Numerical Methods

• Chapter 1: Errors and Approximations. Notes and past questions on Errors and Approximations for TU BIT Numerical Methods.
• Chapter 2: Root Finding Methods. Notes and past questions on Root Finding Methods for TU BIT Numerical Methods.
• Chapter 3: Interpolation and Approximation. Notes and past questions on Interpolation and Approximation for TU BIT Numerical Methods.
• Chapter 4: Curve Fitting and Regression. Notes and past questions on Curve Fitting and Regression for TU BIT Numerical Methods.
• Chapter 5: Numerical Differentiation. Notes and past questions on Numerical Differentiation for TU BIT Numerical Methods.
• Chapter 6: Numerical Integration. Notes and past questions on Numerical Integration for TU BIT Numerical Methods.
• Chapter 7: Systems of Linear Equations. Notes and past questions on Systems of Linear Equations for TU BIT Numerical Methods.
• Chapter 8: Eigenvalues and Eigenvectors. Notes and past questions on Eigenvalues and Eigenvectors for TU BIT Numerical Methods.
• Chapter 9: Ordinary Differential Equations. Notes and past questions on Ordinary Differential Equations for TU BIT Numerical Methods.
• Chapter 10: Partial Differential Equations. Notes and past questions on Partial Differential Equations for TU BIT Numerical Methods.

• Explain how bisection method differ from secant. Derive the formula for Newton Raphson. Use Newton Raphson method to solve the equation $... (2082)
• Write an algorithm to compute the value of interpolation using Newton’s divided difference method.Write a program to compute the value of... (2082)
• List out any two applications of system of linear equation. Differentiate between Gauss-Seidel and Jacobi iteration method. Solve the fol... (2082)
• Differentiate between round-off error and truncation error. Explain how they affect numerical computations, with the help of an example.... (2082)
• Derive the formula for two points forward difference. Derive the formula for two points backward difference. [2.5+2.5] (2082)
• Fit the exponential curve $y = ae^{bx}$ for (1,15), (2,22), (3,33), (4,48), (5,70) using least square method. [5] (2082)
• Solve the following system of linear equation using Cholesky decomposition method: $$ \begin{aligned} 4x + 6y - 8z &= -8 \\ 6x + 13y - 11... (2082)
• Find the first and second derivative at $x = 2.5$ of the following data points. $$\begin{array}{|c|cccccc|}\hline x & 1.5 & 2 & 2.5 & 3 &... (2082)
• Integrate $\int_{0}^{3} (2x^3 + 1) dx$ using Simpson's $\frac{1}{3}$ rule with $n=6$. [5] (2082)
• Solve $\frac{dy}{dx} = x^2 + y$, with $y(0) = 1$ for $x = 1.5$, using RK fourth order method. [5] (2082)
• Explain boundary value problem with example. Describe how higher order differential equation can be solved. [2+3] (2082)
• Define eigenvalue and eigenvector. Distinguish between regression and interpolation. [2.5+2.5] (2082)
• Write an algorithm and a C-Program to obtain roots of non-linear equation using Newton Raphson Method.[10] (2080)
• Solve the following ordinary differential equation using shooting method. $y'' + xy' - xy = 2x$ with boundary conditions $y(0) = 1$ and $... (2080)
• Compare and contrast between Jacobi iterative methods and Gauss Seidal method? Solve the following equation using Gauss Seidal method. $$... (2080)

Frequently asked questions

Based on the official syllabus.