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
Attachment: click here
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
Attachment: click here
