Advanced Mathematical Methods (MA7154) Scanned Lecture Notes - Evangeline Edition

  • 7Feb
  • 2015
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    AFFILIATED INSTITUTIONS
    ANNA UNIVERSITY :: CHENNAI 600 025
    REGULATIONS - 2013
    M.E. STRUCTURAL ENGINEERING
    First Semester
    MA7154 Advanced Mathematical Methods
    Scanned Lecture Notes (All Units) - Evangeline Edition

    Advanced Mathematical Methods Scanned Premium Lecture Notes from Reputed Institutions and Faculties, Contains All Units. Syllabus is Based on Anna University , Post Graduate M.E. Structural Engineering R2013 Regulations.

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    Syllabus :
    ADVANCED MATHEMATICAL METHODS

    UNIT-1
    LAPLACE TRANSFORNS TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATION (1-48)
    UNIT-2
    FOURIER TRANSFORMS (49-78)
    UNIT-3
    CALCULUS OF VARIATION (79-120)
    UNIT-4
    CONFORMAL MAPPING AND ITS APPLICATION (121-148)
    UNIT-5
    TENSOR ANALYSIS (149-174)


    Content :
    UNIT-1

    LAPLACE TRANSFORMS TECNIQUES FOR PARTIAL DIFFERENTIAL EQUATION
    Laplace transform
    First shifting theorem
    Change of scale property
    Initial value theorem
    Final value theorem
    Error function
    Transform of Bessel function
    Unit step function or heavi side function
    Inverse laplace transform
    Complex inversion formula or mellin fourier integral
    Convolution theorem or faltung theorem
    Solving O.D.E using laplace transform
    Wave equation
    One dimensional heat equation
    Two dimensional heat equation

    UNIT-2

    FOURIER TRANSFORM
    Fourier integral transform
    Inversion fourier transform
    Parseval’s identity
    Bernoulli’s integral
    Differentiation of fourier sine and cosine
    Convolution theorem

    UNIT-3

    CALCULUS OF VARIATION
    Functional
    Euller’s equation
    Other forms of euler’s equation
    Test for the extremal of a function
    Variational problems for functionals dependent on two function
    Geodesic
    Functions depends on higher order derivation
    Variational problems with moving boundaries
    Constrains in the form of functional (isoperimetric problems)
    Rayleigh – ritz method

    UNIT-4

    CONFORMAL MAPPING AND ITS APPLICATION
    Bilinear transformation
    Fixed points or inverient points
    Cross-ratio
    Confirmal mapping
    Transformation
    1. Translation
    2. Magnification
    3. Magnification and rotation
    4. Magnification ,rotation and translation
    5. Inversion and reflection
    SCHWARTZ-CHRISTOFFEL TRANSFORMATION
    Application of conformal mapping
    Dirichelt’s and Neumann problems
    Dirichlet’s problems for half plane
    Properties of analytical function
    Brachestrone problems , revolution statement

    UNIT-5

    TENSOR ANALYSIS
    Properties of tensor analysis
    Contravariant tensor (vector)
    Second order tensor
    Addition of two tensor
    Contraction of tensor
    Quotient law
    Symmentric and skew-symmetric tensor
    Metric tensor
    Conjugate or reciprocal tensor
    Associative tensor
    Christoffel symbol
    Derivation of fundamental tensor
    Transformation of christoffel symbol
    Covariant derivative of a covariant vector
    Curl of a covariant vector
    Covariant derivative of a contravariant vector
    Divergence of a contravarient vector

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    i am ready for purchase I semester ME structural engg all sub notes. but through online display bank interface is no correct.