University of Mumbai Syllabus For Semester 4 (SE Second Year) Applied Mathematics 4: Knowing the Syllabus is very important for the students of Semester 4 (SE Second Year). Shaalaa has also provided a list of topics that every student needs to understand.

The University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 syllabus for the academic year 2021-2022 is based on the Board's guidelines. Students should read the Semester 4 (SE Second Year) Applied Mathematics 4 Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 Syllabus pdf 2021-2022. They will also receive a complete practical syllabus for Semester 4 (SE Second Year) Applied Mathematics 4 in addition to this.

## University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 Revised Syllabus

University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 and their Unit wise marks distribution

### University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 Course Structure 2021-2022 With Marking Scheme

# | Unit/Topic | Marks |
---|---|---|

100 | Complex Integration | |

200 | Matrices | |

300 | Correlation | |

400 | Probability | |

500 | Sampling Theory | |

600 | Mathematical Programming | |

Total | - |

## Syllabus

- 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

- Eigen values and eigen vectors
- Cayley-Hamilton theorem (without proof)
- Similar matrices, diagonalisable of matrix
- Derogatory and non-derogatory matrices, functions of square matrix

- Scattered diagrams, Karl Pearson’s coefficient of correlation, covariance, Spearman’s Rank correlation
- Regression Lines

- 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)

- 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.

- 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).