|
|
|
|
| |
Course Outline for Basic & Applied
Sciences MS101
APPLIED PHYSICS (4 + 1)
Properties of Matter : Elasticity; moduli
of Elasticity, Experimental determination of Young’s
modulus, Bending of beams, Cantilever. Fluids: Steady
and turbulent flow, Bernoulli’s theorem, Viscosity,
determination of Coefficient of viscosity by Poiseuille’s
method. Surface tension, Surface energy, Angle of contact,
determination of surface tension by rise in a capillary
tube.
Heat & Thermodynamics :
Heat, Temperature, Theories of heat, Adiabatic and isothermal
processes, The four laws of thermodynamics, Thermodynamic
functions, Maxwell’s Thermodynamic relations. Efficiency
of Heat Engines, Carnot’s Cycle, Entropy.
Optics : Waves and Oscillations,
Simple Harmonic Motion, types of wave- motion, theories
of light, Interference , Diffraction, Polarisation, Double
refraction, Dispersion, Deviation.
Electricity and Magnetism :
Electric charges, Electric field, Electric potential,
Coulomb’s law, Gauss’s law, Capacitors and
dielectrics, Electric current, Ohm’s Law, Magnetic
field, Magnetic force on current, Ampere’s law,
Faraday’s law, and Lenz’s law. Varying current,
Alternating current, concept of phase, L-R, C-R, and LCR
circuits. Magnetic properties of matter: dia, para, &
ferromagnetism.
Semiconductor Physics and Devices
: Conduction of Electrons in a Metal, Semiconducting
materials, Acceptors, holes, N & P type doped and
compensated Semi conductors. Energy bands, Allowed and
Forbidden states, Junctions, Forward and Reverse bias,
Diode action as P-N Junction; Transistor and its characteristics.
|
MS102
APPLIED MATHEMATICS-I (3+1)
Sets : Definition, examples
and set operations. Venn diagram, De Morgan’s laws.
Binary relations, equivalence relations.
Number Systems : N,Z,Q and R and their
properties. Binary number system.
Intervals : Subsets of real numbers,
Inequalities.
Complex Numbers : Argand diagram.
De Moirve’s theorem, n-th roots. Some well-known
complex functions.
Mappings : Definition. Composition
of two mappings. Inverse mapping.
Prepositional Logic : Statements.
Logical operators. Truth tables. Equivalent statements,
Toutologies. Logical implications.
Methods of Proof : Mathematical induction,
Recurrence relations.
Boolean Algebra : Definition, Boolean
expressions and Boolean functions. Examples, Identities
of Boolean algebra, duality. Representing Boolean functions,
Logic gates, Karnaugh maps. |
MS103 APPLIED MATHEMATICS-II
(3+1)
Functions and Limits : Functions of real
variables. Well-known examples, Right and left side limits
and continuous functions. Local maximum and minimum values,
Point of inflexion.
Derivatives : Definition and its meaning
in applications. Rules of differentiation, Derivatives
of well-known functions, L’Hopital rule. Tangent
and normal at a point on the curve. Second order derivatives,
Derivative test for maximum and minimum values.
Integration : Integral as anti-derivative,
Properties of integrals, Techniques of integration.
Definite and indefinite integrals. Improper integrals.
Integral as area. Fundamental theorems of calculus.
Applications : Calculation of areas,
volumes and volumes of solids of revolution, center
of gravity, moments, Length of arcs, Curvature and radius
of curvature.
Functions of Two Variables : Partial
derivatives. Double integral, Maximum and minimum values
of functions of two variables, Lagrange’s method
of multipliers. Polar and cylindrical coordinate systems.
|
MS
105 ENGINEERING CHEMISTRY & MATERIAL SCIENCE (4 +
0)
Gases : Gas Laws, Kinetic Gas Equation,
Van der Waal’s Equation, critical phenomenon, liquidification
of gases, specific heat (molar heat capacity).
Properties of Solutions &
Liquids : Surface Tension, Viscosity, Osmosis,
Osmotic Pressure, pH-Buffer Solution, Spectrophotometry,
Basic concepts of Colloidal Chemistry, classification,
purification (dialysis).
Thermochemistry : Chemical
Thermody-namics, Hess’ Law, Heat of reaction, Relation
between H and U measurement of heat reaction, Bomb Calorimeter.
Electrochemistry : Laws
of Electrolysis, E.M.F. series, corrosion (Theories, inhibition
& protection).
Water and Sewage : Sources
of water, impurities, hardness, water softening, purification
of water for potable and industrial purposes, electrodialysis,
Introduction to environmental pollution; main sources
and effects. Sewage treatment.
Fuels : Types of fuels,
classification of fossil fuels.
Metals & Alloys :
Properties and general composition of metals and alloys
such as Iron, Copper, Aluminum, Chromium, Zinc, uses in
engineering field.
Chemistry of Engineering Materials : Inorganic
Chemistry of Engineering materials: Cement, Glass. Organic
Engineering Materials: Polymers, Rubbers, Plastics, Paints.
Semiconductors and Dielectric materials.
|
MS201 APPLIED MATHEMATICS-III
(VECTORS AND ODE)(3+1)
Linear Algebra : Algebra of matrices,
Inverse of a matrix. Gauss-Jordan method for solution
of a system of algebraic linear equations.
Vectors : Scalar and vector quantities,
Differentiation and integration of vector functions.
Gradient, divergence and curl. Gauss’ divergence
theorem. Stokes’ theorem.
