• Differentiation

Polynomial functions, Relational functions, Inverse functions, Composite functions, Trigonometric functions, Differentials Curves, Tangents, Maxima, minima, Mean-value theorem, Logarithmic function, Hyperbola function, Exponential functions.

• Integration

Indefinite integral, Definite integral, Areas, arc lengths and volumes, Centroid , Moments of inertia, Partial fractions, Rational function, Trigonometric functions, Infinite series, Power series, Taylor series

• Analytic Geometry

Curves, tangents, normals , circle, parabola, ellipse, hyperbola, Second degree curves, Polar co-ordinates, Sphere, cone, cylinder, quadric surfaces, Tangential vectors, Curvature of normal vectors, Partial differentiation, Gradient, Directional derivative, Tangent plane, Curvature, Maxima and minima of functions of several independent variables, Lagrange multiples, Double integrals, Triple integrals, Curves, Surfaces, Line integrals, Surface integrals, Gauss’s theorem, Stokes’s theorem

• Linear Algebra

Matrices, Linear system of equations, Rank of a matrix, Inverse of a matrix, Linear independence, Eigenvalues, eigenvectors, Quadratic forms, Orthogonality, Symmetric and hermetian matrix

• Differential Equations

First order equation, Second order differential equation, Homogeneous equation and nonhomogeneous equation, Method of undetermined coefficients and variation of parameters, Power series method

• Set Theory

Basic concepts of set relations and functions, Mapping, Venn diagrams, Elementary probability theories, Permutations, Combinations

• Statistics

Mean, median, mode, variance, Normal distribution

Variables and arrays, expressions , relational and logical operators, library functions, input and output , control statements, for , while and do-while statements , if and switch statements , functions, arguments to a function, automatic external and static variables, passing arrays to a function, arrays and strings pointers and 1-d arrays , array of pointers , structures and data files . Data structures linked lists, stacks, queues, basic algorithms of sorting and searching. Non linear equations, bisection method, Newton method, Gauss elimination method for set of linear equations, interpolation, trapezoidal rule, Simpson rule of integration, curve fitting.

• Mechanics

Vectors, uniform circular motion, relative motion in 1D and 2D, force, Newton’s law of motion , friction, work and kinetic energy , potential energy, conservation of energy , work done by non conservative forces , system of partial linear momentum . conservation of linear momentum , impulse and linear momentum, translation and rotation, kinetic energy of rotation , torque, angular momentum, conservation of angular momentum, Newton’s law of gravitation , gravitational potential energy , simple harmonic motion, forced oscillation and resonance.

• Waves/Acoustics

Transverse and longitudinal waves, wavelength and frequency, phasors, standing waves and resonance, energy and power of a travelling string wave, sound wave, speed of sound, intensity and sound level

• Heat And Thermodynamics

Temperature, heat, work, first law of thermodynamics, heat transfer mechanism.

• Electricity And Magnetism

Electric charge , coulombs law, electric field, electric potential, capacitance, electric current , resistance circuits, electric power, work energy magnetic field, inductance, LRC circuits

• Light

Wave theory, reflection, refraction, diffraction, basics of illumination, color theory

Functional planning of buildings, building materials, masonry construction, fire protection, building components, vertical transportation, doors and windows, roof and roof coverings, plumbing services, acoustics and sound insulation in buildings, ventilation, air conditioning and thermal insulation, building illumination, construction management.

• Statics

Force, Resultant of a system of parallel forces, Equilibrium of force systems, Calculation of support reactions

• Stress Resultants

Normal force, Shear force, Bending moment, Torsion

• Pin-Jointed Trusses

Truss analysis, Statistical determinacy, Method of joints, Method of sectors

• Cables And Arches

Light weight cables carrying concentrated loads, Heavy cables, Three pinned arch, Bending moment diagrams

• Stress And Strain

Direct stress in tension and compression, Shear stress in tension and compression, Direct strain, Shear strain, Volumetric strain, Stress-strain relationships, Relationships between elastic constants, Strain energy in simple tension and compression

• Bending Of Beams

Symmetrical bending, Combined bending and axial load, Strain energy in bending , Unsymmetrical bending, Section properties, Principal axes and second moments of area, Load, shear force and bending moment relationship

• Shear Of Beams

Shear stress distribution in symmetrical and unsymmetrical section, Strain energy due to shear

• Torsion Of Beams

Torsion of solid and hollow circular section bars, Strain energy due to torsion , Torsion of solid section beams , Working of even-section under torsion

• Deflection Of Beams

Differential equation of symmetrical bending , Singularity function, Moment-area method, Deflection due to shear

• Complex Stress And Strain

Stress at a point, Stresses on inclined planes, Strain at a point, Strain on inclined planes, Principle strains

• Virtual Work And Energy Methods

Work, Principle of virtual work , Energy methods, Reciprocal theorem

• Statically Indeterminate Structures

Force method , Displacement method , Degree of statical indeterminacy, Kinematic indeterminacy , Statically indeterminate beams, Statically indeterminate trusses, Braced beams, Portal frames, Two-pinned arches, Slope deflection method

• Structural Statistics

Euler theorem for slender columns, Statistics of beams under transverse and axial loads, Energy method for the calculation of buckling loads in columns