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# KTU B.Tech S3 Lecture Note – LINEAR ALGEBRA AND COMPLEX ANALYSIS

S3 Lecture Note  LINEAR ALGEBRA  COMPLEX ANALYSIS

MODULE I

• Complex differentiation

Limit, continuity and derivative of complex functions

Analytic Functions

Cauchy–Riemann Equation

Harmonic functions, Harmonic Conjugate

MODULE II

Geometry of Analytic functions Conformal Mapping,

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Circles and straight lines, extended complex plane, fixed points Special linear fractional Transformations,

Conformal mapping by w=  sinz & w = cos z

MODULE III

• Complex Integration

Cauchy’s Integral Theorem

Cauchy’s Integral Formula- Derivatives of Analytic Functions

Taylor and Maclaurin series

Laurent’s series

MODULE IV

• Residue Integration

Residue Integration Method, Formulas for Residues.

Several singularities inside the contour Residue  Theorem.

MODULE V

• Linear system of Equations

Linear systems of Equations,

Linear independence-rank of a matrix Vector Space-Dimension-basis-vector spaceR 3

Solution of linear systems, Fundamental theorem of non homogeneous linear s/m ,Homogeneous linear s/m

MODULE VI

• Matrix Eigen value Problem

Determination of Eigen values and Eigen vectors-Eigen space

Symmetric, Skew Symmetric and Orthogonal matrices –simple properties

Basis of Eigen vectors- Similar matrices Diagonalization of a matrixQuadratic forms- Principal axis theorem

S3 Lecture Note  LINEAR ALGEBRA  COMPLEX ANALYSIS

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