'Linear Algebra for Chemical Engineers' is a course offered in the first semester of B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.
Course Outcomes
| CO Code | Course Outcome Statement |
| CO01 | Using the basic concepts of vector and matrix algebra, including linear dependence / independence, basis and d imension of a subspace, rank and nullity, vector and inner product spaces, analyze matrices and systems of linear algebraic equations. |
| CO02 | Using appropriate numerical techniques, solve systems of linear algebraic equations and determine inverses of invertible matrices, and apply these solutions to engineering problems. |
| CO03 | Use the characteristic polynomial to compute the eigenvalues and eigenvectors of a square matrix, diagonalize matrices, identify linear transformations of finite dimensional vector spaces and compose their matrices. Apply the eigensystem analysis to solve engineering problems. |
| CO04 | Develop numerical techniques to solve single and systems of nonlinear algebraic equations and apply them to solve engineering problems. |
| CO05 | Define correlation between variables, use it to develop linear regression models and apply them to engineering p roblems. |
| CO06 | Use software for scientific computation (e.g., MATLAB), to enhance and facilitate mathematical understanding, a s well as an aid in solving engineering problems and presenting solutions. |
CO - PO Mapping
| CO Code | PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO 10 | PO 11 | PO 12 | PSO 1 | PSO2 | PSO3 |
| CO01 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||||||
| CO02 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||||||
| CO03 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||||||
| CO04 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||||||
| CO05 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||||||
| CO06 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 2 | 2 |
Unit -1
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
Unit -2
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.
Unit -3
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.
TEXT BOOKS
- Gilbert Strang, Linear Algebra and Its Applications, 4th Edition, Cengage Learning, 2006
- Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India Ltd., 2011
- Bruce Finlayson, Introduction to Chemical Engineering Computing, John Wiley & Sons, 2006
REFERENCE BOOKS
- Michael Greenberg, Advanced Engineering Mathematics, 2nd Edition, Pearson, 2011
- Kenneth J. Beers, Numerical Methods for Chemical Engineering: Applications in MATLAB, Cambridge University Press, 2006
- AlkisConstantinides, NavidMostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications, Prentice Hall International Series, 1999.
- Pradeep Ahuja, Introduction to Numerical Methods in Chemical Engineering, PHI Learning Pvt Ltd, 2010
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