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MINOR Importance and course content of minor courses of each department

Electrical List of minor courses in the EE department : Minor Courses offered in the Autumn Semester : 1) EE 221 Digital Electronics: Introduction to Boolean Algebra, finite state machines, basic memory elements like shift registers, bipolar and MOS logic families. Brief idea of ROM, RAM, PLA etc. 2) EE 327 Signal Processing: Introduction to LTI systems, continuous and discrete signals, Fourier transform, Fast Fourier Transform, Discrete Fourier Transform, Sampling theorem, digital filters and spectral estimation. 3) EE 321 Power Electronics: Power electronic devices and circuit topologies, PWM.

Minor Courses offered in the Spring Semester : 1) EE 232 Analog Electronics: Introduction to OP-AMPs, feedback systems, Analog to Digital interfacing, waveform generation. 2) EE 342 Control and Communications: Analog communication systems, Pulse coding modulation, Pulse Amplitude Modulation. 3) EE 203 Electronic Devices: Modeling devices, PN junction diodes, discrete transistor amplifier, BJT and MOS transistors. The aim of the minor courses offered by the Electrical Engineering department is to give an overview of the basic subjects in the field : 1) Communication and Signal Processing 2) Control and Computing 3) Power electronics and Power systems The idea of memory elements of ROM and PLA are required as these are the basic building blocks of storage of many computational devices. In this age where processing is autonomous, the elementary knowledge of finite state machines is useful for a logical

approach to programming. For any engineeringsystem, the measured quantity is generally a signal in some form; however this signal is distorted with noise. Therefore, to obtain measurements, it is necessary to process a clean signal for precision. This is particularly useful in the process control and instrumentation sector. Chips are designed for various applications in every field of engineering, also BJT and power diodes are used for various small or high voltage applications, as a result to find definite results for point of operation, stability etc. modelling of devices is required to put them in a form which can be solved by a computer or such like. The knowledge of the characteristics of these devices helps to place them in a familiar form, thus optimizing calculations. Together these courses aim to cater to the multifarious and ever-growing needs of the industry.

Mechanical The minor in mechanical engineering complements studies in a major field closely allied to mechanical engineering, such as materials science and engineering, aeronautics and astronautics, electrical engineering, management, and a number of other possibilities. A student can be awarded a minor in mechanical engineering provided he completes any five of the following courses: Design Engineering 1) Solid Mechanics (ME 201M, 6 credits, Spring Semester): Introduction. Analysis of Axially Loaded Components – Statically Determinate and Indeterminate Problems; Castigliano’s Theorem. Analysis of Shear Loaded Components. Beams; Shear Force and Bending Moment Diagrams. Stress and Strain Tensors. Mohr Circle. Stress-strain Relations; Stress-straintemperature Relations. Basic Equations of Elasticity. Material Testing - Properties under tension, impact, fatigue and creep. Strain Rosettes. Stresses in Beams. Torsion of Circular Shaft. Introduction to Elastic-plastic Bending of Beams and Torsion of Circular Shaft. Thick Cylinder; Interference Fit; Rotating Disc. 2) Kinematics and Dynamics of Machines (ME 316M, 6 credits, Autumn Semester): Introduction to Mechanisms. Position, velocity and acceleration analysis. Design of Cam Follower Mechanisms. Gear tooth profiles, spur gears and helical gears. Epicyclic Gear Trains. Dynamic Analysis of Mechanisms. Balancing. Analysis and Applications of Discrete and Continuous System Vibration. Thermal & Fluids Engineering

