MA7154 Advanced Mathematical Methods Scanned Lecture Notes (All Units) Ashok Edition

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AFFILIATED INSTITUTIONS

ANNA UNIVERSITY :: CHENNAI 600 025

REGULATIONS - 2013

M.E. STRUCTURAL ENGINEERING

MA7154 Advanced Mathematical Methods

Scanned Lecture Notes (All Units)

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.

Content :
UNIT-1

Laplace transform
First shifting theorem
Change of scale property
Initial value theorem
Transform of Bessel function
Unit step function on Heaviside function
Inverse laplace transform
Complex inversion formulae or mellin fourier transform
Convolution theorem 
Wave equation
One dimensional heat equation
Two dimensional heat equation

UNIT-2
Fourier transform
Parsavel identity
Differentiation of fourier sin and cosine

UNIT-3
Variational function
Geotesices
Functional dependent on higher order derivations
Functional dependent on function several independent variable
Variational problem with moving boundaried
Constrains in the form of function
Rayleigh –ritz method

 UNIT-4
CONFORMAL MAPING
Transformation
1. Translation
2. Magnification
Magnification rotate and translate
Inversion and reflection
Schwartz-christoftel transformation
Application of conformal mapping
Dirichlets problem for the unit circle

UNIT-5
Tensor analysis
Kronecker delta
Contravarient tensor
Addition of 2 tensor
Contraction of tensor
Quotient law
Symmetric and skew symmetric tensor
Matric tensor
Associate tensor
Christofel symbol
Derivational of the fundamental tensor
Transformation of christofel symbol
Co-varient derivative of a co-varient vector
Curl of a co-varient vector
Co-varient derivation of a contravarient vector
Divergent of a contra-varient vector

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