MA2111 Mathematics I
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MA2111 Mathematics - I

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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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