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 2022-2023 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 2022-2023. 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 2022-2023 With Marking Scheme

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

C | Module 1 | |

101 | Calculus of Variation | |

102 | Functions Involving Higher Order Derivatives | |

CC | Module 2 | |

201 | Linear Algebra: Vector Spaces | |

202 | Vectors in N-dimensional Vector Space | |

CCC | Module 3 | |

301 | Linear Algebra: Matrix Theory | |

CD | Module 4 | |

401 | Complex Integration | |

402 | Complex Variables | |

Total | - |

## Syllabus

### University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 Syllabus for Module 1

- Euler Langrange equation.
- Solution of Euler‘s Langrange equation (only results for different cases for function) independent of a variable, independent of another variable, independent of differentiation of a variable and independent of both variables.
- Isoperimetric problems, several dependent variables.

- Rayleigh-Ritz method

### University of Mumbai Semester 4 (SE Second Year) Applied Mathematics 4 Syllabus for Module 2

- Properties
- Dot product
- Cross product
- Norm and distance properties in n-dimensional vector space.
- Metric spaces, vector spaces over real field
- Properties of vector spaces over real field, subspaces.
- Norms and normed vector spaces.
- Inner products and inner product spaces
- The Cauchy-Schwarz inequality, orthogonal Subspaces
- Gram-Schmidt Process.

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

- Characteristic equation
- Eigenvalues and Eigenvectors
- Properties of Eigenvalues and Eigenvectors
- Cayley-Hamilton theorem, examples based on verification of CayleyHamilton theorem.
- Similarity of matrices
- Diagonalisation of matrix Functions of square matrix
- Derogatory and non-derogatory matrices Quadratic forms over real field
- Reduction of quadratic form to a diagonal canonical form
- rank, index, signature of quadratic form
- Sylvester‘s law of inertia
- value-class of a quadratic form of definite, semidefinite and indefinite Singular Value Decomposition.

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

- Line Integral
- Cauchy‘s Integral theorem for simply connected regions
- Cauchy‘s Integral formula
- Taylor‘s and Laurent‘s series.

- Zeros
- Singularities
- Poles of f(z)
- Residues
- Cauchy‘s Residue theorem
- Applications of Residue theorem to evaluate real Integrals of different types.