Ordinary Differential Equations :
Formulation, Order, degree and linearity of differential
equation. Complementary and particular solution. Initial
and boundary value problems.
Solution of Ordinary Linear Differential Equations
of First Order : Methods of solution. Bernoulli’s
differential equation.
Linear Second Order Differential Equation :
Characteristic equation and different types of it. Methods
of solving homogeneous linear differential equations
with constant coefficients. Particular solution by variation
of parameters, method and solution by indeterminate
coefficient method.
Laplace Transform : Definition and
properties, Laplace transform of derivatives and integrals.
Inverse Laplace transform. Solving the linear constant
coefficient differential equation by Laplace transform.
Z-Transform : Definition, examples and
properties. Solution of difference equation.
|
MS202
APPLIED MATHEMATICS-IV (PDES AND FUNCTIONS OF COMPLEX
VARIABLES)(3+1)
Partial Differential Equations : Origin
and formulation. Solution of first order special types
and second and higher order partial differential equations.
Homogeneous partial differential equations of order one.
Lagrange’s method of solution.
Sequences and Series : Simple tests
of convergence. Binomial theorem. Power series and geometric
series.
Fourier Series : Euler’s-Fourier
formulae. Even and odd functions. Expansion of a function
in Fourier series. Fourier integrals. Fourier transform.
Fourier sine and cosine expansions.
Functions of Complex Variables : Examples,
Limits, Continuity and differentiability, Caucly-Reiman
equations, Zeros and Poles. Conformal mapping, contour
integration.
|
| MS203
THERMODYNAMICS (3 + 0) Thermodynamic
Properties : Introduction, Working substance;
System; Pure substance; PVT surface; Phases; Properties
and state; Units; Zeroth Law; Processes and cycles; Conservation
of mass.
Energy and its Conservation :
Relation of mass and energy; Different forms of energy,
Internal energy and enthalpy; Work; Generalized work equation
Flow and non-flow processes; Closed systems; First Law
of Thermodynamics; Open systems and steady flow, Energy
equation for steady flow; System boundaries; Perpetual
motion of the first kind.
Energy and Property Relation
: Thermo dynamics equilibrium; reversibility;
Specific heats and their relationship; Entropy; Second
Law of Thermodynamics; Property relations from energy
equation; Frictional energy.
Ideal Gas : Gas laws;
Specific heat of an ideal gas; Dalton’s Law of Partial
Pressure; Third Law of Thermodynamics; Entropy of an ideal
gas; Thermodynamic processes.
Thermodynamic Cycles :
Cycle work; Thermal efficiency and heat rate, Carnot cycle;
Stirling cycle; Reversed and reversible cycles; Most efficient
engine.
Consequences of the Second Law
: Calusius’s inequality; Availability and
irreversibility; Steady flow system.
Two-Phase Systems :
Two-phase system of a pure substance; Changes of phase
at constant pressure; Steam tables; Superheated steam;
Compressed liquid; Liquid and vapour curves; Phase diagrams;
Phase roles; Processes of vapours; Mollier diagram; Rankine
cycle; Boilers and anciliary equipment.
Internal Combustion Engines :
Otto cycle; Dual combustion cycle; Four-stroke and two-stroke
engines; Types of fuels.
Reciprocating Compressor :
Condition for minimum work; Isothermal efficiency; Volumetric
efficiency; Multi-stage compression; Energy balance for
a two-stage machine with intercooler.
|
| MS204
ABSTRACT ALGEBRA (3+1) Groups :
Definition, Sub groups. Examples, Cosets, Lagrange’s,
theorem, Modular arithmetic and theorems about it.
Vector Spaces : Defintion and Examples,
Bases and dimensions.
Rings : Definition, Examples, Statement
of some theorems.
Fields : Definition, Examples, Statement
of some Theorems.
Number Theory : Prime numbers, Fermat’s
theorem. Factorization of integer.
|
MS301 PROBABILITY
AND STATISTICS (3+1)
Data Sets : Types of data. Stem and leaf
plot, Mean, standard derivation and quartiles, Range.
Box and dot plot.
Probability : Axiomatic definition
of probability, Interpretations of probability, Laws
of probability. Conditional probability. Dependent and
independent events, Bayes’ theorem, Reliability
and its calculations for some important systems.
Probability Distributions : Discrete
distributions, binomial, geometric, negative binomial,
and Poisson distributions. Continuous distribution,
uniform, exponential and normal distributions.
Simulation : Random numbers and their
generation, generation of random deviates from different
distributions, special and general methods of simulation.
Simulation of probability models and tests of goodness
of fit.
Lab. Work : Use of minitab and mathematica
or math lab.
|
MS302 NUMERICAL
METHODS (3+1)
Computer Arithmetic and Errors : Types
of errors, Significant numbers, Error in function.
Iteration : Successive approximations,
Bisection method, Newton Raphson method.
Interpolation : Simple difference
table, Divided difference table, Newton’s method
of interpolation. Lagrange’s formulae for interpolation
using linear or quadratic polynomials.
Operators : Differential operators.
Forward and backward difference operators.
Numerical Solution of differential Equations
: Euler’s method, Picard’s method
and Runge Kutta method.
System of Linear Equations : Lower
and upper triangular matrices, LU factorization. Doolittle
and Grout method. Gauss Seidil iteration method.
Lab. Work : Numerical solution using
Mathlab. or Mathematica
|
|
|
