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 2021-2022 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 2021-2022. 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 2021-2022 With Marking Scheme

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

100 | Module 1 The Laplace Transform | |

200 | Module 2 Matrices | |

300 | Module 3 Complex Analysis | |

400 | Module 4 Cauchy’S Formula and Theorem | |

500 | Module 5 Statistics | |

600 | Module 6 Optimization | |

Total | - |

## Syllabus

- The Laplace transform:- 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).

- Matrices:-

- Eigenvalues and eigenspaces of 2x2 and 3x3 matrices;
- existence of a basis and finding the dimension of the eigenspace (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.

- Complex analysis:-

- 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.

- Statistics:

- (No theory questions expected in this module) Mean, median, variance, standard deviation;
- binomial, Poisson and normal distributions;
- correlation and regression between 2 variables.

- 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.