S3 Lecture Note LINEAR ALGEBRA COMPLEX ANALYSIS

**MODULE I**

**Complex differentiation**

Limit, continuity and derivative of complex functions

Harmonic functions, Harmonic Conjugate

**MODULE II**

Geometry of Analytic functions Conformal Mapping,

Cross Ratio, Cross Ratio property-Mapping of disks and half planes Conformal mapping by w

Conformal mapping by w= sinz & w = cos z

**MODULE III**

- Complex Integration

Cauchy’s Integral Formula- Derivatives of Analytic Functions

**MODULE IV**

**Residue Integration**

Singularities, Zeros, Poles, Essential singularity, Zeros of analytic functions.

Residue Integration Method, Formulas for Residues.

Several singularities inside the contour Residue Theorem.

**MODULE V**

**Linear system of Equations**

Coefficient Matrix, Augmented Matrix Gauss Elimination and back substitution, Elementary row operations.

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

**MODULE VI**

**Matrix**Eigen value**Problem**

Determination of Eigen values and Eigen vectors-Eigen space

Symmetric, Skew Symmetric and Orthogonal matrices –simple properties

S3 Lecture Note LINEAR ALGEBRA COMPLEX ANALYSIS

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