MP 215

Ordinary and Partial differential equation: Solution of ordinary differential equations with variable Coefficients, system of linear differential equations, heat wave and Laplace equation in two and three dimensions. Separation of variable technique, some boundary value problems and applications. Numerical solutions of differential equation. Complex analysis: Function of complex variables, differentiation and integration, analytic functions, cache theorem and cache formula. Contour integration, power, series expansion, conformal mapping vector analysis: Scalar and vector fields, vector, operator, application to geometry, line, surface and volume integral, divergence theorem of gauss stock’s and Green theorem. Curvilinear and orthogonal coordinates.

MP 012

Calculus of integration and differentiation: Methods of integration, applications of definite integration ( areas, volumes, circular surfaces, length of curvature, central points ) first order ordinary differential equations, introduction to probability theory : sample space, probability axioms, some basic theories, counting methods, conditional probability, random variables, mathematical expectation, some discrete and continuous distributions, Analytical geometry : shifting and rotating of axes, conic sections and their specifications : parabola , ellipse, hyperbola .

MP 317

Numerical analysis (Gauss elimination method, numerical solution of nonlinear algebraic equations, numerical integration, interpolation, numerical solution of differential equations, error analysis), introduction to probability theory (sample space, conditional probability and Bayes’ theorem, discrete and continuous random variables, distribution functions, expectation and variance, some special distributions, moments and moment generating function, central limit theorem and law of large numbers, Chebyshev’s inequality).

MP 219

Stochastic analysis of signals, probability and random processes (univariate random variables, bivariate and multivariate random variables, bivariate and multivariate joint distribution functions, marginal distribution functions, independence, covariance and correlation coefficient, conditional distribution functions and conditional expectation, Markov chains, continuous time random processes, auto correlation and auto covariance, power spectrum functions and spectral analysis).

MP 311

Numerical analysis (Gauss elimination method, numerical solution of nonlinear algebraic equations, Curve fitting, numerical integration, interpolation, numerical solution of differential equations, error analysis), Optimization (linear and nonlinear programming), computer applications.

MP 021

Statics : vector algebra, analytical and geometrical solutions for : reduction of different systems of forces ( intersecting or non intersecting ) in two dimensions, operations of force analysis in two dimensions, equivalence of force systems, body equilibrium, rigid bodies, equilibrium of ideal systems : groups of bodies , groups of rigid bodies and its applications friction : volplane, loop, applications on the real mechanical systems .

MP 123

Central Force Motion: Polar Coordinates – Properties of central Force Motion – Equation of Motion – Applications to Space Mechanics – Nonconservative Systems: Energy dissipation – Real System – Kinetics of System of Particles: Equations of Motion – Motion of the Mass Center of System of Particles – Systems Gaining or Losing Mass: Motion of Rockets – Motion of Chains and Cables- Plane Kinematics of Rigid Bodies: Translational, Rotation and General plane motion- Instantaneous center of rotation in plane motion – Rolling without sliding – Gears – Mechanisms – Kinetics of Plane Motion of Rigid Bodies : Angular Momentum – Kinetic Energy – Equations of Motion – Moment of Inertia – Applications- Initial Motion –Impulse and Momentum of Plane motion of Rigid Bodies : Principle of Impulse and Momentum for a rigid Body and for a System of Rigid Bodies – Collision of Rigid Bodies –Gyroscopic Motion: Gyroscopes-Gyroscopic Couple –Application- Rotation of a Three-Dimensional Body about a Fixed Axis : Dynamic Reaction –Balancing- Mechanical Vibrations: Free Vibrations – Damped Free Vibrations – Forced Vibrations.

MP 125

Plane Kinematics of Rigid Bodies: Translational, Rotational and General plane motion- Instantaneous center of rotation in plane motion – Rolling without sliding – Gears – Mechanisms – Kinetics of Plane Motion of Rigid Bodies: Angular Momentum – Kinetic Energy – Equations of Motion – Moment of Inertia – Applications- Initial Motion –Impulse and Momentum of Plane motion of Rigid Bodies: Principle of Impulse and Momentum for a rigid Body and for a System of Rigid Bodies – Collision of Rigid Bodies – Gyroscopic Motion: Gyroscopes-Gyroscopic Couple –Application- Rotation of a Three-Dimensional Body about a Fixed Axis : Dynamic Reaction –Balancing- Mechanical Vibrations: Free Vibrations – Damped Free Vibrations – Forced Vibrations.

MP 127

Central Force Motion: Polar Coordinates – Properties of central Force Motion – Equation of Motion – Applications to Space Mechanics –– Motion of Charged Particles: In a Uniform Steady Electrical Field – In a Uniform Steady Magnetic Field Kinetics of System of Particles: Equations of Motion – Motion of the Mass Center of System of Particles – Systems Gaining or Losing Mass: Motion of Rockets – Motion of Chains and Cables- Plane Kinematics of Rigid Bodies: Translational, Rotational and General plane motion – Instantaneous center of rotation in plane motion – Rolling without sliding – Gears – Mechanisms – Kinetics of Plane Motion of Rigid Bodies : Angular Momentum – Kinetic Energy – Equations of Motion – Moment of Inertia – Applications- Initial Motion –Impulse and Momentum of Plane motion of Rigid Bodies : Principle of Impulse and Momentum for a rigid Body and for a System of Rigid Bodies – Collision of Rigid Bodies – Mechanical Vibrations : Free Vibrations – Damped Free Vibrations – Forced Vibrations.

MP 031

Properties of matter : systems of standard units and conversion constants between them, dimensional analysis and its applications , moment of inertia, angular displacement, velocity and acceleration of angular motion, torque, angular kinetic energy, work and power for angular motion, angular momentum, relation between angular and linear motion ,theory of perpendicular and parallel axes , moments of inertia for symmetrical bodies about rotational axes, stress, strain, modulus of elasticity, hook’s law ,Poisson ratio, relation between young’s modulus, bulk modulus and shear modulus , energy stored in strain bodies, fluid statics : continuity equation, Bernoulli’s equation and its applications, viscosity ,stock’s equation, viscosity of gases, Newton’s gravitational law, determination of gravitational constant, gravitational field, gravitational potential and its potential energy, coefficient of surface tension, tangential angel, capillarity phenomenon, work and energy for thin membrane, Thermo dynamics : internal energy, specific internal energy, temperature, heat energy, heat capacity, specific heat, phase change, latent heat, heat transfer, conduction convection and radiation, one dimensional Fourier equation in steady state, ( thermal equilibrium ), heat conduction coefficient, heat resistance, applications of Fourier equations on simple walls, methods of heat transfer by convection, Newton’s cooling law, total heat transfer coefficient, black body radiation, emissivity, Steven and boltzmann law for radiation, ability of heat radiation, work and heat energy, first law of thermodynamics , heat content function, simple operations of thermo dynamics in ideal gases, Transitional operations, molecular diffusion on gases, heat conduction energy, viscosity, first and second fik’s laws, steady state .

MP 133

Electromagnetic induction, magnetic circuits, thermal ionic emission, valves and diodes, scattering, pressure and vacuum determinants, temperature measurements.

MP 042

Engineering Drawing: Sectional views. Intersection of engineering surfaces. Civil drawing including retaining walls and some steel points. Some applications in architectural drawing. Introduction to computer aided design using AutoCad program in 2D and 3D drawings. Geometrical Projection: Indexed projection (representation of points, straight lines, planes, intersection of planes). Applications of indexed projection (problems of cut and fill).