Syllabus for Mechanical Engineering Prescribed by University Of Mumbai SYLLABUS FOR FIRST YEAR ENGINEERING (FOR ALL BRANCHES)
I) Applied Mathematics I
1. Complex numbers
; Idea of Argand diagram (Problems based on Geometry are not expected)
Cartesian, Polar and Exponential form of complex number.
; De‟Moivre‟s theorem (without proof), Power and roots of exponential and
; Hyperbolic and logarithmic functions, inverse trigonometric functions.
; Separation of real and imaginary parts of all types of functions 2. Vector algebra and vector calculus
; Vector triple product (proof is not expected), product of 4 vectors.
; Differentiation of a vector functions of a single scalar variable. Proofs of
theorems on derivatives of sum and product are not expected.
; Curves in space, Serret Frenet formulae (without proof), curvature, torsion,
osculating plane, normal plane and rectifying plane.
3. Mean value theorems
; Rolles theorem, Lagrange‟s and Cauchy‟s mean value theorem (Proofs are not
; geometrical interpretations are expected)
; Taylor‟s and Maclaurin‟s theorem (without proof), Taylor‟s and Maclaurin‟s
4. Differential calculus
; Successive differentiation of nth derivatives of function such as (ax+b)m,
(ax+b)-1, , sin(ax+b), cos(ax+b), log (ax+b), sin (bx+c), cos (bx+c)
; Leibniz theorem (without proof), Expansions of power series, indeterminate
forms and L‟ Hospital rule.
5. Partial differentiation
; Partial derivatives of first and higher order, total differentials, composite
functions and implicit functions
; Euler‟s theorem on homogeneous functions with two and three independent
variables (with proof), deductions from Euler‟s theorem.
; Errors and approximations, Maxima & minima of a function of two variables
1. Higher Engineering Mathematics – Dr. B.S. Grewal, Khanna Publications
2. A text book of Applied Mathematics – P.N. & J.N. Wartikar, Pune Vidyarthi
3. Advanced Engineering Mathematics – Erurin Kreyszing, Wiley Eastern Ltd.
4. Engineering Mathematics-I - G.V. Kumbhojkar, C. Jamanadas & Co.
5. Applied Mathematics-I - Dr. B.V. Jungam, K.P. Patil, Mrs. N.M.Kumthekar,
II) Applied Science I
Section I– Applied Physics
1. Solid State Physics
; Crystal structure: structure of cubic crystals, special form in cubic crystals,
diamond structure, Barium Titanate Miller indices, planes & directions, Legacy
and critical radius ratio in tonic crystals.
; Formation of energy brands and classification of solids, conductor,
semiconductor, insulator, Physics of semiconductor junctions, (bipolar) photo
2. Sound Waves
; Audible, ultrasonic and infrasonic waves propogation, piezo-electric effect,
principles of ultrasonic transducers and oscillations, production of ultrasonic
waves, echo sounding, thickness measurement, cavitation and non-destructive
testing and flow detection.
3. Electricity and Magnetism:
; Motion of charges, particles in electric and magnetic fields, magnetic and
electro-static focusing system and its use in CRO, use of CRO for measuring
amplitude of D.C. and A.C., voltage and phase difference between two A.C.
4. Quantum Physics:
; Introduction to wave nature of particles, De Broglie waves
Section II - Applied Chemistry
5. Water and its Treatment
; Introduction to hard and soft water
; Hardness: types, units, estimation be EDTA method, numericals, understanding
effect of hard water in various industries.
; Softening of water
; Lime-soda process, Zeolite - Permutit method, ion exchange method,
comparison of methods, numerical problems based on lime-soda and Zeolite
6. High polymers & elastomers:
; Introduction & definition of polymers and elastomers
; Classification of polymers: homopolymer & copolymer, linear branched and
cross linked, organic and inorganic
; Types of polymerization: addition (e.g. polyethylene, polypropelene),
condensation 9 e.g. phenol formaldehyde, urea formaldehyde, urea
; Plastics: classification (thermoplastic and thermosetting), compounding of
plastics, fabrication of plastics - compression, extrusion, transfer and injection
moulding, industrial applications.
