Numerical Analysis: Interpolation Techniques

Aug 8, 2024

Numerical Analysis Lecture Notes

Instructor: Dr. Gajendra Purohit
Topic: Numerical Analysis
Date: [Insert Date]

Overview

  • Today’s focus: Numerical Differentiation and Numerical Integration.
  • Key concept in Numerical Analysis: Interpolation.
  • Introduction to various formulas related to integration and interpolation.

Interpolation

  • Definition: A method to estimate values within a range of known data points.
  • Types of Interpolation:
    • Equal Intervals
    • Unequal Intervals

Equal Intervals

  • When estimating population for a specific year (e.g., 1973):
    • Forward Trend: Use Newton Forward Formula.
    • Backward Trend: Use Newton Backward Formula.
    • Center Value: Use Central Difference Formulas.
    • Next Video: Focus on Central Difference.

Unequal Intervals

  • Requires identification of equal vs. unequal intervals.
  • Formulas Used:
    • Newton Divided Difference for unequal intervals.
    • Next Video: Will cover this topic in detail.

Applications of Interpolation

  • Interpolation concepts can also be applied to derivatives.
  • Discuss how ordinary differential equations can be solved using numerical analysis.

Additional Resources

  • More videos on related topics available through the i-tab link.
  • Topics include:
    • Complex Numbers
    • Fourier Matrices
    • Partial Differential Equations
    • Gamma and Beta Functions

Conclusion

  • Emphasis on conceptual understanding and problem-solving skills.
  • Support for students preparing for competitive exams.
  • The objective of lectures is to enhance understanding and exam performance.