Mathematics - iii (Differential Calculus) - Vol 4 | 3. Numerical Differentiation by Abraham | Learn Smarter
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3. Numerical Differentiation

Numerical differentiation is a vital method for estimating derivatives of functions based on discrete data points, particularly when analytical solutions are not available. Various finite difference formulas—forward, backward, and central differences—are employed, depending on the positioning of the point of interest within the data. While highly effective, numerical differentiation requires careful application to mitigate errors arising from truncation and round-off.

Sections

  • 3

    Interpolation & Numerical Methods

    Numerical differentiation estimates derivatives from discrete data points using interpolation techniques.

    Learning Practice

  • 3.1

    Fundamentals Of Numerical Differentiation

    Numerical differentiation provides methods to estimate the derivatives of functions based on discrete data points, particularly when traditional calculus cannot be used.

    Learning Practice

  • 3.2

    Newton’s Forward Difference Formula For Derivatives

    Newton's Forward Difference Formula provides a method for estimating derivatives using discrete data from functions that are known only at specific points.

    Learning Practice

  • 3.3

    Newton’s Backward Difference Formula For Derivatives

    Newton’s Backward Difference Formula provides a method for approximating the derivatives at the end of a data table using discrete data points.

    Learning Practice

  • 3.4

    Central Difference Formulas

    The section details the central difference formulas used for approximating the first and second derivatives of functions represented by discrete data points.

    Learning Practice

  • 3.5

    Error In Numerical Differentiation

    This section discusses the sources of error in numerical differentiation methods and their implications in computations.

    Learning Practice

  • 3.6

    Worked Example

    This section presents a worked example of how to use the central difference formula to estimate the derivative of a function given in tabular form.

    Learning Practice

  • 3.7

    Applications Of Numerical Differentiation

    Numerical differentiation techniques are essential in various scientific and engineering contexts where functions are represented as discrete data points.

    Learning Practice

References

unit 4 ch3.pdf

Class Notes

Memorization

What we have learnt

  • Numerical differentiation e...
  • Different formulas (forward...
  • Careful selection of formul...

Final Test

Revision Tests