This TANCET syllabus is only for mechanical, automobile & aeronautical engineering Students. In this syllabus, study material has been covered for topics expect mathematics. Click the working link to go the study material page of desired topic.
SYLLABUS
PART – I
ENGINEERING MATHEMATICS (Common to all Candidates)
i) Determinants and Matrices:

Solving system of equations

Rank of the Matrix

Eigenvalues and eigenvectors

Reduction of quadratic form to canonical form.

ii) Calculus and Differential Equations:

Partial derivatives

Jacobians

Taylor’s expansion

Maxima and Minima.

Linear ordinary differential equations with constant coefficients

Simultaneous first order linear equations with constant coefficients.

Formation of partial differential equation (PDE)

Solution of first order PDE

Solution of linear higher order PDE with constant coefficients.

iii) Vector Calculus:

Double and triple integrations and their applications

Gradient, Divergence, Curl and Laplacian

Green’s, Gauss divergence and Stroke’s theorem.

iv) Functions of Complex Variables and Complex Integration :

Analytic functions

Conformal Mapping

Bilinear transformation

Cauchy’s integral theorem and integral formula

Taylor and Laurent Series

Singularities

Residues

Residue theorem and its applications.

v) Transforms:

Laplace Transform

Inverse transforms

Application to solution of linear ordinarydifferential equations with constant coefficients.

Fourier integral theorem

Fourier transform pair

Sine and Cosine transforms.

Transform – Inverse Ztransform

Solution of difference equations using Ztransform.

vi) Numerical Methods :

Solution of linear system by direct and iterative methods

Interpolation and approximation

Numerical Differentiation and Integration

Solving Ordinary Differential Equations.

vii) Applied Probability :

Probability and Random variables

Standard Discrete and Continuous distribution

Moments

Moment generating function and their properties.

TwoDimensional Random
Variables – Covariance – Correlation and Regression. 
PART – II
BASIC ENGINEERING & SCIENCES (Common to all Candidates)
1) Applied Mechanics:

Law of Mechanics

Lame’s theorem

Forces, Moments and Couples

Displacement, velocity and Acceleration

Friction

Moment of Inertia

2) Mechanical Engineering:

Laws of thermodynamics

Open and closed systems

Equation of state

Heat and Work.

3) Physics:

Latices

Ultrasonic flaw detector

Xray radiography

Interference Fringes

Planck’s quantum theory

Laser and Fibre Optics.

4) Material Science :

Fracture

Magnetic and Dielectric materials

Conductor and Semi conductor materials

Ceramic and Super conductor materials.

5) Civil Engineering:

Fluid Statics and Dynamics

Boundary Layer

Pumps and Turbines

Environmental Pollution.

6) Electrical Engineering:

Ohm’s law

Kirchoff’s law

A.C. circuits

D.C. machines

Transformers

Synchronous machines

Instrumentation.

7) Computers:

Computer organization

Architecture

Arrays

Pointers

User defined function –C program

8)
Chemistry:

Chemical kinetics

Fuels and Combustion.

PART – III
i) Mechanics : Statics of Particles, Equilibrium of Rigid Bodies, Properties of Surfaces and Solids, Dynamics of Particles, Friction and Elements of Rigid Body Dynamics – Basics of Mechanisms, Kinematics of Linkage Mechanisms,Kinematics of Cam Mechanisms, Gears and Gear Trains, Friction, Force Analysis, Balancing and Vibration.
ii) Strength of Materials and Design : Stress, Strain and Deformation of Solids, Transverse Loading on Beams and Stresses in Beams, Deflection of Beams, Energy Principles, Thin cylinders and spherical resells Torsion Fundamentals of Design for Strength and Stiffness of Machine Members, Design of Shafts and Couplings, Design of Fasteners and Welded Joints, Design of Springs and Engine Parts, Design of Engine parts, Bearings and Flywheels,
Design of Transmission Systems for Flexible Elements, Spur Gears and Parallel Axis Helical Gears, Bevel, Worm Gears and Crossed Helical Gears, Design of Gear Boxes, Design of Cam, Clutches and Brakes.
iii) Material Science and Metallurgy : Constitution of Alloys and Phase Diagrams, Heat Treatment, Ferrous and Non ferrous Metals, NonMetallic Materials, Mechanical Properties and Testing, Crystal Defects and Strengthening of Materials Conducting and Semiconducting Materials, Magnetic and Dielectric Materials, Nuclear Physics,Superconducting and New Engineering Materials.
iv) Thermodynamics : Basic Concepts and First Law, Second Law, Entropy and Availability, Properties of Steam, Psychrometry, Ideal and Real Gases and Thermodynamic Relations, Fuels and Combustion,  Gas Power Cycles,Stream Turbines, Internal Combustion Engines, Internal Combustion Engines Testing and Performance, Gas Turbines,  Steam Nozzle, Air Compressor, Refrigeration and AirConditioning, Boilers, Cogeneration and Waste Heat Recovery.
v) Heat Transfer : Conduction, Phase Change Heat Transfer and Heat Exchangers, Radiation, Mass TransferRefrigeration Cycle, Refrigerants, System Components and Balancing, Psychrometry, Air Conditioning Systems,Unconventional Refrigeration Cycles.
vi) Production Technology : Foundry Technology, Hot & Cold Working, Forging, Advances in Forming Process, Principles and Applications of Joining Processes, Theory of Metal Cutting, Centre Lathe and special Purpose Lathes,Reciprocating Machines, Milling Machines and Gear Cutting, Abrasive Process, Broaching, CNC Machine Tools and Part Programming.
vii) Automotive Engines : Engine Construction and Operation, SI Engine Fuel System, Cooling and Lubrication System, Combustion and Combustion Chambers, Two Stroke Engines, Diesel Engine Basic Theory, Fuel Injection System, Air Motion, Combustion and Combustion Chambers, Supercharging and Turbocharging, Diesel Engine Testing and Performance.
viii) Automotive Transmission and Pollution : Clutch and Gear Box, Hydrodynamic Drive, Planetary Gear
Boxes, Automatic Transmission Applications, Hydrostatic and Electric Drive  S.I. Engine Combustion and Emissions,
CI Engine Combustion and Emissions, Control Techniques for Reduction of SI and CI Engine Emission, Test
Procedure & Instrumentation for Emission Measurement and Emission Standards.
ix) Aerodynamics : Basic Fluid Mechanics, Two Dimensional Inviscid Incompressible Flow, Airfoil Theory, Subsonic Wing Theory, Laminar and Turbulent Flow, Fundamental Aspects of Compressible Flow, Shock and Expansion Waves,Two Dimensional compressible Flow, High Speed Flow Over Airfoils, Wings and Airplane Configuration.
x) Aerospace Propulsion : Fundamentals of Gas Turbine Engines, Subsonic and Supersonic Inlets for Jet Engines, Centrifugal and Axial Flow Compressors, Combustion Chambers for Jet Engines, Turbines for Jet Engines, Nozzles for Jet Engines, Ramjet
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