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 2021-2022 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 2021-2022. 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 2021-2022 With Marking Scheme
| # | Unit/Topic | Marks |
|---|---|---|
| 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
- 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
- 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.
- 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.
- 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.
