slope = (n * sum_xy - sum_x * sum_y) / (n * sum_x2 - sum_x**2) intercept = (sum_y - slope * sum_x) / n return slope, intercept def poly_fit(x, y, degree): coeffs = np.polyfit(x, y, degree) return np.poly1d(coeffs) strain = np.array([0.0, 0.05, 0.10, 0.15, 0.20]) stress = np.array([0.0, 35.2, 68.4, 99.7, 128.5])
root_bisect = bisection(deflection, 0, 1.5) root_newton = newton_raphson(deflection, d_deflection, 2.5) Numerical Methods In Engineering With Python 3 Solutions
I’ll develop a structured guide for (based on the popular textbook by Jaan Kiusalaas), including concept summaries + Python solutions for key engineering numerical methods. slope = (n * sum_xy - sum_x *
print(f"Bisection root: root_bisect:.6f") print(f"Newton root: root_newton:.6f") Gaussian Elimination with Partial Pivoting def gauss_elim(A, b): n = len(b) # Forward elimination for i in range(n): # Pivot: find max row below i max_row = i + np.argmax(np.abs(A[i:, i])) if max_row != i: A[[i, max_row]] = A[[max_row, i]] b[[i, max_row]] = b[[max_row, i]] # Eliminate below for j in range(i+1, n): factor = A[j, i] / A[i, i] A[j, i:] -= factor * A[i, i:] b[j] -= factor * b[i] intercept def poly_fit(x