GATE 2025 Mechanical Engineering Syllabus: Check Exam Dates, Pattern, Books, Syllabus, and More

Linear Algebra

Matrix Algebra | Systems of Linear Equations | Eigen Values and Eigen Vectors

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, lines, surface and volume integrals, applications of Gauss, Stokes, and Green’s Theorems

Differential Equations

First Order Equations (linear and non-linear) | Higher Order Linear Differential Equations with Constant Coefficients | Euler-Cauchy Equations | 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 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 Trapezodial and Simpson’s Rules | Single and Multi-Step Methods for differential equations

Engineering Mechanics

Free-Body Diagrams and Equilibrium | Friction and its applications, including rolling friction, belt pulley, brakes, clutches, screw jack, wedge, vehicles, etc. | Trusses and Frames | Virtual Work | Kinematics and Dynamics of rigid bodies in plane motion | Impulse and Momentum (Linear and Angular) and Energy Formulations | Lagrange’s Equation

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

Mechanics 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 | Concept of Shear Centre | Deflection of Beams | Torsion of Circular Shafts | Euler’s Theory of Column’s | Energy Methods | Thermal Stresses | Strain Gauges and Rosettes | Testing of Materials with Universal Testing Machine | Testing of Hardness and Impact Strength

Vibrations

Free and forced vibration of single degree of freedom systems | Effect of Damping | Vibration Isolation | Resonance | Critical Speeds of Shafts

Machine Design

Design of 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

Fluid Mechanics

Fluid Properties | Fluid Statistics | Forces on Submerged Bodies | Control-Volume Analysis on Mass, momentum, and Energy | Fluid Acceleration | Differential Equations of Continuity and Momentum | Bernoulli’s Equation | Dimensional Analysis | Viscous Flow of Incompressible Fluids | Boundary Layer | Elementary Turbulent Flow | Flow Through Pipes | Head Losses in Pipes | Bends and Fittings | Basics of Compressible Fluid Flow

Heat Transfer

Modes of Heat Transfer: One-dimensional heat Conduction, Resistance Concept and Electrical Analogy | Heat Transfer through Fins | Unsteady Heat Conduction | Lumped Parameter System | Heisler’s Charts, Thermal Boundary Layer | Dimensionless Parameters in free and forced convective heat transfer | Heat Transfer Correlations for flow over flat plates and through pipes | Effect of Turbulence | Heat Exchanger Performance | LMTD and NTU methods | Radiative Heat Transfer | Stefan and Boltzmann Law | Wien’s Displacement Law | Black and Grey Surfaces | View Factors | Radiation Network Analysis

Thermodynamics

Thermodynamic systems and processes | Properties of pure substances | Behavior of ideal and real gases | Zeroth and First laws of Thermodynamics | Calculation of Work and Heat in various processes | Second law of thermodynamics | Thermodynamic property charts and tables | Availability and Irreversibility | Thermodynamic relations

Applications

Power Engineering: Air and Gas Compressors | Vapour and gas power cycles | Concepts of regeneration and heat | I.C Engines: Air Standard Otto, Diesel and dual cycles | Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles | Properties on moist air | Psychometric chart | Basic psychrometric processes | Turbomachinery: Impulse and reaction principles, velocity diagrams, Peloton-wheel, Francis and Kaplan turbines | Steam and gas turbines

Engineering Materials

Structure and properties of engineering materials | phase diagrams | heat treatment | stress-strain diagrams for engineering materials 

Casting, forming, and Joining Processes

Different types of castings | Design of Patterns | Moulds and Cores | Solidification and cooling; riser and gating design | Plastic deformation and yield criteria | Fundamentals of hot and cold working processes | Load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes, principles of powder metallurgy | Principles of welding, brazing, soldering, and adhesive bonding.  

Machining and Machine Tool Operations

Mechanics of Machining | Basic Machine Tools | Single and multi-point Cutting Tools | Tool geometry and Materials | Tool life and Wear | Economics of Machining | Principles of non-traditional Machining Processes | Principles of Work holding | Jigs and Fixtures | Abrasive Machining Processes | NC/CNC machines and CNC programming

Metrology and Inspection

Limits, fits, and tolerances | Linear and angular measurements | comparators | Interferometry | Form and finish measurement | Alignment and testing methods | Tolerance analysis in manufacturing and assembly | Concepts of coordinate-measuring machine (CMM)

Computer-Integrated Manufacturing

Basic concepts of CAD/CAM and their integration tools | Additive manufacturing

Producing Planning and Control

Forecasting models | Aggregate production planning | Scheduling | Materials requirement planning | Lean manufacturing

Inventory Control

Deterministic models | Safety stock inventory control systems

Operations Research

Linear programming | Simplex method | Transportation | Assignment | Network flow models | Simple Queuing models | PERT and CPM