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You are here:Open notes-->Anna-University-->MA2111-Mathematics---I

# How to study this subject

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
TEXT BOOK:
1. Bali N. P and Manish Goyal, �Text book of Engineering Mathematics�, Third edition,
Laxmi Publications(p) Ltd.,(2008).
2. Grewal. B.S, �Higher Engineering Mathematics�, 40
th
Edition, Khanna Publications,
Delhi, (2007). 5
REFERENCES:
1. Ramana B.V, �Higher Engineering Mathematics�, Tata McGraw Hill Publishing
Company, New Delhi, (2007).
2. Glyn James, �Advanced Engineering Mathematics�, 7
th
Edition, Pearson Education,
(2007).
3. Jain R.K and Iyengar S.R.K,� Advanced Engineering Mathematics�,
3
rd
Edition, Narosa Publishing House Pvt. Ltd., (2007).

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