Course Period: 31st July 2023 to 30th November 2023 ( Monday 2:30PM to 3:55 PM ; Thursday- 4:00PM to 05:25 PM)
Number of Credits: 3 credits
Vectors; matrix; operation of vector and matrix; Tensor: definition, notation, orthogonal properties, order of a tensor, operations, contraction, contravariant and covariant tensors; Solution of different problems by MATLAB.
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; solution of realistic civil engineering problems by MATLAB.
PDE: classification, canonical forms, analytical solutions, Fourier series and transformation-based solution; Numerical solution techniques for PDE; use of MATLAB to solve realistic problems.
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); MATLAB to solve different problems.
What you'll learn:
The candidates will understand the philosophy of using mathematics to solve different kinds of civil engineering problems.
The candidates will understand how to formulate a physical problem in the context of mathematics.
The candidates will understand how to solve different problems numerically by MATLAB and manual calculations.
About the Instructor: Dr. Biswarup Bhattacharyya is an Assistant Professor in the Structural Engineering specialization in the Department of Civil Engineering at IIT Hyderabad. He completed his Ph.D. at the Université Claude Bernard Lyon 1, France. He also has a post-Ph.D. research experience from ETH Zurich, Switzerland and Purdue University, USA, before joining IITH. His research areas include Uncertainty Quantification, Physics-informed machine learning, Digital twin, Reliability analysis, and Stochastic modelling. He has published several research papers in peer-reviewed international journals and international conferences. He also serves as a scientific committee member for several international conferences. He serves as a reviewer for several peer-reviewed international journals and conferences.