Practice Concept of Euler’s Method - 9.1 | 9. Euler’s Method | Mathematics - iii (Differential Calculus) - Vol 4
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9.1 - Concept of Euler’s Method

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the formula used in Euler's Method to estimate the next y-value?

💡 Hint: Remember, we start with the current y-value and add the slope multiplied by step size.

Question 2

Easy

If the step size is 0.2, what is the slope at point (0, 1) if the function is defined as $f(x,y) = x + y$?

💡 Hint: Evaluate the function at the initial condition.

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Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the basic formula of Euler's Method?

💡 Hint: Remember the structure of the equation as it incorporates previous values.

Question 2

True or False: Euler's Method is only applicable for first-order ODEs.

  • True
  • False

💡 Hint: Think about the nature of the differential equations it addresses.

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Challenge Problems

Push your limits with challenges.

Question 1

Using Euler’s Method, estimate the value of $y(2)$ for the equation $\frac{dy}{dx} = y^2 - x$ given $y(0) = 1$ and using a step size of 0.5. Assess three iterations.

💡 Hint: Break down the calculations step-by-step, evaluating the function at each point.

Question 2

Using a differential equation $\frac{dy}{dx} = -2y + x$ and $y(0)=1$, apply Euler's Method to find $y(0.5)$ with step size 0.1. After applying, discuss the implication of your results.

💡 Hint: Remember to keep recalculating your new y-value with each x increment!

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