3) Thermodynamics (ME 209M, 6 credits, Autumn Semester): Introduction to thermodynamics. System, surroundings, boundaries, classification of systems. Units and dimensions. Conversion factors. Properties of systems. Equilibrium, processes, interactions. The work interaction. Thermodynamic definition of work. Characteristics of the work interaction. Evaluation of work. Adiabatic boundary. Adiabatic systems and processes. Adiabatic work. The First Law. Basic form. Energy of a system. The heat interaction. Sign convention. Diathermic boundary. Zeroth law. Isothermal states. Empirical temperature. Principles of thermometry. Scales of temperature. Gas thermometer. The ideal gas. Ideal gas temperature scale. The state principle. Equations of state. Properties of gases. Properties of steam. Introduction to steam tables. Other equations of state. Van-der-Waals gas. Critical state. Reduced equation of state. First law for open systems. Derivation of the general form. Special cases. Steady-flow energy equation. The Second Law. Kelvin-Planck and Clausius statements. Equivalence of statements. Carnot theorem. Thermodynamic temperature. Kelvin scale. Carnot engine. Equivalence of thermodynamic Kelvin scale and ideal gas Kelvin scale. Clausius inequality. Definition of entropy. Evaluation of entropy. Principle of increase of entropy. Formulation of second law for closed and open systems. Auxiliary functions. Property relations. Maxwell’s equations. Applications to equations of state. Combined first and second laws. Availability and exergy. Lost work.

4) Fluid Mechanics (ME 203M, 6 credits, Autumn Semester): Domain of Fluid mechanics, Concept of Continuum, Mean free path, Knudsen number, applicability of continuum, chain rule, Differential-Integral analysis, dimensionality of the problem, Scalar, Vector, Tensor, Stream line, Streak line, path line and time line, thermodynamic properties, equation of state, viscosity, Newtonian and Non-Newtonian, kinematic viscosity, surface tension and contact angle. Pascal’s law, Hydrostatic equation, Force on planar surfaces, Force on a curved surface, Manometry, Buoyancy, Stability of floating objects, pressure distribution in solid body translation and rotation. Reynolds transport theorem, Conservation of mass, linear momentum, for fixed, moving and accelerating control volumes. Conservation of angular momentum and energy for fixed control volumes. Acceleration of a particle, Substantial derivative, Derivation of mass balance for incompressible flow, Concept of linear deformation and physical interpretation of mass balance, Angular deformation, vorticity and irrotational flow, Momentum equations for Cartesian coordinates, generalization to vector forms, Generalized Newtonian Stress-Strain relation (just statement), Navier-Stokes Equations, Concept of stream function, Bernoulli’s equation, stagnation pressure, Pitot tube, Energy grade lines. Buckigham π theorem, Non-dimensionalization of governing equation, Modelling and similitude. Fully developed flow between parallel plates and pipe flows, Concept of friction factor (Fanning and Darcy), Introduction to turbulent flow and the problem of closure, empirical treatments of turbulent flow (law of wall, Moody’s plot), minor losses in fittings, pipes in series and parallel, concept of hydraulic diameter for noncircular pipe, flow measurement using orifice plates, flow nozzles and venturis. Derivation of

isentropic law, Pulse propagation speed in ideal gas, Mach cone, Compressible frictionless flow in a variable area system. Flow in a C-D Nozzle, Choking, Normal shocks. Concept of a boundary layer, Displacement and momentum thickness definitions, Momentum integral equation for flat plates and its solution to estimate drag coefficient, similarity transformation and its application for flat plate, empirical equations for turbulent flow. Introduction to separation, vortex shedding, drag in cylinders, sphere, lift and drag in aerofoils (purely qualitative treatment with just final relations for solving some typical problems). Introduction to pumps and turbines (classification and types), General characteristics, Homologous curves, Throttle and bypass governing.

