ec2k 301: engineering mathematics iii - Sahrdaya

EN2K 101 : MATHEMATICS I
(Common for all programmes)
Module I: Differential Calculus (15 hours)
Indeterminate forms - L` hospital`s rule - Radius of curvature - Centre of
curvature -Evolute - Functions of more than one variable - Idea of partial
differentiation - Euler`s theorem for homogeneous functions - Chain rule of
partial differentiation - Applications in errors and approximations -
Change of variables - Jacobians - Maxima and minima of functions of two or
more variables - Method of Lagrange multipliers. Module II: Infinite Series (15 hours)
Notion of convergence and divergence of infinite series -Ratio test -
Comparison test - Raabe`s test - Root test - Series of positive and
negative terms - Idea of absolute convergence - Test for alternating series
- Power series - Interval of convergence - Taylors and Maclaurins series
representation of functions - Leibnitz formula for the nth derivative
of the product of two functions - Use of Leibnitz formula in the Taylor
and Maclaurin expansions. Module III: Matrices (21 hours)
Concept of rank of a matrix -Reduction of a matrix to echelon and normal
forms - System of linear equations - Consistency of linear equations -
Gauss` elimination - Homogeneous linear equations - Fundamental system of
solutions - Inverse of a matrix - Solution of a system of equations using
matrix inversion - Eigen values and eigen vectors - Cayley-Hamilton
theorem - Eigen values of Hermitian, skew-Hermitian and unitary matrices -
quadratic forms - Matrix associated with a quadratic form - Technique of
diagonalization using row and column transformations on the matrix -
Definite, semidefinite and indefinite forms - Their identification using
the eigen values of the matrix of the quadratic form. Module IV: Fourier series and harmonic analysis (15 hours)
Periodic functions - Trigonometric series - Fourier series - Euler formulae
- Even and odd functions - Functions having arbitrary period - Half range
expansions - Approximation by trigonometric polynomials - Minimum square
error - Numerical method for determining Fourier coefficients - Harmonic
analysis.
EN2K 102 : MATHEMATICS II
(Common for all programmes)
Module 1: Ordinary differential equations (21 hours)
A brief review of the methods of solutions of first order equations -
Separable, homogeneous and linear types - Exact equations - Orthogonal
trajectories - General linear second order equations - Homogeneous linear
equation of the second order with constant coefficients - Fundamental
system of solutions - Method of variation of parameters - Cauchy's equation
- Simple applications of differential equations in engineering problems,
including problems in mechanical vibrations, electric circuits and bending
of beams. Module II: The Laplace transforms (15 hours)
Gamma and Beta functions - Definitions and simple properties - The Laplace
transform - Inverse transform - Laplace transform of derivatives and
integrals - Shifting theorems - Differentiation and integration of
transforms - Transforms of unit step function and impulse function -
Transform of periodic functions - Solution of ordinary differential
equations using Laplace transforms. Module III: Vector differential calculus (15 hours)
Vector function of single variable - Differentiation of vector functions -
Scalar and vector fields - Gradient of a scalar field - Divergence and curl
of vector fields - Their physical meanings - Relations between the vector
differential operators. Module IV: Vector integral calculus (15 hours)
Double and triple integrals and their evaluation - Line, surface and volume
integrals - Green`s theorem - Gauss` divergence theorem - Stokes` theorem
(proofs of these theorems not expected) - Line integrals independent of the
path. EN2K 103A : ENGINEERING PHYSICS(A)
(common for AI, CS, EE, EC, IT & IC)
Module I (11 hours)
Interference of light - Interference from plane parallel thin films -
Colours of thin films by reflected light - Newtons rings - Measurement of
wave length - Thin wedge shaped air film - Air wedge - Testing of optical
planes of surfaces.
Diffraction of light - Introduction of Fresnel and Fraunhofer diffraction -
Distinction between the two diffractions - Simple theory of plane
transmission grating.
