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Applied Mathematics 3 Semester 3 (SE Second Year) BE Chemical Engineering University of Mumbai Topics and Syllabus

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

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

Units and Topics

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100 The Laplace Transform
  • Definition and properties (without proofs)
  • All standard transform methods for elementary functions including hyperbolic functions; Heaviside unit step function, Dirac delta function; the error function
  • Evaluation of integrals using Laplace transforms
  • Inverse Laplace transforms using partial fractions and H(t-a)
  • Convolution (no proof).
200 Matrices
  • Eigen values and eigen spaces of 2x2 and 3x3 matrices
  • Existence of a basis and finding the dimension of the eigen space (no proofs)
  • Nondiagonalisable matrices
  • Minimal polynomial
  • Cayley - Hamilton theorem (no proof)
  • Quadratic forms
  • Orthogonal and congruent reduction of a quadratic form in 2 or 3 variables; rank, index, signature; definite and indefinite forms.
300 Complex Analysis
  • Cauchy-Riemann equations (only in Cartesian coordinates) for an analytic function (no proof)
  • Harmonic function
  • Laplace’s equation; harmonic conjugates and orthogonal trajectories (Cartesian coordinates); to find f(z) when u+v or u - v are given
  • Milne-Thomson method; cross-ratio (no proofs); conformal mappings; images of straight lines and circles.
400 Complex Integration
  • Complex Integration Cauchy’s integral formula; poles and residues
  • Cauchy’s residue theorem
  • Applications to evaluate real integrals of trigonometric functions
  • Integrals in the upper half plane; the argument principle.
500 Statistics
  • Mean, median, variance, standard deviation
  • Binomial, Poisson and normal distributions
  • Correlation and regression between 2 variables.
  • Note:- No theory questions expected in this module
600 Optimization
  1. Non-linear programming
  • Lagrange multiplier method for 2 or 3 variables with at most 2 constraints
  • Conditions on the Hessian matrix (no proof)
  • Kuhn-Tucker conditions with at most 2 constraints.
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