MA2111- Mathematics -1 Anna University Question Paper Nov/Dec - 2011 Regulation 2008/2012/2013

Subject : Mathematics -1

Subject Code: MA2111

University: Anna University

Type: Anna University Question Paper

Semester: First Semester

Department: Common  to all branches

Regulation: 2008/2010/2013

MA2111- Mathematics -1 Anna University Syllabus:

UNIT I MATRICES                                                                          12

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     12

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                                            12

Curvature 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                       12

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                                                    12

Double integration – Cartesian and polar coordinates – Change of order of

integration – Change of variables between Cartesian and polar coordinates – Triple

integration in Cartesian co-ordinates – Area as double integral – Volume as triple

integral

TOTAL : 60 PERIODS

Download: MA2111- Mathematics -1 Anna University Question Paper Nov/Dec 2011 Regulation 2008/2012/2013

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