**Chap 1. Complex Integration**

**1.1** Complex Integration –Line Integral, Cauchy‟s Integral theorem for simply connected regions, Cauchy‟s Integral formula(without proof)

**1.2** Taylor‟s and Laurent‟s series ( without proof)

**1.3** Zeros, poles of f(z), Residues, Cauchy‟s Residue theorem.

**1.4** Applications of Residue theorem to evaluate Integrals of the type

$\int_0^{2\pi} f(cos\theta \ , \sin \theta) \ d\theta$, $\int_{-\infty}^{\infty} f(x) \ dx$

**Chap 2. Matrices**

**2.1** Eigen values and Eigen vectors.

**2.2** Cayley-Hamilton theorem(without proof)

**2.3** Similar matrices, diagonalisable matrix.

**2.4** Derogatory and non-derogatory matrices, Functions of square matrix.

**Chap 3. Probability**

**3.1** Baye‟s Theorem

**3.2** **Random Variables:** Discrete &continuous random variables, expectation, Variance, Probability Density Function & Cumulative Density Function.

**3.3** Moments & Moment generating function.

**3.4** **Probability distribution:** Binomial distribution, Poisson &Normal distribution. (For detail study)

**Chap 4. Sampling Theory (Large Sample test)**

**4.1** Sampling Distribution, Test of Hypothesis, Level of significance, Critical region, One Tailed and Two Tailed test,

**4.2** Test of significant for Large Samples:-Means of the samples and test of significant of means of two large samples.

**Chap 5. Sampling Theory (Small Sample test)**

**5.1** Test of significant for small samples:-Students t-distribution for dependent and independent samples

**5.2** Chi square test:-Test of goodness of fit and independence of attributes,Contingency table.

**Chap 6.Mathematical Programming**

**6.1** Types of solution, Standard and Canonical form of LPP, Basic and feasible solutions, simplex method.

**6.2** Artificial variables, Big –M method (method of penalty).

**6.3** Duality and Dual simplex method.

**6.4** Non Linear Programming Problems with equality constrains and inequality Constrains (two or three variables with one constrains) (No formulation, No Graphical method).