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«B. A. (Hons.) / B. Sc. (Hons.) Mathematics Syllabus for Semester System First Semester Code Course Periods/ Week Credits BHM-101 Calculus 4 4 BHM-102 ...»

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• E. B. Saff and A. D. Snidder: Fundamental of Complex Analysis with Applications to Engg. and Science, Pearson Education.

• A. David Wunsch, Complex Variables with Applications, Pearson Publication, 2009.

• Punnuswamy: An Introduction to Complex Analysis, Narosa Publication.

BHM-604: Operations Research and Linear Programming

Unit I:

Operations Research (OR) and its Scope, Modeling in OR, Scientific Method in Operations Research, Linear Programming: Definition, mathematical formulation, standard form, Solution space, solution – feasible, basic feasible, optimal, infeasible, multiple, redundancy, degeneracy, Solution of LP Problems - Graphical Method, Simplex Method.

Unit- II:

Duality in LP, Dual Simplex Method, Economic interpretation of Dual, Transportation Problem, Basic feasible solution using different methods (North-West corner, Least Cost, Vogel’s Approximation Method), Optimality Methods, Unbalanced transportation problem, Degeneracy in transportation problems, Assignment Problem, Hungarian Method for Assignment Problem.

Unit III:

Elementary inventory models, Replacement models, Group replacement problem, Sequencing theory, m machines and n jobs problem, Graphical method for sequence problem.

Unit IV:

Game Theory, pure and mixed strategies, Saddle point, Two-Persons-Zero-Sum Game, Game with mixed strategies, Dominance rule, Graphical Method, Inter - relation between the theory of games and linear programming, Solution of game using Simplex method.

Books Recommended:

• J. K. Sharma, Operations Research – Theory and Application, Macmillian Pub.

• J. K. Sharma, Operations Research – Problems and Solutions, Macmillian Pub.

• G. Hadly, Linear Programming, Narosa Publishing House

• A. H. Taha, Operations Research – An Introduction. Prentice Hall

• Hillier and Lieberman, Introduction to Operations Research, McGraw Hill.

BHM-605: Mechanics Unit I Basic Concept of Mechanics:

- Fundamental laws of Newtonian mechanics, inertial frame of reference, particle, mass, rigid body force, external and internal forces, forces acting at a point, triangle law of forces and polygon law of forces, Lami's theorem, equilibrium of a system of particles, necessary conditions for equilibrium of forces.

Unit II Moments, moment of a force about a point and a line, parallel forces, couple, theorem of Varignon, Necessary conditions for equilibrium (moment), Coplanar forces, Reduction of a general plane force system, parallel force system in two and three dimensions.

Unit III

Centre of gravity and centre of parallel forces, Centre of gravity of some simple bodies:

rod, triangle, arc, plane area, surface of revolution, sum of difference of two bodies, segment of a sphere and some simple curves, Work and Energy, Conservative field and potential energy, Principle of conservation of energy for a particle.

Unit IV Components of velocity and acceleration (Cartesian, radial and transverse, tangential and normal), uniformly accelerated motion, Resisted motion, Projectile and motion in a non-resisting medium, Constrained motion on a smooth vertical circle, collisions (direct).

Books Recommended:

• Statics, A. S. Ramsey, Cambridge University Press

• A Text book of Dynamics, F. Chorlton, CBS Publishers & Distributors Pvt Ltd

• Dynamics Part-1 and 2, A. S. Ramsey, Cambridge University Press.

• Classical Mechanics, Goldstein, Pearson Education.

• Principle of Mechanics, Synge and Griffith, Mcgraw-Hill Book Company.

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