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