7.1 - Numerical Solution of Ordinary Differential Equations (ODEs)
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Practice Questions
Test your understanding with targeted questions
What is an ordinary differential equation (ODE)?
💡 Hint: Think about differential equations.
Define an Initial Value Problem (IVP).
💡 Hint: Consider what values are given at the start.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does IVP stand for in the context of ODEs?
💡 Hint: Remember what values we start with in these problems.
True or False: Improved Euler's Method is the same as Euler's Method.
💡 Hint: Think about how the slope is calculated.
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Challenge Problems
Push your limits with advanced challenges
Solve the ODE dy/dx = -2y + 2 with the initial condition y(0) = 1 using Euler’s Method with h = 0.1 for two steps.
💡 Hint: Use the iterative formula and be careful with signs.
Compare the results of the Predictor-Corrector Method against the Improved Euler’s Method for the ODE dy/dx = x + y with y(0) = 1.
💡 Hint: Use initial guesses wisely for the predictor.
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