Section 1

Engineering Mathematics

Build a strong mathematical foundation covering linear algebra, calculus, differential equations, probability and numerical methods required for GATE Mechanical Engineering.

Linear Algebra

  • ✔ Matrix Algebra
  • ✔ Linear Equations
  • ✔ Eigen Values
  • ✔ Eigen Vectors

Calculus

  • ✔ Limits & Continuity
  • ✔ Differentiability
  • ✔ Mean Value Theorems
  • ✔ Maxima & Minima
  • ✔ Taylor & Fourier Series
  • ✔ Double & Triple Integrals
  • ✔ Gradient, Divergence & Curl
  • ✔ Vector Integration

Differential Equations

  • ✔ First Order ODE
  • ✔ Higher Order ODE
  • ✔ Euler-Cauchy Equation
  • ✔ Initial & Boundary Value Problems
  • ✔ Laplace Transform
  • ✔ Heat, Wave & Laplace Equations

Complex Variables

  • ✔ Analytic Functions
  • ✔ Cauchy-Riemann Equations
  • ✔ Contour Integrals
  • ✔ Taylor Series
  • ✔ Laurent Series

Probability & Statistics

  • ✔ Probability Concepts
  • ✔ Conditional Probability
  • ✔ Random Variables
  • ✔ Binomial Distribution
  • ✔ Poisson Distribution
  • ✔ Normal Distribution
  • ✔ Mean, Median & Mode
  • ✔ Standard Deviation

Numerical Methods

  • ✔ Linear Equations
  • ✔ Non-linear Equations
  • ✔ Trapezoidal Rule
  • ✔ Simpson's Rule
  • ✔ Single Step Methods
  • ✔ Multi Step Methods

📘 Complete Engineering Mathematics for GATE Mechanical

Covers Linear Algebra, Calculus, Differential Equations, Complex Variables, Probability & Statistics and Numerical Methods based on the latest GATE Mechanical Engineering syllabus.

Section 2

Applied Mechanics & Design

Master Engineering Mechanics, Strength of Materials, Theory of Machines, Vibrations and Machine Design through the latest GATE Mechanical Engineering syllabus.

Engineering Mechanics

✔ Free Body Diagrams
✔ Equilibrium
✔ Friction
✔ Belt & Pulley
✔ Brakes & Clutches
✔ Trusses & Frames
✔ Virtual Work
✔ Kinematics & Dynamics

Mechanics of Materials

Stress & Strain
Mohr's Circle
Pressure Vessels
Shear Force
Bending Moment
Beam Deflection
Torsion
Thermal Stress

Theory of Machines

Mechanisms
Velocity Analysis
Acceleration
Cams
Gear Trains
Flywheel
Governors
Gyroscope

Vibrations

Free Vibration
Forced Vibration
Damping
Resonance
Critical Speed
PID Controller
Transfer Function

Machine Design

Failure Theories
Fatigue
S-N Curve
Bolted Joints
Welded Joints
Shafts & Gears
Bearings
Springs, Brakes & Clutches
Section 3

Fluid Mechanics & Thermal Sciences

Master Fluid Mechanics, Heat Transfer, Thermodynamics and Engineering Applications according to the latest GATE Mechanical syllabus.

Topics

🌊
Fluid Mechanics
🔥
Heat Transfer
⚙️
Thermodynamics
🚀
Applications

🌊 Fluid Mechanics

Fluid Properties
Fluid Statics
Buoyancy & Floating Bodies
Mass, Momentum & Energy
Bernoulli Equation
Velocity Potential
Boundary Layer
Pipe Flow & Head Losses
Compressible Flow
Converging & CD Nozzles

🔥 Heat Transfer

Conduction
Convection
Radiation
Heat Transfer Through Fins
Lumped System Analysis
Boundary Layer
Boiling & Condensation
Heat Exchangers (LMTD & NTU)
Stefan-Boltzmann Law
Radiation Network

⚙️ Thermodynamics

Pure Substances
Ideal & Real Gases
Zeroth Law
First Law
Second Law
Entropy
Availability
Irreversibility
Property Charts
Thermodynamic Relations

🚀 Engineering Applications

Power Engineering

Vapour Cycle, Gas Cycle, Regeneration, Reheat

IC Engines

Otto, Diesel, Dual Cycle, Combustion

Refrigeration

Vapour Compression, Heat Pump, Psychrometrics

Turbomachinery

Pelton, Francis, Kaplan Turbines

Compressors

Air & Gas Compressors

Pumps

Pump Characteristics & Performance

Section 4

Materials, Manufacturing & Industrial Engineering

Learn Engineering Materials, Manufacturing Processes, CAD/CAM, Production Planning, Automation, Operations Research and Quality Engineering for GATE Mechanical Engineering.

Engineering Materials

Crystal Structure
Phase Diagram
Heat Treatment
Metals & Alloys
Polymers
Composites
Ceramics
Stress–Strain Curve

Manufacturing

Casting
Forming
Welding
Powder Metallurgy
Sheet Metal
Solid State Welding
Brazing & Soldering
NDT Methods

Machining & Automation

Machine Tools
Cutting Tools
Tool Wear
CNC Programming
CAD / CAM
PLC
Hydraulic Systems
Pneumatic Systems

Advanced Manufacturing

3D Printing
Additive Manufacturing
CMM
Tolerance Analysis
Inspection
Interferometry
Surface Finish
Comparators

📊 Production Planning & Control

Work Study
Productivity
Forecasting
Aggregate Planning
Scheduling
MRP
Lean Manufacturing
Six Sigma
Inventory Control
Quality & Reliability

📈 Operations Research

Linear Programming
Simplex Method
Transportation Model
Assignment Problem
Network Flow
Queuing Models
PERT
CPM