Manufacturing Engineering 5) Manufacturing Processes I (ME 206M, 6 credits, Spring Semester): Casting processes: dispensable and permanent mould processes; analysis of melting, pouring and solidification phenomena; design of pattern, core, feeder and gating system; casting defects and inspection. Joining processes: fusion and solid-state welding; brazing and soldering; weld joint design, cooling rate, and joint properties; welding defects and inspection. Bulk and Sheet Forming processes: rolling, forging, extrusion and drawing; sheet metal working; forming limit diagram; loads, friction and lubrication; forming defects and inspection. Powder processing: Powder manufacture, characterization, compaction and sintering; metal injection moulding; hot and cold isostatic pressing. Polymers and Composites: Thermoplastics, thermosets, elastomers and composites; related processes; injection mould design; moulding defects and inspection. Advanced processes: Free form fabrication (rapid prototyping), and net shape manufacturing processes.

6) Manufacturing Processes II (ME 338M, 6 credits, Autumn Semester): Fundamentals of Material Removal Processes: Chip formation, tool geometry and materials, mechanics of machining, Tool temperature, Tool wear, Tool-life, Surface finish, Machinability, Economics of machining. Fundamentals of Machine Tools: General-purpose, semi-automatic and Automatic machine tools, Set-ups and operations on - Lathe, Drilling, Milling, Grinding, Broaching machines; Machining processes for production: Gear cutting (Hobbing and Shaping), Thread cutting, Centerless grinding; Finishing operations: Honing, Lapping, etc. Introduction to Jigs and Fixture Design: Principles of location and clamping. Nonconventional Machining Processes: Electric discharge Machining (EDM), Electrochemical Machining, LASER and Abrasive Flow Machining, etc. Dimensional Metrology: Limits, Fits and dimensional tolerances; Design of limit gages, Taylor’s principle, Gage tolerancing; Geometrical tolerances of form, orientation, position, location, run-out; Basic definitions and measurement principles, MMC/RFS conditions. Comparators and Metrological Instruments: Principles of optical, pneumatic, electric/electronic instruments; Inspection of

gears and screw threads; Surface finish and its measurement, Coordinate Dimensional metrology, CMM - construction and operation.

Metallurgy 1) Structure of Materials (MM201): Classification of materials. Geometry of crystals, symmetry and point groups, Bravais lattice, unit cells. Atomic packing factor and theoretical density. Fractional coordinates, Crystallographic directions and planes. Interplanar spacings and angles, zone axis. Diffraction of X-Rays, Bragg’s Law, structure factor and intensity calculations. Applications of XRD: Identification of phases, lattice parameter determination, solvus line, crystallite size, superlattice lines. Amorphous materials and glasses. Polymeric structures. Defects in crystals. Point defects, dislocations, Burgers vector and its representation. Planar defects: stacking faults, twins, grain boundaries. Equilibrium phase diagrams, cooling curves, phase rule, lever rule and invariant reactions. Introduction to important binary phase diagrams. Some examples: Fe-Fe3C, Cu-Zn, Al-Cu. Concept of microstructure. Optical microscopy. Microstructures in steels and cast iron. 2) Thermodynamics of Materials (MM202): Laws of thermodynamics, concepts of reversibility, internal energy, enthalpy, entropy, maximum work, free energy, fugacity, activity and chemical potential, homogeneous and heterogeneous equilibria, phase rule, properties of solutions and concepts of partial molal properties, alternative standard states and interaction parameters, statistical concepts of entropy. Basic kinetic laws, order of reactions, rate constant, elementary and complex reactions, rate limiting steps and Arrhenius equations, theories of reaction rates - simple collison theory, activated complex theory. 3) Phase Transformations: Free energy (MM303) (prerequisite – MM 202) - composition diagrams for binary systems. Diffusion in interstial and substitutional solid solutions. Atomic mobility and vacancy diffusion. High diffusivity paths. Kirkendall effect. Diffusion in ceramics, Applications of diffusion equations. Homogeneous and heterogeneous nucleation in a single component system. Interface and diffusion controlled growth. Coherent, semicoherent and incoherent interfaces. Transformations controlled by heat flow. Solidification of a single phase alloy. Dendritic and cellular growth. Kinetics of eutectic and eutectoid transformations, precipitation and dispersion hardening. Cold work, recovery and recrystallization. Grain growth. Order-disorder changes. Elements of martensitic transformation. Hardening and tempering phenomena. 4) Electronic Properties of Materials (MM302) (pre-requisite - MM 201): Dielectric properties: Polarization: types and mechanisms, Macroscopic and local electric fields, Dielectric constant, polarizibility, Clausius-Mosotti relation, Dielectric susceptibility,

