EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Question
Chapter 2.7, Problem 2E
Interpretation Introduction
Interpretation:
To identify all the equilibrium points and their stability for the
Concept Introduction:
Potential is
The
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II. Consider the function g defined by
1
g(x, y) = cos (x# /) +
logg (r - y)
Do as indicated.
1. Determine
dyðr
2. Calculate the instantaneous rate of change of g at the point (4,1,2) in the direction
of the vector v = (1, 2).
Consider the function g defined by
1
g(x, y) = cos (TIVy)+
log3 (x – y)"
Do as indicated.
Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction
of the vector v = (1,2).
Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find all of the
functions with this gradient.
(a) (3x² + e¹0) i + (10x e¹0 - 9 siny) j
(b) (10x el0y 9 sin y) i + (3x² + e¹0y) j
a) I have placed my work and my answer on my answer sheet
Chapter 2 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5E
Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.7 - Prob. 1ECh. 2.7 - Prob. 2ECh. 2.7 - Prob. 3ECh. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9E
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- A hose feeds into a small screen box of volume 20 cm³ that is suspended in a swimming pool. Water flows across the surface of the box at rate 38 cm³/s. Estimate div(v)(P), where v is the velocity field of the water in the pool and P is the center of the box. (Use decimal notation. Give your answer to one decimal place.) div(v)(P) = What are the units of div(v)(P)? The units of div(v) (P) are perarrow_forward3. Find the directional derivative of f(x, y) = cos(3x+4y) at the point (π/6,π/6) along the direction of the vector (-4,-3).arrow_forwardII. Consider the function g defined by 1 g(r, y) = cos (TIV log3(x – y) Do as indicated. 1. Determine 2. Calculate the instantaneous rate of change of g at the point (4, 1, 2) in the direction of the vector v = (1,2). 3. In what direction does g have the maximum directional derivative at (r, y) = (4, 1)? What is the maximum directional derivative?arrow_forward
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