Polarisation of light - Double refraction - Nicol prism - Quarter and half
wave plates - Production and detection of elliptically and circularly
polarised light - Rotatory polarisation - Lawrent's half shade Polarimeter
- Applications of polarised light. Module II ( 11 hours)
Quantum mechanics - Newtonian mechanics and quantum mechanics - The wave
function - Schrodinger's wave equation for free particle - Potentials in
Schrodinger equation - Time dependent Schrodinger equation - Time
independent Schrodinger equation -
Expectation values - Derivation of Schrodinger equation - Application -
Particle in a box
( motion in one dimension )
Ultrasonics - Piezo effect - Piezo electric crystal production and
detection of ultrasonics - Applications of ultrasonics
NMR and ESR - Basic principles of Nuclear Magnetic Resonance (NMR) and
Electron Spin Resonance (ESR) - Experimental method for detection of NMR
and ESR - Applications. Module III (11 hours)
Laser Physics - Basic concepts of laser - Spontaneous and stimulated
emission - Absorption - Population inversion - Optical pumping -
Construction and components of laser - Ruby Laser, Helium - Neon Laser and
semiconductor Laser - Applications - Basic principle of holography and its
application.
Fibre Optics - Basic Principle - Fibre constructions - Fibre dimensions -
Light propagation in fibre - Signal distortion in optical fibres and
transmission losses (brief ideas only) - Light wave communication using
optical fibres and its advantages - Applications. Module IV (11 hours)
Semiconductor physics - Energy band diagrams - Classifications of
semiconductors on the basis of Fermi level and Fermi energy - Impurity
level in N-type and P-type semiconductors - Applications of Semiconductors
- zener diode, light emitting diode, solar cell, phototransistor, photo
resister (LDR).
Hall effect introduction - Measurement of Hall voltage and Hall coefficient
- Importance of Hall effect.
Super conductivity - Properties of superconductors - Josephson effect and
tunnelling (qualitative) BCS theory of superconductivity (qualitative) -
Applications of superconductivity. EN2K 104A : ENGINEERING CHEMISTRY(A)
(common for AI, CS, EE, EC, IT & IC)
Module I (13 hours)
Structure of Solids - Geometry of crystalline solids - Space lattices -
Crystal structure - Bragg's law of X-ray diffraction - Covalent solids -
Ionic solids - Metals and alloys - Noncrystalline states - Crystal
imperfections - Point defects - Dislocations.
Conductors and resistors - Free electron theory - Super conductors -
Semiconductors - Intrinsic and extrinsic - Semiconductor materials and
their fabrication - Liquid crystals.
Dielectric materials - Polarization - Feroelectric materials.
Module II (9 hours) Electrochemistry - Electrode potentials - Types of electrodes - Salt bridge
- emf measurement - Concentration cells - Acids and bases - Buffer
solutions - pH measurement - Glass electrode - Polarization - Over voltage
- Secondary cells and fuel cells.
Module III (9 hours) Corrosion - Protective coatings and pollution - Dry corrosion - Oxidation
processes -Wet corrosion - Electrochemical theory - Different forms of
corrosion - Prevention and control - Protective coating - Pretreatment of
surface - Metallic and nonmetallic coatings - Electro deposition -
Cementation - Metal spraying - Air pollution - Types - Causes - Power
generation pollution - Thermal pollution - Petrochemical smog - Methods of
control.
Module IV (13 hours)
High polymers and lubricants - Polymerisation and functionality - Chain,
condensation and copolymerisation - Mechanism - Coordination Polymerisation
- Polymerisation processes - Structure, properties and molecular weight of
polymers - Thermosetting and thermoplastics materials - Application in
electrical and electronic industries - Elastomers - Vulcanization -
Synthetic rubbers. Lubricants - Theory of friction - Mechanisms of lubrication -
Classification and properties of lubricants - Additives - Synthetic
lubricants - Solid lubricants.
EN2K 105 : HUMANITIES
(common for all programmes)
Module I (10 hours)
Introduction to English Usage and Grammar
Review of grammar - Affixes, prefixes, suffixes, participles and gerunds -
Transformation of sentences - Commonly misspelt words - Correction of
mistakes - Punctuation - Idioms - Style - Vocabulary building
Reading Comprehension
Exposure to a variety of reading materials, articles, essays, graphic
representation, journalistic articles, etc.
Writing Comprehension
Skills to express ideas in sentences, paragraphs and essays Module II (10 hours)
Technical Communication and Report Writing
Growing need and importance of technical communication - aspects of
technical description of machinery, equipment and processes - Giving
instructions in an industrial situation - Note taking and note making -
Correspondence on technical topics - Different types of technical reports Module III (10 hours)
Humanities in a Technological Age
Importance of humanities to technology, education and society - Relation of
career interests of engineers to humanities - Relevance of a scientific
temper - Science, society and culture Introduction to writings of modern
Thinkers on society