Credits: 3 (3–0–0)
Description
Review of linear algebra: Vectors, Matrices, Functions, Coordinate transformation (linear and orthogonal), Eigen values and Eigen vectors; Eigenvalue Problems: Matrix and diagonalization; Tensors and its applications in materials science (elastic anisotropy etc.,); Vector Calculus for different geometries – Linear and planes, directional derivative, gradients and integral theorems; Partial Differentiation – properties and solution techniques; Integration: Single, multiple, line and change of variables; Ordinary Differential Equations: Analytical and Numerical Solution methods of ODEs; Data Analysis: Probability and statistics - Curve fitting; Computing Probability, smoothening and reconciliation of data, concept and parameters of distribution, regression analysis (linear and nonlinear), Error estimation and analysis, confidence intervals, hypothesis testing; Numerical Techniques: Roots of equation, solution of Linear and Nonlinear systems of equations (Bisection, Newton raphson), Interpolation and extrapolation.