engineering syllabus mumbai university revised SEMESTER 1
1.Subjects are arranged from Hard to Easy.
2.Finish study of hard subject FIRST, easy subjects can be completed in 1 week time
3.DO NOT under any circumstances, try and cover all the topics here ,leave out 25% in all subjects,and the rest 75% be a master of it. If you try and be a hero ,you will fail.
|Applied Mathematics -I
1.1.1 Review of complex numbers. Cartesian, Polar and
Exponential form of a complex number.
1.1.2 De Moiver’s Theorem (without proof). Powers and roots
of Exponential and Trigonometric functions.
1.1.3 Circular and Hyperbolic functions.
Complex numbers and successive differentiation.
1.2.1 Inverse circular and Inverse Hyperbolic Functions
1.2.2 Separation of real and imaginary parts of all types of
1.2.3 Successive differentiation –nth derivative of standard
functions-eax, (ax=b)-1, (ax=b)m, (ax=b)-m, log (ax + b)
sin (ax + b) Cos (ax+b). eax sin (bx+c). eax cos (bx+c).
1.2.4 Leibnitz’s theorem (without proot) and problems.
1.3.1 Partial derivatives of first and higher order, total differential
coefficients, total differentials, differentiation of composite
and implicit functions.
1.3.2 Euler’s theorem on Homogeneous function with two and
three independent Variables (with proof), deductions from
Application of partial differentiation, Mean Value theorems
1.4.1 Errors and approximations. Maxima and Minima of a
function of two independent variables. Lagrange’s method
of undetermined multipliers with one constraint.
1.4.2 Rolle’s theorem, Lagrange’s mean value theorem,
Cauchy’s mean value theorem (all theorems without
proof). Geometrical interpretation and problems.
Vector algebra & Vector calculus
1.5.1 Vector triple product and product of four vectors.
1.5.2 Differentiation of a vector function of a single scalar
variable. Theorems on derivatives (without proof). curves
in space concept of a tangent vector (without problems)
1.5.3 Scalar point function and vector point function. Vector
differential operator del. Gradient, Divergence and curl-
definitions, Properties and problems. Applications-Normal,
directional derivatives, Solenoidal and lrrotational fields.
Infinite series, Expansion of functions and indeterminate forms.
1.6.1 Infinite series-Idea of convergence and divergence. D’
Alembert’s root test, Cauchy’s root test.
1.6.2 Taylor’s theorem (Without proof) Taylor’s series and
Maclaurin’s series (without proof) Expansion of standard
series such as ex, sinx, cosx, tanx, sinhx, coshx, tanhx,
log(1+x), sin-1x – tan-1x, binomial series, expansion of
functions in power series.
1.6.3 Indeterminate forms-
. sin 1 , , 0 , , 0 , ,
0 0 0 iesalso volvingser problem rule BHospitals x
– ¥ ¥ – ¥ ¥
01 1.1 Systems of Coplanar Forces:-
Resultant of concurrent forces, parallel forces & Non concurrent Non parallel
system of forces. Moment of Force about any point, Couples, Varignon’s
Theorem. Distributed forces in plane.
1.2 Introduction to Centroid & Centre of Gravity, Introduction to Moment of
Inertia & its theorem.
02 2.1 Equilibrium of system of coplanar forces :-
Condition of equilibrium for concurrent forces, Parallel forces & Non
concurrent Non parallel general system of forces & couples.
2.2Types of supports, loads, beams. Determination of reactions at supports for
various types of loads on beams.
2.3 Analysis of plane trusses by using Method of Section and Method of
03 3.1 Friction :-
Introduction to laws of friction, Cone of friction, Equilibrium of bodies on
inclined plane. Application of problems involving wedges, ladders, screw
3.2 Belt friction: transmission of power by belts and ropes, centrifugal and
initial tension in the belts and ropes. Condition of maximum power
transmission. Flat belts and flat pulleys & ropes on grooved pulleys.
04 4.1 Kinematics of Particle:-
Velocity and acceleration in terms of rectangular coordinate system,
Rectilinear motion. Motion along plane curved path. Tangential and Normal
components of acceleration. Motion Curves (a-t, v-t, s-t curves). Projectile
motion. Relative motion.
