Numerical Computations in MATLAB

learn to compute eigenvalues and eigenvectors in MATLAB, verify properties like determinant equals product of eigenvalues and trace equals sum, and diagonalize matrices using the eig function.

Explore singular value decomposition (SVD) in MATLAB by factorizing a matrix as U S V^T, extracting nonnegative singular values, and linking to PCA for dimensionality reduction and image compression.

Fit a polynomial to data with the polyfit function in MATLAB, extracting coefficients for a chosen degree, then assess fit under noise, plot results, and explore confidence intervals and outliers.

Explore interp1, interp2, and interp3 for interpolation on one-, two-, and three-dimensional data. Compare linear, nearest, pchip, cubic, and spline methods and understand extrapolation when evaluating at new points.

Use interpft to interpolate data in the frequency domain, then apply the inverse transform to get the interpolated values in the original domain, highlighting periodic patterns.

Explore cubic spline interpolation in MATLAB to fit smooth two dimensional paths from handle points, using x and y coordinates and a parametric t for path planning.

Learn to interpolate scattered data in 2d and 3d with matlab griddata, using linear, nearest, natural cubic, and triangulation-based methods, and visualize results with mesh plots.

Learn to perform numerical integration in MATLAB using integral and quadgk for single-variable functions, including improper and complex cases, with customizable tolerances and path-based methods.

learn to compute double and triple integrals numerically with MATLAB using integral2 and integral3, including function handles and variable limits.

Explore how MATLAB uses sum, cumsum, and reshape to perform discrete integrals and matrix sums, and apply trapz for trapezoidal approximations with sample spacing.

Learn to perform numerical differentiation in MATLAB using diff and the gradient function, compare errors with analytic derivatives, and apply the del2 laplacian operator for two-dimensional functions.

Learn to evaluate, construct, and fit polynomials using polyval, poly, and polyfit; multiply with conv and divide with deconv, differentiate and integrate with polyder and polyint, using coefficient vectors.

Explore numerical methods for solving ordinary differential equations in MATLAB, comparing non stiff and stiff solvers, converting higher-order to first-order systems, and visualizing results with example models.

solve boundary value problems in matlab by converting a second-order ode to a first-order system, defining boundary conditions as functions, and using a boundary-value solver with a mesh.

Learn to solve delayed differential equations in MATLAB using three solvers for constant, state-dependent, and neutral delays. Build models with history definitions, define delays, and visualize results through simple examples.

Explore linear programming and mixed integer linear programming in MATLAB, using linprog and intlinprog to solve problems with inequality constraints, bounds, and standard form matrices A and b.

Learn to formulate quadratic programming in MATLAB by defining H, f, A, b, Aeq, beq, and bounds, then solve a simple example with x ≈ [0.4, 1.6] and objective -8.4.

Explore nonlinear optimization with MATLAB using fminbnd, fminsearch, fminunc, and fmincon to solve single and multi-variable problems, unconstrained and constrained, including root finding and box design.