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

## Syllabus

- Brief revision of vectors over a real field, inner product, norm, Linear Dependance and Independence and orthogonality of vectors.

- 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.

- Brief revision of Scalar and vector point functions, Gradient, Divergence and curl.

- 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)

- Unconstrained optimization, problems with equality constraints Lagranges Multiplier method.

Problem with inequality constraints Kuhn-Tucker conditions.

- Discrete and Continuous random variables, Probability mass and density function,
- Probability distribution for random variables, Expected value, Variance.

- Binomial, Poisson and Normal Distributions. For detailed study.

- 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.

- 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.

- 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.

- One way classification, Two-way classification(short-cut method)

- Chi-square distribution and its properties, Test of the Goodness of fit and Yate’s correction

- Correlation, Co-variance, Karl Pearson Coefficient of Correlation & Spearman’s Rank Correlation Coefficient (non-repeated & repeated ranks )

- Regression Coefficients & lines of regression