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• 3:49 PM, Sunday, 24 Oct 2021

 Course Dual Degree (B. Tech + M.S / M.Tech) Semester Sem. III Subject Code MA211 Subject Title Linear Algebra, Complex Analysis and Fourier Series

##### Syllabus

Linear Algebra: matrices- solution space of system of equations Ax=b, eigenvalues and eigenvectors, Cayley-Hamilton theorem – vector spaces over real field, subspaces, linear dependence, independence, basis, dimension – inner product – Gram-Schmidt orthogonalization process – linear transformation- null space & nullity, range and rank of linear transformation.

Complex Analysis: complex numbers and their geometrical representation – functions of complex variable – limit, continuity and derivative of functions of complex variable – analytical functions and applications – harmonic functions – transformations and conformal mappings – bilinear transformation – contour integration and Cauchys theorem – convergent series of analytic functions – Laurent and Taylor series – zeroes and singularities – calculation of residues – residue theorem and applications.

Fourier Series and Integrals: expansion of periodic functions with period 2 – Fourier series of even and odd functions – half-range series – Fourier series of functions with arbitrary period – conditions of convergence of Fourier series – Fourier integrals.

##### Text Books

1. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).

2. Mathews, J. H. and Howell, R., Complex Analysis for Mathematics and Engineering, Narosa (2005).

##### References

1. Brown, J. W. and Churchill, R. V., Complex Variables and Applications, 9th ed., McGraw- Hill (2013).

2. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).

3. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, 4th ed., Alpha Science Intl. Ltd. (2013).