MECHANICAL ENGINEERING SYLLABUS BREAKDOWN FOR GATE EXAM

1. 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, maxima, and minima, Taylor series.
- Differential equations: First-order equations (linear and nonlinear), higher-order linear differential equations with constant coefficients.
- Probability and Statistics: Mean, median, mode, standard deviation, probability, random variables, binomial, Poisson and normal distributions.

2. Applied Mechanics and Design:
- Engineering Mechanics: Free body diagrams and equilibrium, trusses and frames, virtual work.
- Mechanics of Materials: Stress and strain, elastic constants, axially loaded members, torsion, bending and shear stresses, Mohr's circle, deflection of beams.
- Theory of Machines: Kinematics and dynamics of single and multi-link mechanisms, gears, flywheels, balancing of reciprocating and rotating masses.
- Vibrations: Free and forced vibration of single-degree-of-freedom systems, effect of damping, resonance, critical speeds.

3. Fluid Mechanics and Thermal Sciences:
- Fluid Mechanics: Fluid properties, fluid statics, manometry, buoyancy, control-volume analysis of mass, momentum, and energy, fluid kinematics, Bernoulli's equation, viscous flow of incompressible fluids, boundary layer, elementary turbulent flow.
- Heat-Transfer: Modes of heat transfer, conduction, convection, radiation, heat exchangers, heat transfer by fins.
- Thermodynamics: Zeroth, first, and second laws of thermodynamics, ideal and real gases, properties of pure substances, calculation of work and heat transfer, thermodynamic relations, entropy, availability, irreversibility, and availability analysis.

4. Manufacturing and Industrial Engineering:
- Engineering Materials: Structure and properties of engineering materials, heat treatment, stress-strain diagrams for engineering materials.
- Metal Casting: Design of patterns, gating, and riser design, casting defects, solidification, and cooling.
- Joining Processes: Welding, brazing, soldering, adhesive bonding, metal forming, high energy rate forming processes, powder metallurgy.
- Metrology and Inspection: Limits, fits, and tolerances, linear and angular measurements, comparators, gauge design, interferometry, measurement of surface roughness, and form.

5. General Aptitude:
- Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning, and verbal deduction.
- Numerical Ability: Numerical computation, numerical estimation, numerical reasoning, data interpretation.

Note: The above syllabus is an extensive breakdown of the subjects included in the GATE ME exam. It is important to refer to the official GATE syllabus for precise and updated information.