; Rubber structure – Cis and trans isomer, properties and drawbacks,
vulcanization - mechanism, agents, advantages, effects on properties, synthetic
rubber – manufacture, properties and uses of polyurethane, silicon rubber.
7. Pollution and pollution control:
; Definition of pollution and pollutant
; Introduction to atmospheric pollution: nature of atmospheric pollutants and
their effect, methods of reducing atmospheric pollution in brief
; Introduction to water pollution: nature of water pollutants and their effect,
methods of reducing water pollution in brief
8. Introduction to lubricants:
; Definition of lubricants, lubrication, purpose of lubrication
; Classification of lubricants with examples: solid, semi-solid, liquid, blended,
; Mechanism of lubrication – thick film, thin film and extreme lubrication
; Properties of ideal lubricant (definition and significance) – viscosity, viscosity
index, flash and fire point, cloud and pour point, saponification value, acid value,
numerical problems on saponification value and acid value
1. Concept of Modern Physics – Arthur Beiser, Tata McGraw Hill
2. Engineering Physics – R.K. gaur and S.L.Gupta, Dhanpat Rai Publishing Co.
3. Modern Physics – J.B. Rajam, S. Chand & Co.
o Engineering Chemistry – Jain & Jain, Dhanpat Rai Publishing Co.
5. A Text Book of Engineering Chemistry – M.M. Uppal, Khanna Publishers
6. Environmental Chemistry – B.K. Sharma, Goel Publishing House
III) Engineering Mechanics
Section I - Statics
1. System of coplanar forces:
; Resultant of (i) Concurrent forces, (ii) Parallel forces and (iii) Non-concurrent
non parallel system of forces. Moment of force about any point, couples,
Varignon‟s theorem, Distributed forces in plane.
2. Equilibrium of System of coplanar forces:
; Conditions of equilibrium for (i) Concurrent forces, (ii) Parallel forces, (iii) Non-
concurrent non-parallel (general) system of forces and couples.
; Types of supports, determination of reactions at supports for various types
of determinate structures (with/without internal hinge)
; Centroids of plane areas. Center of gravity of wires bent into different shapes.
; Analysis of determinate pin jointed plane frames by method of joint and method of
3. Forces in space:
; Resultant of (i) Concurrent forces, (ii) Parallel forces & (iii) General force system.
Moment of a force about a point, finding scalar and vector components of the
force & the moment of the force about an axis.
; Laws of friction, Cone of friction, Equilibrium of bodies on inclined plane,
Application to problems involving wedges and ladders, Screw and belt
friction-only simple type involving tension on both side of pulley to be covered. 5. Principle of virtual work:
; Equilibrium of an ideal system, Applications to link systems with single degree of
Section II - Dynamics
6. Kinematics of particle:
; Rectilinear motion, acceleration time and velocity time graphs & their uses.
; Velocity and acceleration in terms of rectangular co-ordinate system. Motion
along plane curved path, tangential & normal components of acceleration,
projectile motion, simple harmonic motion.
7. Kinematics of rigid bodies: Relative velocity, translation, pure rotation & plane motion of rigid bodies, link mechanism, instantaneous center of rotation for the
velocity & velocity diagrams for bodies in plane motion.
8. Kinetics of particles & kinetics of rigid bodies:
; D‟Alembert‟s principle, equation of dynamic equilibrium, linear motion,
; Area moment of inertia, parallel axis theorem, perpendicular axis theorem, mass
moment of inertia about centroidal axis and about any other axis. D‟Alembert‟s
principle for bodies under rotational motion about a fixed axis and plane motion.
Application to motion of bars, cylinders, spheres only.
