University of Mumbai Syllabus For Semester 3 (SE Second Year) Applied Mathematics 3: Knowing the Syllabus is very important for the students of Semester 3 (SE Second Year). Shaalaa has also provided a list of topics that every student needs to understand.

The University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Semester 3 (SE Second Year) Applied Mathematics 3 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 3 (SE Second Year) Applied Mathematics 3 Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Semester 3 (SE Second Year) Applied Mathematics 3 in addition to this.

## University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Revised Syllabus

University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 and their Unit wise marks distribution

### University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Course Structure 2022-2023 With Marking Scheme

# | Unit/Topic | Weightage |
---|---|---|

100 | The Laplace Transform | |

200 | Matrices | |

300 | Complex Analysis | |

400 | Complex Integration | |

500 | Statistics | |

600 | Optimization | |

Total | - |

## Syllabus

- Definition and properties (without proofs)
- All standard transform methods for elementary functions including hyperbolic functions; Heaviside unit step function, Dirac delta function; the error function
- Evaluation of integrals using Laplace transforms
- Inverse Laplace transforms using partial fractions and H(t-a)
- Convolution (no proof).

- Eigen values and eigen spaces of 2x2 and 3x3 matrices
- Existence of a basis and finding the dimension of the eigen space (no proofs)
- Nondiagonalisable matrices
- Minimal polynomial
- Cayley - Hamilton theorem (no proof)
- Quadratic forms
- Orthogonal and congruent reduction of a quadratic form in 2 or 3 variables; rank, index, signature; definite and indefinite forms.

- Cauchy-Riemann equations (only in Cartesian coordinates) for an analytic function (no proof)
- Harmonic function
- Laplace’s equation; harmonic conjugates and orthogonal trajectories (Cartesian coordinates); to find f(z) when u+v or u - v are given
- Milne-Thomson method; cross-ratio (no proofs); conformal mappings; images of straight lines and circles.

- Complex Integration Cauchy’s integral formula; poles and residues
- Cauchy’s residue theorem
- Applications to evaluate real integrals of trigonometric functions
- Integrals in the upper half plane; the argument principle.

- Mean, median, variance, standard deviation
- Binomial, Poisson and normal distributions
- Correlation and regression between 2 variables.
- Note:- No theory questions expected in this module

- Non-linear programming

- Lagrange multiplier method for 2 or 3 variables with at most 2 constraints
- Conditions on the Hessian matrix (no proof)
- Kuhn-Tucker conditions with at most 2 constraints.