Notes in Mathematics

May 19th, 2015
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Characteristic equation – Eigen values and eigen vectors of a real matrix – Properties – Cayley-Hamilton theorem (excluding proof) – Orthogonal transformation of a symmetric matrix to diagonal form – Quadratic form – Reduction of quadratic form to canonical form by orthogonal transformation.

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181101MATHEMATICS I 3 1 0 4UNIT I MATRICES 12Characteristic equation Eigen values and eigen vectors of a real matrix Properties Cayley-Hamilton theorem (excluding proof) Orthogonal transformation of a symmetric matrix to diagonal form Quadratic form Reduction of quadratic form to canonical form by orthogonal transformation.UNIT II THREE DIMENSIONAL ANALYTICAL GEOMETRY 12Equation of a sphere Plane section of a sphere Tangent Plane Equation of a cone Right circular cone Equation of a cylinder Right circular cylinder.UNIT III DIFFERENTIAL CALCULUS 12Curvature in Cartesian co-ordinates Centre and radius of curvature Circle of curvature Evolutes Envelopes Evolute as envelope of normals.UNIT IV FUNCTIONS OF SEVERAL VARIABLES 12Partial derivatives Eulers theorem for homo

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