Basic of linear algebra.
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.
About the Instructor
Dr. Biswarup Bhattacharyya is an Assistant Professor in the Department of Civil Engineering (Specialization: Structural Engineering) at IIT Hyderabad. He has completed PhD from the Université Claude Bernard Lyon 1, France and has postdoc experiences from the ETH Zurich, Switzerland and Purdue University, USA. His research areas include Machine learning for uncertainty quantification, reliability analysis, structural health monitoring of computational mechanics and dynamics problems. He teaches Mathematical Methods in Civil Engineering, Machine Learning and Scientific Computing for Civil Engineers, and Structural Analysis.
Instructor ProfileCourse Assessment
Assessment may consist of assignments &/or quizzes &/viva &/or exams.