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

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


100 Matrices
101 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 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 Vector Calculus
201 Brief Revision of Scalar and Vector Point Functions
  • Brief revision of Scalar and vector point functions, Gradient, Divergence and curl.
202 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 Non Linear Programming
301 Unconstrained Optimization
  • Unconstrained optimization, problems with equality constraints Lagranges Multiplier method.
302 Problem with Inequality

Problem with inequality constraints Kuhn-Tucker conditions.

400 Probability Distributions
401 Discrete and Continuous Random Variables
  • Discrete and Continuous random variables, Probability mass and density function,
  • Probability distribution for random variables, Expected value, Variance.
402 Probability Distributions
  • Binomial, Poisson and Normal Distributions. For detailed study.
500 Sampling Theory
501 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 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 Student’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 Analysis of Variance(F-test)
  • One way classification, Two-way classification(short-cut method)
505 Chi-square Distribution
  • Chi-square distribution and its properties, Test of the Goodness of fit and Yate’s correction
600 Correlation and Regression
601 Correlation, Co-variance
  • Correlation, Co-variance, Karl Pearson Coefficient of Correlation & Spearman’s Rank Correlation Coefficient (non-repeated & repeated ranks )
602 Regression Coefficients
  • Regression Coefficients & lines of regression
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