MA8352 Linear Algebra And Partial Differential Equations

Important Topics to Clear M3

Regulation 2017

 UNIT I VECTOR SPACES   

 Linear combinations and linear system of equations

Linear independence and linear dependence

Bases and dimensions.

UNIT II LINEAR TRANSFORMATION AND DIAGONALIZATION  

Linear transformation

Dimension theorem

Matrix representation of a linear transformations

Eigenvalues and eigenvectors

UNIT III INNER PRODUCT SPACES  

 Gram Schmidt orthogonalization process

Adjoint of linear operations

Least square approximation.

UNIT IV PARTIAL DIFFERENTIAL EQUATIONS   

Lagrange‘s linear equation

Solution of linear equations of higher order with constant coefficients

Linear non-homogeneous partial differential equations.

UNIT V FOURIER SERIES SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS   Dirichlet‘s conditions

Method of separation of variables

 Fourier series solutions in Cartesian coordinates. 

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