MA2111 MATHEMATICS1 Anna University Semester1 FullNotesCollection
UNIT I
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MATRICES
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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.
UNIT II THREE DIMENSIONAL ANALYTICAL GEOMETRY
Equation 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
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes – Envelopes – Evolute asenvelope of normals.
UNIT IV FUNCTIONS OF SEVERAL VARIABLES
Partial derivatives – Euler’s theorem for homogenous functions – Total derivatives – Differentiation of implicit functions – Jacobians –Taylor’s expansion – Maxima and Minima – Method of Lagrangian multipliers.
UNIT V MULTIPLE INTEGRALS
Double integration – Cartesian and polar coordinates – Change of order of integration – Change of variables between Cartesian andpolar coordinates – Triple integration in Cartesian co-ordinates – Area as double integral – Volume as triple integral
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