18.1 - Fundamental Concepts
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Practice Questions
Test your understanding with targeted questions
Define an Ordinary Differential Equation.
💡 Hint: Focus on the function and derivatives.
What is a numerical method?
💡 Hint: Think about how we use methods to calculate values.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of an Ordinary Differential Equation (ODE)?
💡 Hint: Think about the components of an ODE.
True or False: Stability ensures that errors grow uncontrollably.
💡 Hint: Remember the definition of stability.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the ODE y' = -3y with initial condition y(0) = 2, apply Euler’s method with a step size of 0.5 to find the approximation at x = 1.
💡 Hint: Pay attention to how you apply the recurrence relation.
Analyze the convergence of the numerical solution for the ODE y' = -y as h approaches zero, discussing the impact on accuracy.
💡 Hint: Consider what happens as you make step sizes smaller.
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