Mathematics - iii (Differential Calculus) - Vol 4 | 9. Euler’s Method by Abraham | Learn Smarter
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9. Euler’s Method

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

  • 9

    Numerical Solutions Of Odes

    This section explores Euler's Method, a numerical technique for estimating solutions to ordinary differential equations (ODEs) when exact solutions are impractical.

    Learning Practice

  • 9.1

    Concept Of Euler’s Method

    Euler's Method is a foundational numerical technique for approximating solutions to first-order ordinary differential equations (ODEs), employing a step-by-step approach based on the Taylor series expansion.

    Learning Practice

  • 9.2

    Algorithm (Step-By-Step)

    This section outlines the step-by-step algorithm for implementing Euler's Method to approximate solutions of first-order ODEs.

    Learning Practice

  • 9.3

    Example Problem

    This section demonstrates the application of Euler's method to solve a specific ordinary differential equation.

    Learning Practice

  • 9.4

    Graphical Interpretation

    Euler’s method approximates solutions to ordinary differential equations (ODEs) using tangent lines, although it can lack accuracy depending on the step size.

    Learning Practice

  • 9.5

    Error In Euler’s Method

    This section discusses the error involved in Euler's Method, focusing on local and global truncation errors.

    Learning Practice

  • 9.6

    Applications

    This section discusses various applications of Euler's method in practical fields.

    Learning Practice

References

unit 5 ch2.pdf

Class 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