Week 5 Section_ Euler's Method (24W)_Solutions (1)

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Apr 3, 2024

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Week 5: Euler’s Method Solutions Geometric Representations of Euler’s Method 1. Use the geometric representation of Euler’s method to answer the questions below (using colors on slide or digital copy at link above): a. What does black represent on this graph? Black represents the state space b. What does red represent? Red represents the true trajectory that the system travels as it evolves over time c. What does green represent? What role do they serve in Euler’s Method? Green represents the change vector that is associated with that state d. What does orange represent? Orange represents the percentage of the change vector being selected by the timestep e. What does blue represent? Why aren’t these segments as long as the green arrows? Blue represents the actual change in state that is used for the current step of Euler’s method

Computing Euler’s Method 2. Suppose you have the following logistic model: 𝑋' = 0. 1𝑋(1 − 𝑋 200 ) Suppose there are currently 100. Using Euler's method with a step size of weeks, estimate the size of the populations in ∆𝑡 = 0. 1 0.2 weeks . 0 0.1 100 5 0.5 100.5 0.1 0.1 100.5 4.999875 0.4999875 100.9999875 0.2 0.1 100.9999875

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Week 5 Section_ Euler's Method (24W)_Solutions (1)

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