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 |
---|---|---|

C | Module 1 | |

101 | Laplace Transform (Lt) of Standard Functions | |

102 | Properties of Laplace Transform | |

103 | Inverse Laplace Transform | |

104 | Applications of Laplace Transform | |

CC | Module 2 | |

201 | Introduction | |

202 | Fourier Series of Functions | |

CCC | Module 3 | |

301 | Solution of Bessel Differential Equation | |

CD | Module 4 | |

401 | Scalar and Vector Product | |

402 | Vector Differentiation | |

403 | Properties | |

404 | Vector Integral | |

D | Module 5 | |

501 | Complex Variable | |

502 | Mapping | |

Total | - |

## Syllabus

### University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus for Module 1

- Definition. unilateral and bilateral Laplace Transform
- LT of sin(at), cos(at), e
^{at},t^{n}, sinh(at), cosh(at), erf(t) - Heavi-side unit step
- dirac-delta function
- LT of periodic function.

- Linearity,
- first shifting theorem,
- second shifting theorem,
- multiplication by t
^{n}, division by t , - Laplace Transform of derivatives and integrals,
- change of scale,
- convolution theorem,
- initial and final value theorem,
- Parsavel‘s identity.

- Partial fraction method
- long division method
- residue method.

- Solution of ordinary differential equations.

### University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus for Module 2

- Definition
- Dirichlet‘s conditions
- Euler‘s formulae.

- Exponential, trigonometric functions, even and odd functions, half range sine and cosine series.
- Complex form of Fourier series, orthogonal and orthonormal set of functions, Fourier integral representation.

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

- Series method, recurrence relation, properties of Bessel function of order +1/2 and -1/2 Generating function, orthogonality property.
- Bessel Fourier series of functions.

### University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus for Module 4

- Scalar and vector product of three and four vectors and their properties.

- Gradient of scalar point function
- divergence and curl of vector point function.

- Solenoidal and irrotational vector fields
- conservative vector field.

- Line integral
- Green‘s theorem in a plane
- Gauss‘ divergence theorem
- Stokes‘ theorem.

### University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus for Module 5

- Analytic Function: Necessary and sufficient conditions, Cauchy.
- Reiman equation in polar form.
- Harmonic function, orthogonal trajectories.

- Conformal mapping.
- bilinear transformations.
- cross ratio.
- fixed points.
- bilinear transformation of straight lines and circles.