Numerical Methods: Lecture 18 | Cubic Splines | Piecewise Function

🔍 In this video, we learn the strategy for developing piecewise functions, focusing specifically on splines—a powerful tool for smooth interpolation across data points. Instead of relying on basic linear (1st-degree) or quadratic (2nd-degree) polynomials, we explore the advantages and formulation of cubic splines. ✅ Topics Covered: - Dividing the dataset into intervals. - Defining a cubic polynomial for each subinterval. - Applying continuity, smoothness, and boundary conditions. - Setting up and solving the system of equations to find spline coefficients. By the end of the video, you will understand how to formulate the complete set of cubic spline equations that smoothly pass through a given set of data points. 📚 Perfect for students of Numerical Methods, Engineering, Mathematics, and anyone interested in computational problem-solving. Linkedin Account : https://www.linkedin.com/in/muhammad-nouman-aslam-khan-60057722/?lipi=urn%3Ali%3Apage%3Ad_flagship3_feed%3BkSWSu7iJSPW3IHgRawrAAQ%3D%3D #numericalmethods #approximate #bisectionmethod #newtonraphsonmethod #chemicalengineering #materialsengineering #engineering #overview #numericalanalysis #MATLAB #NumericalDifferentiation #taylorseries #error #roundoff #absolute #intermediate#value#theorem #bisectionmethod #pseudocode #fixed #fpm #iterations #fixedpointtheorem #convergence #uniqueness #existence #bounds #numericalanalysislecture #errorapproximation #engineeringmathematics #appliednumericalmethodsforengineers #numericalmethods4thsemester #NumericalMethods #NewtonMethod #SecantMethod #RootFinding #MATLAB #falsepositionmethod #basiccommands #implementation #systemoflinearequations #pivoting #partialpivoting #algorithm #NumericalMethods #JacobiMethod #GaussSeidel #Convergence #LinearAlgebra #EngineeringMath #nonlinear#NumericalMethods #FixedPointMethod #NewtonsMethod #NonlinearEquations #EngineeringMath #MATLAB #RootFindings #CurveFitting #Prediction #DataFitting #lagrangeinterpolation #lagrange #lagrangepoint #spline #cubicspline #polynomials