Review: System of linear Equations, linear independence. (3 hrs)

Eigen values and Eigen vectors: Definitions and properties. Positive definite, negative definite and indefinite. (8 hrs) Diagonalization and Orthogonal Diagonalization. Properties of Matrices. Symmetric and Skew Symmetric Matrices, Hermitian and Skew Hermitian Matrices and Orthogonal matrices. (Sections: 8.1-8.4) (10 hrs)

Numerical Computations: L U factorization, Gauss Seidal and Gauss Jacobi methods for solving system of equations. Power Method for Eigen Values and Eigen Vectors. (Sections: 20.2, 20.3, 20.8) (8 hrs)

Evaluation Pattern

1. Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Tenth Edition, 2018.

• Advanced Engineering Mathematics by Dennis G. Zill and Michael R.Cullen, second edition, CBS Publishers, 2012.
• ‘Engineering Mathematics’, Srimanta Pal and Subhodh C Bhunia, John Wiley and Sons, 2012, Ninth Edition.

Course Outcomes

CO1: Understand the notion of eigenvalues and eigenvectors, analyze the possibility of diagonalization and hence compute a diagonal matrix, if possible.

CO2: Apply the knowledge of diagonalization to transform the given quadratic form into the principal axes form and analyze the given conic section.

CO3: Understand the advantages of the iterative techniques and apply it to solve the system of equations and finding eigenvectors.

Mapping of course outcomes with program outcomes: