Faculty Name: Dr. Biswarup Bhattacharyya

Course Name: Mathematical Methods in Civil Engineering (CE5170)

Course Period: Jul to Dec 2025

Number of Credits: 3 credits

Course Contents: Vectors; matrix; operation of vector and matrix; Norms of vector and matrix; Tensor: definition, notation, orthogonal properties, order of a tensor, operations, contraction, quotient rule.

Laplace transformation; Fourier series; Fourier transformation

First and second order ODE; Initial and boundary value problems; Numerical solution techniques for homogeneous and non-homogeneous problems.

PDE: classification, canonical forms, analytical solutions, Fourier series and transformation-based solution.

Numerical integration, numerical differentiation, numerical methods to find roots of equations, numerical methods for curve fitting

System of linear equations: matrix form, Cramer’s rule, inverse, singularity; Inconsistent equations; Gauss-Elimination method; Gauss-Seidel method; LU decomposition; Eigenvalue and eigenvectors; Orthogonalization; Gram-Schimdt orthogonalization; Singular value decomposition (SVD), Least square method, Positive definite matrix

What you'll learn: The students will learn fundamentals of mathematical methods for engineering applications. Along with that, there will be an opportunity to learn coding using mathematics for engineering problems. The advanced engineering mathematics required for a basic understanding of Machine Learning will also be taught.