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# Applied Mathematics 4 Semester 4 (SE Second Year) BE Construction Engineering University of Mumbai Topics and Syllabus

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

## Topics with syllabus and resources

100.00 Matrices
101.00 Brief Revision of Vectors Over a Real Field
• Brief revision of vectors over a real field, inner product, norm, Linear Dependance and Independence and orthogonality of vectors.
102.00 Characteristic Polynomial
• Characteristic polynomial,
• characteristic equation,
• characteristic roots and characteristic vectors of a square matrix,
• properties of characteristic roots and vectors of different types of matrices such as orthogonal matrix, Hermitian matrix, Skew-Hermitian matrix,
• Cayley Hamilton theorem ( without proof) Functions of a square matrix, Minimal polynomial and Derogatory matrix.
200.00 Vector Calculus
201.00 Brief Revision of Scalar and Vector Point Functions
• Brief revision of Scalar and vector point functions, Gradient, Divergence and curl.
202.00 Line Integrals, Surface Integrals, Volume Integrals
• Line integrals, Surface integrals, Volume integrals.
• Green’s theorem(without proof) for plane regions and properties of line integrals, Stokes theorem(without proof),
• Gauss divergence theorem (without proof) related identities and deductions.(No verification problems on Stoke’s Theorem and Gauss Divergence Theorem)
300.00 Non Linear Programming
301.00 Unconstrained Optimization
• Unconstrained optimization, problems with equality constraints Lagranges Multiplier method.
302.00 Problem with Inequality

Problem with inequality constraints Kuhn-Tucker conditions.

400.00 Probability Distributions
401.00 Discrete and Continuous Random Variables
• Discrete and Continuous random variables, Probability mass and density function,
• Probability distribution for random variables, Expected value, Variance.
402.00 Probability Distributions
• Binomial, Poisson and Normal Distributions. For detailed study.
500.00 Sampling Theory
501.00 Sampling Distribution
• Sampling distribution. Test of Hypothesis. Level of significance, critical region.
• One tailed and two tailed tests. Interval Estimation of population parameters.
• Large and small samples.
502.00 Test of Significance for Large Samples
• Test of significance for Large samples: Test for significance of the difference between sample mean and population means,
• Test for significance of the difference between the means of two samples.
503.00 Studentâ€™S T-distribution
• Student’s t-distribution and its properties.
• Test of significance of small samples: Test for significance of the difference between sample mean and population means,
• Test for significance of the difference between the means of two Samples, paired t-test.
504.00 Analysis of Variance(F-test)
• One way classification, Two-way classification(short-cut method)
505.00 Chi-square Distribution
• Chi-square distribution and its properties, Test of the Goodness of fit and Yate’s correction
600.00 Correlation and Regression
601.00 Correlation, Co-variance
• Correlation, Co-variance, Karl Pearson Coefficient of Correlation & Spearman’s Rank Correlation Coefficient (non-repeated & repeated ranks )
602.00 Regression Coefficients
• Regression Coefficients & lines of regression

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