Interpolation in Numerical Methods | Newton Gregory Forward Method with Examples

In this lecture, we explain the Newton Gregory Forward Difference Interpolation Method, an important technique in Numerical Methods used to estimate unknown values within a given set of data points. The video starts with a clear explanation of the difference between interpolation and extrapolation, helping you understand when and why interpolation methods are used. After that, we introduce key concepts such as the shift operator and the forward difference operator, which are essential for constructing interpolation formulas. We then demonstrate how to create a forward difference table, derive the general formula of Newton Gregory Forward Interpolation, and apply it step by step to solve numerical examples. 📚 Topics covered in this lecture: • Difference between Interpolation and Extrapolation • Concept of Shift Operator (E) • Forward Difference Operator (Δ) • Construction of Forward Difference Table • General Newton Gregory Forward Formula • Step-by-step worked examples This method is widely used in Numerical Analysis, Engineering Mathematics, and Scientific Computing for estimating function values when data points are equally spaced. This lecture is especially helpful for students of BS Mathematics, Engineering, Computer Science, and university-level Numerical Methods courses. Watch the full video to master Newton Forward Interpolation with clear concepts and solved examples. This lecture is useful for students studying numerical methods, numerical analysis, linear algebra, engineering mathematics, and computational mathematics. This lecture is useful for BS Mathematics, Engineering, Computer Science, and university students studying numerical methods or linear algebra. Watch the full lecture to clearly understand special matrices, matrix properties, and iterative techniques used in solving linear systems. 📌 Perfect for: • BS Mathematics students • Engineering students • Competitive exam preparation • Numerical Analysis learners Watch till the end for a complete understanding with theory + graphical intuition + practical examples. Subscribe to Learn with Arisha for more detailed lectures on numerical methods and MATLAB tutorials. 🔹More Playlists: ✅ Numerical Methods Quick Concepts | Short Urdu Videos https://youtube.com/playlist?list=PLQN-EgCjaCPE9hGvVPG4LWdyqYCNS-_Z4&si=aOhbAFoR1XanUrlj ✅Numerical Methods – Full Course https://youtube.com/playlist?list=PLQN-EgCjaCPEH08zW7aUvCJR-BfscRZg-&si=9NwkOOWmed6RkDX1 ✅ 3D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFKXGCIzLj-QVcvojLfJVWf&si=-JPTqK-Js0T2lfFV ✅ 2D Plotting in MATLAB | Learn with Arisha https://youtube.com/playlist?list=PLQN-EgCjaCPFUtyWcKDpCbPmcYMC8nnQC&si=McpIOs4a8rcub3Gb ✅ Numerical Analysis Complete Course https://youtube.com/playlist?list=PLQN-EgCjaCPGrYf4xZ0BhxXvPgdZ-Y9ks&si=8SB4AG9_G9CqJ_ue ✅MATLAB for Numerical Computation https://youtube.com/playlist?list=PLQN-EgCjaCPEZZQ5t6xzWn7Xxv3042bjG&si=CGwmwKr6-Dt-y4X- 🚀 Boost Your Numerical Computing Skills! This tutorial is perfect for students, engineers, and programmers who want to understand numerical errors in computational mathematics and MATLAB programming. 💡 Want More Tutorials on Numerical Methods? 👉 Subscribe for more computational math & MATLAB lessons! 👉 Hit the Like button if this video helps! 👉 Have questions? Comment below! 🔔 Stay updated with the latest programming & numerical analysis tutorials! #NewtonForwardInterpolation #Interpolation #NumericalMethods #ForwardDifference #DifferenceTable #EngineeringMathematics #NumericalAnalysis #MathLecture #LearnWithArisha