; Linear momentum, impulse momentum, principle of conservation of momentum,
impact of solid bodies, elastic impact, semi-elastic impact and plastic impact,
work done by a force, potential and kinetic energy and power work-energy
equation, principle of conservation of energy.
1. R.C. Hibbeler - Engineering Mechanics, Mac Millan
2. B.N. Thadani - Engineering Mechanics, Weinall Book Corporation. 3. Beer & Johanson - Engineering Mechanics, Tata McGraw Hill
4. Kumar - Engg. Mechanics, Tata McGraw Hill.
5. S. Junarkar - Engineering Mechanics, Charotar Publishing House. 6. Tayal - Engineering Mechanics, Umesh Publication.
7. Mecklin & Nelson - Engineering Mechanics, McGraw Hill.
8. Mariam - Engineering Mechanics, Join Wiley.
9. S.Rajasekaran & G. Sankarasubramanian - Fundamentals of Engg. Mechanics, Vikas Publishing House.
10. F.L.Singer - Engineering Mechanics, Harper & Row Publishers.
IV) Basic Electrical & Electronics Engineering
1. Units of work, power and energy, Ohm‟s law, effect of temperature on
resistance, series and parallel circuits, lead acid battery construction and
2. AC fundamentals: sinusoidal voltage and current waveforms, RMS and average
value of various waveforms, form factor, crest factor, frequency, R-L, R-C and
R-L-C, 1-phase series circuit (with resonance), parallel circuit (with resonance).
Statement of relation for line current, phase voltage and power in three-phase
circuits for a balanced three-phase load.
3. Elementary network theorems (for DC circuits only), star-delta transformations,
superpositions theorem, Thevenin‟s and Norton‟s theorem, maximum power
4. Principle and working of single-phase transformer, emf equation, voltage and
current ratio of an ideal transformer. Determination of efficiency and regulation
by direct loading.
5.General principles and working of electrical motors and generators: DC series and shunt machine, I-f induction motor.
6. P-N junction diode as rectifier (half wave and full wave), introduction to filters, light emitting diodes (LED)
7. Principle and working of bipolar junction transistor (BJT and FET) and its use as
8. SCR characteristics and its applications for single phase converter and inverter circuits. (Numerical problems not expected).
9. Transducers: Classification of transducers, study of transducers like displacement, temperature, and pressure transducers, flowmeters, LVDT, microphones, loud-speakers (Numerical problems not expected).
10. Basic principles of measurement of electrical quantities. Voltmeters, ammeters, wattmeter, multi-meter, and power supplies (Numerical problems not expected).
1. Vincent Del-torro - Principles of Electrical Engineering, Prentice Hall Pvt.Ltd. 2. R.K. Sugandhi & K.K. Sugandhi - Thyristor theory & applications, Willey
3.Sawhney A.K.- A course in Electrical & Electronic Measurements & Instrumentation, Dhanpat Rai & Sons.
4.I.J. Nagrath & D.P. Kothari - Electrical Machines, Tata McGraw Hill Ltd. 5.Allen Mottershead - Electronic Devices & Circuits - An Introduction, Prentice Hall India Pvt. Ltd.
V) Computer Programming-I
1. Fundamentals of UNIX:
; Multi-user System: Logging in and passwords, Electronic mail, Time for UNIX. ; UNIX file system: Files and Directories, Subdirectories and Path names,
searching the tree for files
; File utilities: Ownership and access to files, Make simple text files, Basic
editing techniques, Print files
; File and data processing utilities: Searching for patterns, Rearranging file,
structures, Sorting a file, Relational files.
2. Structured Programming:
; C Fundamentals.
Character set, Identifiers and Keywords, Data Types, Constants, Variables and Arrays, Declarations, Operators & Expressions, Library functions, Statements, Symbolic Constants, Preprocessor directives
; Data Input and Output
getchar(), putchar(),scanf(),print(),gets(),puts()fuctions ; Control Statements
If-else, while, do-while, go-to, for statements nested control structures, switch,
break, continue statements comma operator
Function prototypes, passing arguments to a function by value, recursion
storage classes, automatic, External, static, register variables in single file
Defining - processing array, passing arrays to functions, introduction to
multidimensional arrays, arrays and strings.
