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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

What is curve fitting? Explain the least squares method to fit a straight line y = a + bx to a given set of data points.

regression
2long10 marks

Explain the finite difference method for solving partial differential equations. Derive the standard five-point formula for Laplace's equation.

pde
3long10 marks

Explain the bisection method for finding the root of a non-linear equation. Find a real root of the equation x^3 - x - 1 = 0 correct to three decimal places using the bisection method.

nonlinearbisection
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Explain Newton's divided difference interpolation formula.

interpolationdivided-difference
5short5 marks

Explain the power method for finding the largest eigenvalue of a matrix.

eigenvalue
6short5 marks

Fit a second-degree parabola y = a + bx + cx^2 to a set of data using the least squares principle.

regression
7short5 marks

Define absolute, relative and percentage errors. Explain the sources of errors in numerical computation.

errors
8short5 marks

Explain the secant method for finding the root of an equation and compare it with the Newton-Raphson method.

nonlinearsecant
9short5 marks

Describe the false position (regula falsi) method with its geometric interpretation.

nonlinearfalse-position
10short5 marks

State and explain Lagrange's interpolation formula with a suitable example.

interpolationlagrange
11short5 marks

Derive the trapezoidal rule for numerical integration and state its error term.

integrationtrapezoidal
12short5 marks

Explain the Gauss-Seidel iterative method to solve a system of linear equations.

linear-systemsiterative