181101 MATHEMATICS – I SYLLABUS | 181101MATHEMATICS – I | ANNA UNIVERSITY M1 SYLLABUS FOR ECE,EEE,IT ,MECH,CSE,|
181101 MATHEMATICS – I SYLLABUS | 181101MATHEMATICS – I | ANNA UNIVERSITY M1 SYLLABUS FOR ECE,EEE,IT ,MECH,CSE,| M1 QUESTION BANK
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”, 40th
Publications, Delhi, (2007).
REFERENCES:
Edition, Khanna
1. Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill
Publishing Company, New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 7th
Education, (2007).
Edition, Pearson
3. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”,
3rd Edition, Narosa Publishing House Pvt. Ltd., (2007).
182101 ENGINEERING PHYSICS – I 3 0 0 3
UNIT I ULTRASONICS 9
Introduction – Production – magnetostriction effect - magnetostriction generator- piezoelectric effect - piezoelectric generator- Detection of ultrasonic waves properties
– Cavitations - Velocity measurement – acoustic grating - Industrial applications – drilling, welding, soldering and cleaning – SONAR - Non Destructive Testing – pulse echo system through transmission and reflection modes - A,B and C –scan displays, Medical applications - Sonograms
UNIT II LASERS 9
Introduction – Principle of Spontaneous emission and stimulated emission. Population inversion, pumping. Einsteins A and B coeffcients - derivation. Types of
lasers – He-Ne, CO
2 ,
Nd-YAG, Semiconductor lasers (homojunction &
heterojunction) Qualitative Industrial Applications - Lasers in welding, heat treatment,
cutting – Medical applications - Holography (construction & reconstruction).
UNIT III FIBER OPTICS & APPLICATIONS 9
Principle and propagation of light in optical fibres – Numerical aperture and Acceptance angle - Types of optical fibres (material, refractive index, mode) – Double crucible technique of fibre drawing - Splicing, Loss in optical fibre – attenuation, dispersion, bending - Fibre optical communication system (Block diagram) - Light sources - Detectors - Fibre optic sensors – temperature & displacement - Endoscope.
UNIT IV QUANTUM PHYSICS 9
Black body radiation – Planck’s theory (derivation) – Deduction of Wien’s displacement law and Rayleigh – Jeans’ Law from Planck’s theory – Compton effect. Theory and experimental verification – Matter waves – Schrödinger’s wave equation
– Time independent and time dependent equations – Physical significance of wave
function – Particle in a one dimensional box - Electron microscope - Scanning electron microscope - Transmission electron microscope.
UNIT V CRYSTAL PHYSICS 9
Lattice – Unit cell – Bravais lattice – Lattice planes – Miller indices – d spacing in cubic lattice – Calculation of number of atoms per unit cell – Atomic radius – Coordination number – Packing factor for SC, BCC, FCC and HCP structures – NaCl, ZnS, diamond and graphite structures – Polymorphism and allotropy - Crystal defects – point, line and surface defects- Burger vector.
TOTAL: 45 PERIODS
TEXT BOOKS
1. R. K. Gaur and S.C. Gupta, ‘Engineering Physics’ Dhanpat Rai Publications, New Delhi(2003)
2. M.N. Avadhanulu and PG Kshirsagar, ‘A Text book of Engineering Physics’,
S.Chand and company, Ltd., New Delhi, 2005.
REFERENCES
1. Serway and Jewett, ‘Physics for Scientists and Engineers with Modern
th
Physics’, 6
Edition, Thomson Brooks/Cole, Indian reprint (2007)
2. Rajendran, V and Marikani A, ‘Engineering Physics’ Tata McGraw Hill
Publications Ltd, III Edition, New Delhi, (2004).
3. Palanisamy, P.K., ‘Engineering Physics’ Scitech publications, Chennai, (2007).
4. Jayakumar. S, ‘Engineering Physics’, R.K. Publishers, Coimbatore, (2003).
5. Chitra Shadrach and Sivakumar Vadivelu, ‘Engineering Physics’, Pearson
Education, New Delhi, (2007).
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