Advanced Mathematical Methods Scanned Premium Lecture Notes from Buvana. Syllabus is Based on Anna University , Post Graduate M.E. Structural Engineering R2013 Regulations.

Content:

Unit-1(Pages: 46)

LAPLACE TRANSFORM TECHNIQUES FOR THE PARTIAL DIFFERENTIAL EQUATION

UNIT-2 (Pages: 24)

FOURIER TRANSFORM

UNIT-3 (Pages: 28)

CALCULUS OF VARIATION

UNIT-4 (Pages: 18)

CONFORMAL MAPPING AND ITS APPLICATION

UNIT-5 (Pages: 19)

TENSOR ANALYSIS

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Unit-1

LAPLACE TRANSFORM TECHNIQUES FOR THE PARTIAL DIFFERENTIAL EQUATION

Laplace transform

First shifting theorem

Change of scale property

Final value theorem

Initial value theorem

Error function

Complementary error function

Transform of Bessel function

Unit step function

Inverse laplace transform

Second shifting property

Complex inversion formula

Convolution theorem

Solving ODE using laplace transform

The wave equation

One dimensional heat equation

Two dimensional heat equation

Boundary condition

UNIT-2

FOURIER TRANSFORM

Parseval’s identity

Differentiation of fourier series and cosine

Flow of heat in a semi – infinite medium

UNIT-3

CALCULUS OF VARIATION

Functionals

The euler’s equation

Other form of eulers equation

Functional dependent on function of several independent variables

Variational problems with moving boundaries

Constrains in the form of function

Rayleigh – ritz method

UNIT-4

CONFORMAL MAPPING AND ITS APPLICATION

Bilinear transformation

Fixed points

Cross ratio

Conformal mapping

Transformation

Magnification

Magnification and rotation

Magnification, rotation and translation

Inversion and reflection

Schwartz – christoffel transformation

Application of conformal planning

Dirchlet’s for half plan

Properties of analytical function

UNIT-5

TENSOR ANALYSIS

Properties of tensor analysis

Contravariant tensor

Second order tensor

Construction of tensor

Quotient law

Conjugate tensor

Associate tensors

Christoffel symbol

Derivation of fundamental tensor

Covariant derivative of a covariant vector

Curl of a covariant vector

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