MA8352 – NOTES & QP
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MA8352 – SYLLABUS
UNIT I VECTOR SPACES
Vector spaces — Subspaces — Linear combinations and linear system of equations — Linear independence and linear dependence — Bases and dimensions.
UNIT II LINEAR TRANSFORMATION AND DIAGONALIZATION
Linear transformation — Null spaces and ranges — Dimension theorem — Matrix representation of a linear transformations — Eigenvalues and eigenvectors — Diagonalizability.
UNIT III INNER PRODUCT SPACES
Inner product, norms — Gram Schmidt orthogonalization process — Adjoint of linear operations — Least square approximation.
UNIT IV PARTIAL DIFFERENTIAL EQUATIONS
Formation — Solutions of first order equations — Standard types and equations reducible to standard types — Singular solutions — Lagrange?s linear equation — Integral surface passing through a given curve — Classification of partial differential equations — 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 — General Fourier series — Half range sine and cosine series — Method of separation of variables — Solutions of one dimensional wave equation and one-dimensional heat equation — Steady state solution of two-dimensional heat equation — Fourier series solutions in Cartesian coordinates.