Declarations, Referencing and de-referencing, passing pointers to functions,
pointer to array. (No reference to dynamic memory allocation) ; Structures and Unions
Defining and processing a structure
1. Programming in C - Balagurusamy, Tata McGraw Hill
2. A structured Programming approach using C - Behrouz Forouzan, Thomas
3. UNIX training guide - Clifford Mould, Wheeler Publications 4. Programming in C - Schuam out line series
5. Let us C - Yashwant Kanetkar, BPB Publications
6. Practical C programming - O‟Reilly Algorithms with C - O‟Reilly
7. Internet for everyone - A Leon, Leon Techworld
SEMESTER - II
I) Applied Mathematics - II
1 Beta and Gamma Functions:
; Beta and Gamma Functions with properties (without proof).
; Relation between Beta and Gamma functions, Duplication formula (with proof) 2 Differentiation under integral sign with constant limits of integration 3 Integral calculus:
; Rectification of plane curves
; Double and triple integration. Idea of Jacobian for evaluating integrals with
transformation (Theorems and problems on Jacobian are not expected)
; Geometrical interpretation and evaluation by change of order and change to polar
; Application of double and triple integral to area, mass and volume 4 Differential equations:
; First order and first degree exact differential equation and those which can be
reduced to exact by use of integrating factor (only four rules of I.F. and I.F. by
; Linear differential equation and equations reducible to linear equation.
; Linear differential equations of higher order with constant coefficients.
Complementary functions. Particular integrals for the equations of the type f (D) y
axax= X where X = e, xm, Sin (ax+b), Cos (ax+b), eV, x.V where V is a function of x
(Derivations of P.I. are not expected)
; Leagendre differential equation. Cauchy‟s linear homogeneous equation and
; Variation of parameter methods and method of undetermined coefficients.
; Standard curves: straight line, circle, parabola, ellipse, hyperbola, rectangular
hyperbola, catenary, semicubical parabola, cissoid, lemniscate, astroid, hypocloid,
222 cycloid, cardioide and ay = x (a-x), 9ay2 = (x-2a) (x-5a)
; Higher Engineering Mathematics - Dr.B.S.Grewal, Khanna Publications
; A text book of Applied Mathematics - P.N. & J.N. Wartikar, Pune Vidyarthi Griha
; Advanced Engineering Mathematics - Erurin Kreyszing, Wiley Eastern Ltd.
; Engineering Mathematics-I -G.V. Kumbhojkar, C. Jamanadas & Co. ; Applied Mathematics-I - Dr.B.V. Jungam, K.P.Patil, Mrs. N.M.Kumthekar, Nandu
II) Applied Science II
Section-I: Applied Physics
; wedge shaped film, Newton‟s rings, Interference: coherence, interference in thin film,
qualitative explanation of Cornu‟s fringes for Finding strains and stresses in bent
; Diffraction Fraunhoffer‟s diffraction at single slit, double slit, diffraction at N
parallel slits, diffraction grating, resolving power. ; Principles and working of optical fibres.
; rays, properties of X-rays, Production of X-rays (Coolidge tube), origin of X-
Mosseley‟s law, X-ray diffraction, Bragg‟s law (with Derivation), Bragg‟s X-ray
spectrometer and determination of crystal structure. Laser: 3.
; population inversion, pumping Spontaneous and stimulated (induced) emission,
device and active system.
; The Ruby laser, H-N laser and CO2 laser, semiconductor laser, Applications of ee
; Radiation detectors, ionization chamber, G.M. “Counter” nuclear reactions, fission,
nuclear reactors fusion,
Section-II: Applied Chemistry
5 Corrosion and its control:
; Introduction: definition, electrochemical theory of corrosion, factors influencing
rate of corrosion.