GATE, Graduate aptitude test in engineering is the highly anticipated and the most difficult exam in the country. The official notification for the session 2017-18 has been released and the exam is proposed to be held in the month of February, the all India level exam is conducted by 8 IITs in collaboration with IISC Bangalore each year to test the aptitude of students in different branches of engineering, the exam is the guaranteed ticket to a secured and bright future as getting through the exam avails you lot many benefits that comprise admission to postgraduate programmes in the elite institution of the county along with fat pay scale jobs in distinctive public sector undertakings. This year the exam will be conducted by IIT Roorkee. Owing to the high difficulty level of GATE syllabus, each year lakhs of aspirants sit for the prestigious exam, yet only a few serious ones can get through it. Since the official notification is out, it is high time that candidates should kick-start their preparation. Mechanical engineering is an important paper of GATE exam. Here we list you the topics of engineering mathematics and applied mechanics and design in GATE syllabus of mechanical engineering to help you with the preparation endeavour.

### Engineering Mathematics

*Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.*

**Calculus**: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.

**Differential equations:** First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace’s equations.

**Complex variables: **Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series.

**Probability and Statistics:** Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.

**Numerical Methods:** Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.

**Applied Mechanics and Design**

**Engineering Mechanics:** Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations, collisions.

**Strength of Materials:** Stress and strain, elastic constants, Poisson’s ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength.

**Theory of Machines:** Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.

**Vibrations:** Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts.

**Machine Design:** Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.