Basics of Linear Algebra – Linear Dependence and independence of vectors – Gaussian Elimination – Rank of set of vectors forming a matrix – Vector space and Basis set for a Vector space – Dot product and Orthogonality – Rotation matrices – Eigenvalues and Eigenvectors and its interpretation – Projection matrix and Regression – Singular Value Decomposition.
Convolution sum, Convolution Integral, Ordinary Linear differential equations, formulation, analytical and Numerical solutions, Impulse Response Computations, formulating state space models of Physical systems.
Examples of ODE modelling in falling objects, satellite and planetary motion, Electrical and mechanical systems. Multivariate calculus, Taylor series, Introduction to Optimization.
Introduction to Probability Distributions and Monte Carlo Simulations.