MA2111 MATHEMATICS1 Anna University Semester1 syllabus
MA2111
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MATHEMATICS – I
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3
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1
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0 4
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UNIT I
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MATRICES
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12
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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 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
TEXT BOOK:
TOTAL: 60 PERIODS
1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, Third edition, Laxmi Publications(p) Ltd.,(2008).
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2. Grewal. B.S, “Higher Engineering Mathematics”, 40
Delhi, (2007).
Edition, Khanna Publications,
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing
Company, New Delhi, (2007).
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2. Glyn James, “Advanced Engineering Mathematics”, 7
(2007).
Edition, Pearson Education,
3. Jain R.K and Iyengar S.R.K,” Advanced Engineering Mathematics”,
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3 Edition, Narosa Publishing House Pvt. Ltd., (2007).
