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  • 8:18 PM, Tuesday, 22 Sep 2020


Course Postgraduate
Semester Electives
Subject Code AE810
Subject Title Linear Algebra and Perturbation Methods

Syllabus

Vector space, norm, and angle – Linear independence and orthonormal sets – Row reduction and echelon forms, matrix operations, including inverses – Effect of round-off error, operation counts – Block/banded matrices arising from discretization of differential equations – Linear de- pendence and independence – Subspaces and bases and dimensions – Orthogonal bases and orthogonal projections – Gram-Schmidt process – Linear models and least-squares problems – Eigenvalues and Eigenvectors – Diagonalization of a matrix – Symmetric matrices – Positive definite matrices – Similar matrices – Linear transformations and change of basis – Singular value decomposition.

Introduction to perturbation techniques – Asymptotic approximations, algebraic equations – Regular and singular perturbation methods – Application to differential equations – Methods of strained coordinates for periodic solutions – Poincare–Lindstedt method. ́

Text Books

Same as Reference

References

1. Strang, G., Introduction to Linear Algebra, 4th ed., Cambridge Univ. Press (2011).

2. Strang, G., Linear Algebra and its Applications, 4th ed., Cengage Learning (2007).

3. Lang S., Linear Algebra, 2nd ed., Springer (2004).

4. Golub, G. H. and Van Loan, C. F., Matrix Computations, 4th ed., Hindustan Book Agency (2015).

5. Nayfe, A. H., Introduction to Perturbation Techniques, Wiley-VCH (1993).

6. Bender, C. M. and Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, Springer (1999).