Numerical Methods in MATLAB for Engineering Students Part 2

Download the notes outline to guide you through the lecture videos, with blank sections to fill in, and access a complete problem booklet plus downloadable MATLAB code for hands-on practice.

Explore curve fitting and interpolation using least squares regression to find the best-fit linear model y = a1 x + a0 for experimental data, and estimate values via interpolation.

Use MATLAB to perform least squares regression on altitude versus temperature, compute a0 and a1 from summations, and visualize the linear fit against the data, including interpolation at five thousand.

learn to fit data with quadratic or higher polynomial regression by minimizing squared error via least squares, deriving normal equations for coefficients and forming a curve through data points.

Perform polynomial regression in MATLAB by building A and B from data sums and solving A inverse B to obtain quadratic coefficients, then apply to population versus year data.

Learn how to perform polynomial regression in MATLAB by fitting a second-order model with polyfit, evaluating with polyVal, and plotting data and the fit.

learn to fit a single polynomial to data points using Lagrange interpolating polynomials, where f(x)=sum Yi Li(x) and Li(x) is a product over j≠i of (x−Xj)/(Xi−Xj).

Learn to construct polynomials that exactly interpolate given data points using degree 1 and degree 2, select boundary points around x=8.4, and evaluate the interpolant to estimate f(8.4) in MATLAB.

Interpolate a degree-2 polynomial for f(x) = 1/x using three data points, build the Lagrange basis, and compare P2(3) to 1/3.

Implement the Lagrange interpolating polynomial algorithm in Matlab using data points and an interpolation point, then verify results with examples 10 and 11.

Learn Newton's interpolated polynomial and divided differences, compute coefficients a1, a2, a3 from data points, and interpolate with the general form, while easily adding data without reworking.

Apply Newton's divided differences to construct a fourth-order interpolating polynomial from five wind-speed and power data points and estimate power at 26 mph.

Implement the Newton divided differences algorithm in MATLAB, build the interpolation table and polynomial, and evaluate at a point using wind and power data.

Explore linear splines for interpolation by connecting data points with first-order polynomials, using three intervals between four points, and implementing a simple interval-based algorithm to compute the interpolated value.

Apply linear spline interpolation to height and time data to estimate the ball's height at t = 3 s, selecting the appropriate interval and coding the routine in MATLAB.

Explore building quadratic splines using second-order polynomials on data intervals, enforcing endpoint values and interior slope continuity, with a zero second derivative making the first interval linear.

Learn how to apply quadratic spline interpolation to connect data points, enforce endpoint and interior knot conditions, and solve for spline coefficients in MATLAB to estimate height at three seconds.

Explore cubic splines, where data points connect with third-order polynomials across n-1 intervals, ensuring smooth first and second derivative continuity and using natural spline end conditions.

Construct a natural cubic spline to interpolate three data points, forming interval polynomials, applying endpoint conditions, first and second derivative continuity, and solving an Ax=B system in MATLAB.

Apply cubic spline interpolation using Lagrange polynomials to connect data points, derive the second derivatives at knots, and solve for coefficients to prepare a MATLAB algorithm.

Learn to construct natural cubic splines for a three-point dataset. Derive h values, solve for the middle coefficient, and form interval polynomials with MATLAB.

Explore the cubic spline algorithm in MATLAB, using the Thomas algorithm to solve a tridiagonal system for cubic spline interpolation and map the top surface of a car.

Explore built-in MATLAB curve fitting: use polyfit and polyval for polynomial fitting, and a cubic spline interpolation via a one-step method with a spline option, plus linear interpolation.