05 5.1 Kinematics of Rigid Bodies
Introduction to general plane motion, Instantaneous center of rotation for the
velocity, velocity diagrams for bodies in plane motion,(up to two linkage
06 6.1 Kinetics of particles
Introduction of basic concepts., Newton’s second law, work energy principle,
D’Alembert’s principles, equation of dynamic equilibrium.
6.2 Moment of Energy principles: Linear momentum, principle of
conservation of momentum, Impact of solid bodies, direct and oblique
impact, impact of solid bodies, semi elastic impact and plastic impact.
Prerequisite A. Concepts of c.m.f, potential difference & current, battery.
B. Capacitors, with uniform & composite medium, energy
stored in a capacitor, R-C time constant.
C. Magnetic field, magnetic circuit, Faraday’s laws of
electromagnetic induction, Hysteresis & Eddy current losses,
energy stored in an inductor time constant in R-L Circuit.
1. DC circuits: (only independent sources).
Ohm’s law resistance, receptivity, series & parallel
connections, star delta transformation, power dissipation in
resistance, effect of temperature on resistance.
Kirchhoffs laws Mesh laws Mesh & Nodal analysis. Source
transformation, Superposition, Thevenin’s. Norton’s and
Maximum power transfer theorems.
2. AC circuits:
Generation of alternating voltage & currents, R.M.S. &
Average value form factor crest factor A.C. Through
resistance inductance & capacitance. R-L,R-C & R-L-C
series & parallel circuits, phasor diagrams. Power & power
factor, series & parallel resonance.
Problems by analytical as well as phical methods.
3. Three phase circuits:
Three phase voltage & current generation, star & delta
connections (balanced load), relationship b between phase &
line currents and voltages, phasor diagrams, measurement of
power by two wattmeter method.
Problems by analytical as will graphical methods.
4. Single phase transformer:
Construction, working principle, c.m.f. equation, ideal &
practical transformer, phasor diagrams, equivalent circuit,
O.C.& S.C. tests, efficiency & regulation. All day efficiency.
5. Electrical Machines: (No numerical is expected).
• DC Generators & Motors: Construction, working
principle, e.m.f. equation, classification & applications.
• Three phase Induction Motor: construction, working
principle, squirrel cage rotor & phase wound rotor,
production of rotating magnetic field, slip.
• Single phase Induction Motor: Construction working
principle, double field revolving theory, split phase,
capacitor start, & shaded pole motor.
6. A. Semiconductor Devices: (No numerical is expected)
P-N Junction diode, Zener diode, their construction,
working and characteristics. BJT its construction,
characteristics & applications. (only CE configuration)
B. Rectifiers: (No numerical is expected)
Analysis of half wave & full wave rectifier with resistive
load and its parameters ripple factor rectification
Rectifier circuit with capacitive filter only.
12. Study of electrical machines.
01 Structured Programming using C++
1.1.C++ as a superset of C programming language
1.2.C++ Fundamentals: Character set, identifiers and
Keywords, data Types, constants, and Variables Declarations,
Operators & Expression, Library functions, statements, Symbolic
Constants, Preprocessor directives
02 2.1. Data Input and Output:
getchar(), putchar() scanf(), gets() puts(), cin, cout, setw(), endi etc.
2.2. Control Statements:
If else, while, do-while, go to, for statements, nested control
structures, switch, break, continue statements, comma operator.
03 3.1 Functions:
Functions prototypes. passing arguments to a function by value and
by reference, recursion, over loading functions, storage classes
Defining-processing array, passing arrays to function introduction to
Multidimensional arrays, arrays and strings.
04 4.1 Pointers
Declaration Referencing and de-referencing, passing pointers to
functions pointer to functions, pointer to arrays
Creation and manipulation of linked list
4.2. Structures and Unions: Defining and processing a structure,
05 5.1 Introduction to object Oriented Programming in C++ 5.2.
Classes, Objects, data encapsulation, access specifies:
Private, public and protected, inheritance in details, operator
overloading of Unary and Binary arithmetic operators, virtual
functions, pure virtual functions.
