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; Maxima and minima; Taylor series; Definite/indefinite integrals; Partial derivatives; Total derivative; Gradient, Divergence, Curl; Vector identities; Directional derivatives; Line, surface, and volume integrals |
Ordinary Differential Equation (ODE) | First-order (linear and non-linear); Higher-order linear with constant coefficients; Euler-Cauchy equations; Initial and boundary value problems |
Partial Differential Equation (PDE) | Fourier series; Separation of variables; One-dimensional diffusion equation; First and second-order one-dimensional wave equation; Two-dimensional Laplace equation |
Probability and Statistics | Sampling theorems; Conditional probability; Descriptive statistics (mean, median, mode, standard deviation); Random variables (discrete/continuous); Poisson and normal distribution; Linear regression |
Numerical Methods | Error analysis; Numerical solutions of linear/non-linear algebraic equations; Newton’s and Lagrange polynomials; Numerical differentiation; Trapezoidal and Simpson’s rule; Single/multi-step methods for first-order differential equations |
Structural Engineering | Engineering Mechanics | System of forces; Free-body diagrams; Equilibrium equations; Internal forces in structures; Friction; Centre of mass; Free vibrations of undamped SDOF systems |
Solid Mechanics | Bending moment and shear force in beams; Simple stress-strain relationships; Bending theory; Flexural/shear stresses; Shear center; Uniform torsion; Transformation of stress; Buckling of column |
Structural Analysis | Statically determinate/indeterminate structures; Force/energy methods; Superposition method; Analysis of trusses, arches, beams, cables, frames; Displacement methods (slope deflection, moment distribution); Influence lines; Stiffness/flexibility methods |
Construction Materials and Management | Construction materials (structural steel, concrete); Construction management; Project planning, network analysis (PERT, CPM); Cost estimation |
Concrete Structures | Working stress, limit state design; Design of beams, slabs, columns; Bond and development length; Prestressed concrete beams |
Steel Structures | Working stress, limit state design; Design of tension/compression members, beams, columns; Connections; Plastic analysis (beams, frames) |
Geotechnical Engineering | Soil Mechanics | Three-phase system; Permeability; Seepage; Effective stress; Compaction; Consolidation; Shear strength; Mohr’s circle; Stress-strain characteristics; Stress paths |
Foundation Engineering | Subsurface investigations; Earth pressure theories; Stability of slopes; Stress distribution; Bearing capacity theories (Terzaghi, Meyerhoff); Settlement analysis; Deep foundations (axial load, pile load test) |
Water Resources Engineering | Fluid Mechanics | Fluid properties; Continuity, momentum, and energy equations; Potential flow; Laminar/turbulent flow; Flow in pipes; Boundary layer; Lift and drag |
Hydraulics | Flow measurement; Dimensional analysis; Hydraulic similitude; Channel hydraulics; Energy-depth relationships; Hydraulic jump; Gradually varied flow |
Hydrology | Hydrologic cycle; Precipitation, evaporation, infiltration; Unit hydrographs; Reservoir capacity; Flood estimation; Groundwater hydrology |
Irrigation | Types of irrigation systems; Crop water requirements; Gravity dams, spillways; Lined/unlined canals; Weir design; Cross drainage structures |
Environmental Engineering | Water and Wastewater Quality and Treatment | Water quality standards; Water distribution systems; Drinking water treatment; Sewerage system design; Wastewater treatment; Sludge disposal; Treated sewage reuse |
Air Pollution | Pollutants, sources, impacts; Air pollution control; Air quality standards, index |
Municipal Solid Wastes | Characteristics; Collection, transportation; Waste management systems (reuse/recycle, energy recovery, treatment, disposal) |
Transportation Engineering | Transportation Infrastructure | Highway geometric design; Railway track design; Airport runway length; Taxiway design |
Highway Pavements | Highway materials; Design of flexible/rigid pavements; IRC codes |
Traffic Engineering | Traffic studies (flow, speed, accident); Traffic flow parameters; Traffic signs; Signal design (Webster’s method); Intersection types; Highway capacity |
Geomatics Engineering | Surveying | Errors and adjustment; Maps; Distance and angle measurement; Levelling; Traversing; Total station; Curves (horizontal/vertical) |
Photogrammetry and Remote Sensing | Scale, flying height; Basics of remote sensing, GIS |
