Numerical Methods for Engineers

Use this for “Bisect x³ − x − 3 = 0 on [1, 2] once, then say how many halvings reach a tolerance of 0.0001.”

Use this for “Take one secant step for x³ − x − 3 = 0 from x₀ = 1.5 and x₁ = 2.”

Use this for “Is the secant method a bracketing method or an open one?”

Use this for “Do Gauss–Seidel sweeps on 4x + y = 9 and x + 3y = 5 from (0, 0) until the change is under 0.0001.”

Use this for “Find the condition number of A = [[1, 1], [1, 1.01]] in the row-sum norm. Is A ill-conditioned?”

Use this for “A table lists y = 2676 at x = 100 and y = 2776 at x = 150. Estimate y at x = 120.”

Use this for “Fit y = mx + b by least squares to (0, 1.1), (1, 2.9), (2, 5.2), (3, 7.1), (4, 8.8) and find r².”

Use this for “A car’s speed, read every 10 s, is 4, 12, 20 and 24 m/s. Estimate the distance it covers with the trapezoid rule.”

Use this for “Estimate the trapezoid rule’s error for x³ from 0 to 2 with 4 panels, taking the average f″ as 6.”

Use this for “Estimate the integral of x³ from 0 to 2 with two-point Gauss quadrature and compare it with the exact value.”

Use this for “Take one RK4 step of h = 0.5 on dy/dt = −0.5y from y = 10, and compare with the exact answer.”

Use this for “Take one Heun step of h = 0.5 on dy/dt = −0.5y from y = 10, and compare with the exact answer.”

Use this for “For dy/dt = −50y, is Euler’s method with h = 0.05 stable? What step size is?”

Use this for “Start the power method on A = [6 2; 2 3] from x₀ = (1, 1). Find Ax₀ and the Rayleigh estimate of the largest eigenvalue.”

Use this for “A square-grid plate node has neighbours at 100, 60, 40 and 20 °C. What is its steady temperature?”

Use this for “f(0.9) = 2.4596, f(1) = 2.7183 and f(1.1) = 3.0042. Estimate f′(1) and f″(1).”