Engineering Mathematics
- Matrix algebra and linear systems
- Eigenvalues and eigenvectors
- Vector spaces and transformations
- Analytic functions & Cauchy-Riemann equations
- Cauchy’s integral theorem & formula
- Taylor and Laurent series expansions
- Solutions of algebraic equations
- Integration: trapezoidal & Simpson’s rule
- Single & multi-step ODE methods
- Conditional probability & Bayes’ theorem
- Random variables & distributions
- Mean, variance, standard deviation
- Limits, continuity, and differentiability
- Definite and improper integrals
- Vector calculus: gradient, divergence, curl
- First and higher-order ODEs
- Laplace transforms and applications
- Heat, wave, and Laplace equations
Applied Mechanics & Design
- Stress-strain relationships
- Bending, torsion, and deflection
- Mohr’s circle and failure theories
- Kinematics of mechanisms
- Cams, gears, and governors
- Balancing and gyroscopic effects
- Free and forced vibrations
- Damping and resonance
- Critical speeds of shafts
- Design for static and fatigue loading
- Joints, shafts, bearings, springs
- Failure criteria and safety factors
Fluid Mechanics & Thermal Sciences
- Fluid statics and buoyancy
- Bernoulli’s principle and applications
- Pipe flow and boundary layers
- First and second laws
- Thermodynamic cycles
- Entropy and availability
- IC Engines: Otto, Diesel, Dual cycles
- Refrigeration & Air Conditioning
- Power plants, compressors, turbines
- Conduction and fins
- Convection correlations
- Radiation and heat exchangers
Materials, Manufacturing & Industrial
- Structure and properties
- Phase diagrams and heat treatment
- Stress-strain behavior
- Pattern design and solidification
- Risers, gating, cooling systems
- Defects and inspection methods
- Deterministic models and EOQ
- Safety stock and reorder point
- Inventory cost optimization
- Casting and forming methods
- Machining and welding
- Additive manufacturing
- Linear programming: simplex, duality, sensitivity analysis
- Transportation, assignment & network flow models
- Queuing theory, PERT & CPM for project scheduling