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

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CBCGS [2017 - current]
CBGS [2013 - 2016]
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Topics with syllabus and resources

100.00 Module 1
101.00 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.
102.00 Functions Involving Higher Order Derivatives
  • Rayleigh-Ritz method
200.00 Module 2
201.00 Linear Algebra: Vector Spaces
202.00 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.
300.00 Module 3
301.00 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.
400.00 Module 4
401.00 Complex Integration
  • Line Integral
  • Cauchy‘s Integral theorem for simply connected regions
  • Cauchy‘s Integral formula
  • Taylor‘s and Laurent‘s series.
402.00 Complex Variables
  • Zeros
  • Singularities
  • Poles of f(z)
  • Residues
  • Cauchy‘s Residue theorem
  • Applications of Residue theorem to evaluate real Integrals of different types.
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