OJEE 2011 Syllabus Lateral Entry Stream Diploma Odisha JEE
Ordinary Differential Equations: Differential equations of first order, Physical applications, Linear differential equations, Homogeneous and non-homogeneous second order linear differential equation with constant co-efficients. Application to free and forced vibration of spring mass systems, method of variation of parameters. Normal form change of dependent and independent variables. Cauchy’s Euler’s equation
Series Method : Properties of power series, solution of ordinary differential equations. Legendre equations. Legendre Polynomials and functions, methods of Frobenius, the Gamma function, the Bessel-Clifford equations, Bassel’s equation, nonhomogeneous equations.
Laplace Transforms : The Laplace transforms (L.T.), L.T. of derivaties and integrals, derivatives and integrals of Laplace transforms, L.T. of periodic functions, Inverse Laplace transforms, Convolution theorem, Application of L. T. to solution of differential equations, special techniques.
Fourier Series : Fourier theorem, Fourier expansion, even and odd functions, half range expansion, seems and scale changes, forced oscillation, Miscellaneous expansion techniques.
Matrices : Notation and terminology, Solution of simultaneous equations by Gaussian elimination, Rank, Computation of rank by reduction of Rewechelon normal form, Algebra of matrix, inverse determinants, linear dependence and independence, solution of homogeneous and non-homogenous systems. Norms and product, Gram-schemidt Process, Projection matrix, eiegenvalues, eigenvectors, Symmetric and simple matrix, System of linear differential equations the homogenous case.
Vectors : Vector algebra, Vector differentiation, Vector operator del, gradient, divergence, curl, integral theorem.
Statics : System of co-planer forces – Condition for equilibrium
– concept of free body diagrams – Methods of solution of engineering problems, problem with friction – Belt friction and screw jack. Force analysis of plane trusses(Method of joints and method of sections). Analysis of frames (Method of members). First moment of area and centroid – theorem of Papus, Second momentum of areas, Polar moment of inertia. Principle of virtual work for a single particle, rigid bodies, ideal systems and constrained bodies.
Dynamics : Kinematics of rigid body – Plane motion, Kinetics of translation and rotating rigid bodies, moment of inertia of bodies.
D’Alembert’s Principle – Application to a single particle rigid body in translation and rotation, ideal systems. Momentum and impulse, Application to principle of linear momentum to a single particle, rigid bodies and ideal systems, Impact – application of principle of angular momentum to a single particle and rotating rigid bodies, Principle of conservation of momentum.
Work and energy : Principle of work and energy for a single particle, rotating rigid body and ideal systems, Principle of conservation of energy.
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