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  • 2:43 PM, Saturday, 08 Aug 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 dependence 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 – reg- ular 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 , 4 th ed., Cambridge Univ. Press (2011).

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

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

4. Golub, G. H. and Van Loan, C. F., Matrix Computations , 4 th 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).