvalues are ₁ = 1,λ₂ = 2, and 13
0 0
= : 0.
(TRUE FALSE)
ii) A linear transformation is operation preserving because the same result occurs
whether you perform the operations of addition and scalar multiplication before
or after applying the linear transformation. ( TRUE FALSE)
iii) A linear transformation that is one-to-one and onto is called an isomorphism.
(TRUE FALSE)
iv) If the standard matrix A for the linear transformation T: R³ → R³ is
-1 0 01
A =
2
00, then T is invertible. (TRUE FALSE)
0
1 1.
v) Let A, B, and C be square matrices of order n. If A is similar to B and B is
similar to C, then A is similar to C. ( TRUE FALSE)
2) a) i) Find the matrix that produces the counterclockwise rotation of 30° about
the z-axis.
ii) Find the image of the vector (1,1,1) for the rotation described in i).
b) Give a geometric description…
Pls help ASAP
1. Except for the door and floor, a shed is built entirely out of plywood. How
many square meters of plywood are needed to build the shed? (1 foot 0.3048 m)
10 ft.
7 ft.
3 ft.
18 ft.
17 ft.
15 ft.
Chapter 11 Solutions
Nonlinear Dynamics and Chaos
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3E
Ch. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.5 - Prob. 1E
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