ADVANCED ENGINEERING MATHEMATICS - II (English)

ADVANCED ENGINEERING MATHEMATICS - II (English)

Regular price ₹ 250.00

Unit-1 Introduction: Objective, scope and outcome of the course.

Unit-2 Complex Variable – Differentiation: Differentiation, Cauchy-Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; elementary analytic functions (exponential, trigonometric, logarithm) and their properties; Conformal mappings, Mobius transformations and their properties.

Unit-3 Complex Variable - Integration: Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy Integral formula (without proof), Liouville’s theorem and Maximum- Modulus theorem (without proof); Taylor’s series, zeros of analytic functions, singularities, Laurent’s series; Residues, Cauchy Residue theorem (without proof).

Unit-4 Applications of complex integration by residues: Evaluation of definite integral involving sine and cosine. Evaluation of certain improper integrals.

Unit-5 Special Functions: Legendre’s function, Rodrigues formula, generating function, Simple recurrence relations, orthogonal property. Bessel’s functions of first and second kind, generating function, simple recurrence relations, orthogonal property.

Unit-6 Linear Algebra: Vector Spaces, subspaces, Linear independence, basis and dimension, Inner product spaces, Orthogonality, Gram Schmidt orthogonalization, characteristic polynomial, minimal polynomial, positive definite matrices and canonical forms, QR decomposition.

  • Author: K.C. Sarangi
  • Publisher: Genius Publications (Latest Edition)
  • Language: English

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