UNIT I MATRICES
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 as envelope 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 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”, 40th
Edition, Khanna Publications,Delhi, (2007).
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing
Company, New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 7th
Edition, Pearson Education,(2007).
3. Jain R.K and Iyengar S.R.K,” Advanced Engineering Mathematics”,3rd Edition, Narosa Publishing House Pvt. Ltd., (2007).
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