Numerical Methods in MATLAB for Engineering Students Part 1

Explore root-finding methods and numerical integration with downloadable notes, derivations, algorithms, and hands-on MATLAB demonstrations.

Explore solving nonlinear equations by analyzing f(x)=0, polynomial degrees and roots, and outline four error measures—true error, tolerance in f(x), tolerance in solution, and relative error.

Apply the bisection method to find a root of f(x)=0 on a closed interval with opposite signs at the ends, updating brackets by midpoints until convergence.

Use the bisection method to find a root of f(x)=0 on [a,b] with opposite end signs, producing an approximate solution or a failure message.

Learn how to apply the bisection method to locate a root of the cubic f(x)=x^3-7x^2+14x-6 on [0,1] to within 1e-2, using iteration, sign changes, and a hand-written table.

Learn Newton's method to find roots by using f(x), its derivative f'(x), an initial guess, tolerance, and max iterations, demonstrated on a cubic example in the interval 1 to 4.

Apply Newton's method in MATLAB to solve a cubic equation using anonymous functions within a script and a function file, and verify convergence with specified tolerance and max iterations.

Solve the ice cream cone volume equation for H with Newton's method, converting pint to cubic inches and using MATLAB to obtain H ≈ 1.4886 inches.

Discover the secant method, a derivative-free approach that uses two initial guesses and connects (x0, f(x0)) and (x1, f(x1)) to locate successive x-intercepts along the graph.

use the secant method in matlab to solve for the mortgage rate from loan, payment, and term, with two initial approximations around 0.02 and 0.04, converging to about 3.1378 percent.