Syllabus

Introduction: Importance of numerical methods, Historical perspective, Basic concepts of Error analysis, Precision, accuracy, significant digit, and calibration. (2 hours)

Algebraic equations: Linear systems- Direct method: Gauss elimination method, Gauss-Jordan method, LU Decomposition method, Tri-diagonal matrix algorithm, Iterative method: Gauss-Siedel method, Jacobi iteration, Non-linear systems- Bracketing methods: Bisection method, Regula-falsi method, Open methods: Secant method, fixed point iteration, Newton-Raphson method, Modifications and extension, root finding. (10 hours)

Regression analysis and curve fitting: linear regression, Polynomial regression, Multiple leaner regression, non-linear regression, Interpolation, Fourier approximation. (6 hours)

Numerical differentiation and integration: Trapezoidal rule, Simpson rules, open integration formula, Integration to determine the total quantity of heat, Root-mean-square current by numerical integration. (6 hours)

Differential equations: Ordinary differential equations: Euler’s method, Improvements of Euler’s method, Runge-Kutta Methods, Systems of Equations, Adaptive Runge-Kutta methods, Boundary value and Eigenvalue problems. Partial differential equations: Elliptic equations, Parabolic equations, Finite difference method. (12 hours)

• To be familiar with error analysis.

• To have a good understanding of regression analysis and have our own correlations for engineering problems.

• To select a specific numerical method to solve practical problems.

• To familiarize different numerical methods to solve engineering problems.

Course Outcomes: At the end of the course, students will be able to
CO1: Develop an idea regarding error analysis.
CO2: Understand the solution techniques for linear and non-linear algebraic equations.
CO3: Understand the regression analysis and curve fitting.
CO4: Understand and apply numerical differentiation and integration techniques.
CO5: Solving ordinary and partial differential equations using various numerical methods.

Steven C. Chapra, Raymond P. Canale, Numerical Methods for Engineers, Mc Graw Hill , 2023

B. S. Grewal, Numerical Methods in Engineering and Science with Programs in C, C++ & MATLAB, Khanna Publishers , 2024

S. S. Sastry, Introductory Methods of Numerical Analysis, PHI , 2024

K. Sankara Rao, Numerical Methods for Scientists and Engineers, PHI , 2021