Vectors and Vector Spaces: Inner Products, Linear Dependence, Dimension, Basis, Gram-Schmidt Orthonormalization; Matrix Representation of Vectors: Matrix Algebra and Vector Algebra.
Systems of Linear Algebraic Equations: Cramer’s Rule, Gauss Elimination, Gauss-Seidel Iteration, Diagonal Dominance, Tridiagonal Matrix Algorithm (TDMA); Applications: Mass Balance in Flow Sheets, Flow networks, solving electrical circuit problems, stoichiometric equations, Linear ODEs and Linear PDEs
Eigenvalues and Eigenvectors: Definitions and Properties, Positive definite, Negative Definite and Indefinite Matrices, Diagonalization and Orthogonal Diagonalization, Quadratic form, Transformation of Quadratic Form to Principal axes, Symmetric and Skew Symmetric Matrices, Hermitian and Skew Hermitian Matrices and Orthogonal Matrices; Power Method for Eigenvalues and Eigenvectors, Applications to Principal Component Analysis.
Solution of nonlinear Algebraic Equations: nonlinear algebraic equations; analytical techniques and Numerical techniques for solving single nonlinear equations; Numerical techniques for solving systems of nonlinear equations – Bisection method and Newton-Raphson method. Systems of nonlinear Algebraic Equations: Multivariable Newton-Raphson Method; Applications: Fluid Mechanics, Thermodynamics (Engines), Equation of State, Vapor-Liquid Equilibrium, Conversion in Reversible Reactions.
Linear Regression: Least Squares, Interpolation and Curve Fitting, Applications: Correlations for Thermodynamic and Transport Properties.
Lab Practice: Iterative methods in matrix theory, power method, bisection and newton Raphson methods, linear regression and curve fitting.
Course Evaluation Pattern:
Test-1 -15 marks (two hour test)
CA - 20 marks (Quizzes / assignments / lab practice) Test – 2- 15 marks (two-hour test)
End semester- 50 marks.
Total - 100 marks.
Supplementary exam for this course will be conducted as a three-hour test for 50 marks.