# Applied Mathematics 4 Semester 4 (SE Second Year) BE Instrumentation Engineering University of Mumbai Topics and Syllabus

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.

CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## 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

## Syllabus

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

101 Calculus of Variation
• 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.
102 Functions Involving Higher Order Derivatives
• Rayleigh-Ritz method

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

201 Linear Algebra: Vector Spaces
202 Vectors in N-dimensional Vector Space
• 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

301 Linear Algebra: Matrix Theory
• 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

401 Complex Integration
• Line Integral
• Cauchy‘s Integral theorem for simply connected regions
• Cauchy‘s Integral formula
• Taylor‘s and Laurent‘s series.
402 Complex Variables
• Zeros
• Singularities
• Poles of f(z)
• Residues
• Cauchy‘s Residue theorem
• Applications of Residue theorem to evaluate real Integrals of different types.