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 trans- formation – contour integration and Cauchy’s 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 2π – 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.

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).

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).

Course Outcomes (COs):

CO1: Understand the basic concepts of vector space and subspaces

CO2: Determine rank and nullity of space and matrix of linear Transformation

CO3: Understand basic concepts of analytic functions and harmonic functions

CO4: Evaluate integrals of features using Cauchy’s theorem and Cauchy integral formula

CO5: Apply Taylor’s and Laurent’s series expansion and find singularities of function

CO6: Understand the convergence of Fourier series and evaluate Fourier series of periodic and even functions