BE IT (Information Technology) Semester 4 (SE Second Year)University of Mumbai
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# Applied Mathematics 4 Semester 4 (SE Second Year) BE IT (Information Technology) University of Mumbai Topics and Syllabus

SubjectApplied Mathematics 4
CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Complex Integration
• Complex Integration – Line Integral, Cauchy’s Integral theorem for simply connected regions, Cauchy’s Integral formula (without proof)
• Taylor’s and Laurent’s series (without proof)
• Zeros, poles of f(z), Residues, Cauchy’s Residue theorem
• Applications of Residue theorem to evaluate Integrals of the type
200.00 Matrices
• Eigen values and eigen vectors
• Cayley-Hamilton theorem (without proof)
• Similar matrices, diagonalisable of matrix
• Derogatory and non-derogatory matrices, functions of square matrix
300.00 Correlation
• Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance, Spearman’s Rank correlation
• Regression Lines
400.00 Probability
• Baye’s Theorem
• Random Variables:- discrete & continuous random variables, expectation, Variance, Probability Density Function & Cumulative Density Function.
• Moments, Moment Generating Function.
• Probability distribution:- binomial distribution, Poisson & normal distribution. (For detail study)
500.00 Sampling Theory
• Test of Hypothesis, Level of significance, Critical region, One Tailed and two Tailed test, Test of significant for Large Samples:- Means of the samples and test of significant of means of two large samples.
• Test of significant of small samples:- Students t- distribution for dependent and independent samples.
• Chi square test:- Test of goodness of fit and independence of attributes, Contingency table.
600.00 Mathematical Programming
• Types of solution, Standard and Canonical form of LPP, Basic and feasible solutions, simplex method.
• Artificial variables, Big –M method (method of penalty).
• Duality, Dual simplex method.
• Non Linear Programming:- Problems with equality constrains and inequality constrains (No formulation, No Graphical method).
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