## MA8352 Linear Algebra and Partial Differential Equations Syllabus Notes Question Paper Question Banks with answers Anna University

#### Anna University Linear Algebra and Partial Differential Equations Syllabus Notes Question Bank Question Papers Regulation 2017

#### MA8352 Linear Algebra and Partial Differential Equations Syllabus Regulation 2017

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.

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MA8352 Linear Algebra and Partial Differential Equations Notes Syllabus

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