Dielectric relaxation time Applications of dielectrics, Piezo- and ferroelectricity and applications, Smart materials systems, Electrical Properties of materials, defects in solids and ionic conductivity, Ohm’s law and Amorphous and polycrystalline semiconductors four probe technique for resistivity measurement, impedance spectroscopy, Hall effect, Magnetic Properties, Basic concepts of magnetism Fundamental quantities and units in magnetism. Hund’s Rules, Orbital and spin moment, Paramagnetism, Curie-Weiss Law, Pauli paramagnetism, Ferromagnets, Molecular field theory, exchange interactions, Antiand ferromagnetism, Anisotropy, Soft and hard magnetic materials, Magnetic phenomena in materials, Applications (magnets, magnetic recording and memories, Metallic bonding: Schrodinger equation (Kinetic & potential energy, Interaction energy & Exchange energy), Free electron gas model, and Conductivity by free electron model. 5) An elective course The four courses are the basic courses in Metallurgical Engineering & Materials Science and give a complete overview of the branch to a student. Metallurgical Engineering and Materials Science is one of the most basic branch of engineering and finds its application in each and every branch of engineering. It is valued even in chemical (Thermodynamics of Materials, Phase transformation), electrical (Electronic properties of materials, Phase transformations), mechanical (Thermodynamics, Phase transformations) industries for various purposes. So companies would prefer students who have some basic knowledge about Metallurgical Engineering and Materials Science.

Computer Science Courses offered: CS 207 Discrete Structures CS 213 Data Structures and Algorithms CS 317 Databases and Information Systems (pre-requisite – CS 213) CS 347 Operating Systems CS 348 Computer Networks (pre-requisite – CS 213) CS 416 Computer and Network Security In addition, a minor student can replace one of the five courses by a R&D project. This is subject to the availability of an instructor to offer the project. __________________________________________________________________

The importance of computers in modern society can hardly be overstated. In virtually every industry and home, in the design of almost all gadgets, the computer is an integral part, facilitating communication and computation. There is an increasing need for domain experts in all areas of Engineering with a broad knowledge of Computer Science and Engineering. The minors programme in Computer Science and Engineering at IIT Bombay is designed to cater to these requirements. It comprises foundational courses like Discrete Structures, Data Structures and Algorithms that train students in abstract thinking, algorithm design and problem solving, while courses like Databases, Operating Systems and Computer Networks expose the students to fundamentals of computer systems. A course on computer security has been introduced keeping in mind its importance today and some future courses are planned. The CS minor courses give the student the skills to work effectively in her parent discipline and also prepares the student to work in the IT industry where jobs require considerable domain knowledge of the parent discipline.

Energy Minor in Energy Engineering The Department of Energy Science and Engineering offers a Minor in Energy Engineering to enable Under-Graduate (UG) students with different backgrounds to understand the different aspects of Energy Engineering. Students will be exposed to the status of energy resources, its interaction with environment and the fundamentals of energy economics, different technologies associated with renewable energy sources, conventional power generation technologies, and different techniques and technologies for energy management and energy conservation. The Minor in Energy provides UG students an opportunity to explore possible opportunities in energy efficiency and clean energy to develop sustainable energy systems for the future. Students of other departments who are opting to pursue a Minor in “Energy” other than their regular/main degree are expected to credit the following courses in the order given below2nd Year I Semester: EN 301 (Introduction to Renewable Energy Technologies) –This course gives the basic introduction to various renewable energy resources and associated technologies. II Semester: EN 403 (Energy Resources, Environment and Economics) (Pre-requisite is EN 301) – This course primarily focuses on the conventional sources of energy, their effects on environment and how these effects can be reduced. It also discusses the fundamentals of energy economics.

