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Knowledge
Euler's Method is a fundamental technique for approximating solutions to first-order Ordinary Differential Equations (ODEs). It provides a systematic approach to estimate values of dependent variables using known initial conditions and derivatives, though its accuracy is influenced by the chosen step size. This method serves as a building block for more advanced numerical techniques.
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Sections
References
unit 5 ch2.pdfClass Notes
Memorization
What we have learnt
- Euler's Method approximates...
- The accuracy of Euler's met...
- This method is key in vario...
Final Test
Revision Tests
What we have learnt
- Euler's Method approximates the solutions of first-order ODEs using a step-by-step approach.
- The accuracy of Euler's method relies on the step size, with smaller sizes yielding better outcomes.
- This method is key in various fields, including engineering, physics, and population modeling.
Key Concepts
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Term: Euler’s Method
Definition: A numerical technique for approximating solutions to first-order ODEs using initial conditions and slope estimates.
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Term: Local Truncation Error (LTE)
Definition: The error made in a single step of the method, proportional to the square of the step size (h^2).
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Term: Global Truncation Error (GTE)
Definition: The cumulative error after multiple steps, proportional to the step size (h).