06 6.1 late binding, friend functions, Object as function parameter
overriding functions and over loaded constructors copy constructor,
static class members.
|Applied Chemistry –I
Introduction, classification, Hydrocarbon Molecules, Thermoplastic,
Basic Concepts Molecular Weight, Molecular Shape, Polymer
Crystallinity. Crystallization, Meting & Glass Transtition Phenomena.
Viscoelasticity, Deformation Fracture, Defects in Polymers.
Polymerization addition, Polymerization Copolymerization and
Advanced polymer Material, Conductiong Polymers Electrical Properties
of Polymers. Liquid Crystal Properties Molecular Electronics & Polymers &
Fabrication of Polymers
i)Compression Moulding ii) Injection Moulding iii) Transfer Moulding iv)
Synthesis Properties & uses of PE PMMA Formaldehyde resign Polymer
Hardness of water, effect of hard water in the manufacture sector types of
hardness, determination of hardness by EDTA method and Problems.
Softening of water by i) Lime soda method with equations in general Hotcld
lime soda method and problems ii)zeolite process & problems iii) Lon
exchange method iv) reverse osmoses, ultrafiltration & its industrial
Methods to determine extent of water pollution i) BOD ii) COD.
Methods to control water pollution.
Industrialization- materials cycle & pollution. Recycling issues.
Definition, classification, characteristic properties, problems on acid value
and saponification value. Theories of lubrication.
Additives for lubricants, selection of lubricant.
Classification Solar energy, hydropower, wind power Biomass energy
using bio technology Hydrogen as a fuel
Solar energy, Production of electricity using solar energy Rechargeable
alkaline storage batteries, Nickel Hydrogen Batteries. Rechargeable Lithium
5 Phase Rule and steels:
Gibbs Phase Rule, One Component System Water, Two Component
System Iron-carcon Equilibrium Diagram with Microstructures.
Limitations & Application of Phase Rule.
Plain Carbon Steel.Limitations.
Introduction to Alloy Steels, special steels.
Principles of shape memory effect & its applications.
Introduction to nano-materials.
Graphite, fullerenes carbon nanatubes, nanowires, nanocones, Haeckelites.
Their electronic and mechanical properties
Production methods for CNTS.
Applications of nono materials in i) Medicine ii) Catalysis iii)
Environmental Technologies iv) Environmental & related fields.
|Applied Physics -I
01 Crystallography & X-rays:
Lattice basis, crystal axes, unit cells, lattice parameters & crystal systems,
SC, BCC, FCC, diamond, Nacl, Zinc blend and HCP crystal structures, Miller
indices. Planes & directions, Liquid crystals & phases, LCD display & its
X-rays- origin of x-rays and x-ray spectra, x-ray diffraction & Bragg’s is
law and determination of crystal structure.
Real crystals- crystal imperfections, point defects and dislocations.
02 Physics of Semiconductors:
Classification of solids, Fermi-Dirac statistics, concept of Fermi level & its
variation with temperature, impurity and applied voltage.
Intrinsic & extrinsic carrier concentrations, carrier drift, mobility resistivity
and Hall effect, carrier diffusion, Einstein’s relations, current density &
Energy band diagrams of p-n junction, formation of depletion region,
derivation for depletion layer width.
03 Super conductivity:
Critical temperature, critical magnetic field, Type I Type II suppr
conductors, high Tc super conductors.
Meissner effect, josephson effect.
SQUIDS, plasma confinement, Maglev.
acoustics of Building, Absorption, Importance of Reverberation Time,
Units of Loudness, Decible, Phon.
Conditions for Good Acoustics methods of Designs for Good Acoustics,
determination of Absorption coefficient, Noise Opllution.
Principles of production, piezoelectric & mangetostriction effect.
Piezoelectric & mangetostriction oscillator: ultrasonic materials- quartz &
ferroelectric materials, cavitations effect.
Applications based on cavitation effect and echo sounding, ultrasonic
imaging & medical diagnosis.
06 Electron optics:
Electostatic & Magnetostatic focusing system
Construction & working of CRT, CRO & its applications.