Advanced Mathematical Methods Premium Lecture Notes - 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.

Syllabus :

ADVANCED MATHEMATICAL METHODS
UNIT-1
LAPLACE TRANSFORNS TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATION (Page No : 1 to 48)
UNIT-2
FOURIER TRANSFORMS (Page No : 49 to 78)
UNIT-3
CALCULUS OF VARIATION (Page No : 79 to 120)
UNIT-4
CONFORMAL MAPPING AND ITS APPLICATION (Page No : 121 to 148)
UNIT-5
TENSOR ANALYSIS (Page No : 149 to 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