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## Applied Mathematics 4

Students studying Computer Science will find this subject very useful. Hundreds of important topics on Applied Mathematics 4 are organized neatly into lessons below.

### Overview

#### Topics Covered

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 ...

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).