3rd Year I Semester: EN 402 (Energy Management) (Pre-requisite is EN 403) –This course deals with the methods of conservation of energy in general and more specifically in the industrial sector. II Semester:


4th Year I/II Semester:


EN XXX are Energy related courses to be selected from the basket of courses offered that Semester by the Department for Minor.

Chemistry Chemistry is a broad science, embracing the concepts of creation of molecules and the manipulation of atoms in microscopic and macroscopic scales. It covers interactions with plants, animals and humans through agriculture, biology and medicine and with the physical world through electronics, new building materials and new sources of energy. The importance of chemistry to the industry cannot be understated. Production of materials with properties tailored to the needs of the consumer, efficient production of any product, leading to less pollution, less investment, and better product performance. And, the list goes on. Also, with talks of Global Warming making rounds, the protection of our environment is another important aspect that any engineer should take into account when he/she is designing a product, which comes under the domain of Chemistry. The minor starts off with an introduction to the fundamentals of Chemistry and continues with a set of three compulsory courses in Inorganic, Organic and Physical Chemistry. The student has to take up another course according to his/her interest, in order that he/she completes the credit requirement for the Minor in Chemistry

Aerospace Minor is a great opportunity to pursue interest in areas beyond one ones basic degree covers. A minor chosen to match ones interests and not merely to augment resume, can speak volumes about a candidate 

It shows that the candidate is willing to go the extra mile to achieve his/her goals

The breadth of exposure significantly improves a person’s ability to think and tackle complex multi-disciplinary problems.

Most engineering systems of today are multi-disciplinary in nature. Minor discipline thus compliments the major discipline, making the person better suited as opposed to a person single mindedly focused on the major.

In my opinion, employers look for candidates with demonstrated flexibility, capable of appreciating and tackling problems in more than one discipline instead of just one. How is minor going to help? 

A minor can magically complement a particular major depending on student who is looking for this synergy.

For instance, a student of electrical engineering, with deep passion for aerospace can have best of both worlds through an aero minor.

A carefully chosen minor can enhance a students placement opportunity in a sector of his choice.

So, the major advantage of minors is in apping. We can pursue our MS/PHD in topics related to minors and yes, it can help a mechanical student from higher studies perspective.

Importance of Aero Minor: 

Minor is configured as a compacted exposure to an area. Five courses in minor are carefully chosen to accomplish this. For example minor in Aerospace has one course that introduces the vocabulary of aerospace and also some basic concepts. One courses each in aerodynamics and structures that are core areas aerospace. One course that explains mechanics of flying and finally a course on intricacies of design synthesis of a aerospace vehicle.

40% of cost of an aircraft of today is for avionics. So this billion dollar industry has great opportunity for electrical engineers. The quality of contribution of these engineers will be far better if they were familiar with what aerospace is all about.

Aerospace today relies on cutting edge manufacturing methods. Role of mechanical engineers is thus obvious. A mechanical engineer who knows an aircraft will be better engineer to get involved in aerospace manufacturing.

Aerospace today uses advanced materials for airframe and also in its engines. Need for low emission engines opens up a role for chemical engineers. Thus goes the list.

Apart from these Minors in SOM, HSS, IDC, Maths and Stats are the ones that are popular amongst the students. We will be giving you info about them as soon as we procure it from the respective HoDs Minor courses offered by Aero dept: AE 153; Introduction to aerospace engineering AE 305: Flight Mechanics (pre-requisite – AE 153) AE 415 : Space flight mechanics AE 332: Aircraft design (pre-requisite – AE 153 and AE 305) AE 457: Space flight navigation and guidance

Write-ups minor