### Industrial Mathematics Course Description

#### Level I – Semester I

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**IMT111β: Classical Mechanics-I (Dynamics) (30 lecture hrs + 15 tutorial hrs) -( Credit Value 2.5)**

Frame of reference, Inertial frames, Forces, Velocity, Acceleration, Linear momentum, Angular velocity, Angular acceleration, Angular momentum, motion of a particle (Newton laws), motion of a system particles, Rotating coordinate systems, moments and products of inertia. Parallel axes theorem, perpendicular axes theorem for moments and products of inertia. Principle axes and principle moments of inertia of a system of particles, Rotating coordinate systems, Infinitesimal rotation, Euler equations, Generalized coordinates, Lagrange’s formulations, Hamiltonian functions, Theory of small oscillation, Impulsive motion.

*Method of assessment: end of semester examination*

IMT1b2β: Mathematical Computing (15 lecture hrs + 60 practical hrs) -( Credit Value 2.5)

Introduction to computer systems and its historical development, contribution from mathematicians (e.g. Libnietz, Boole, Pascal, Babage, Turing, von Neumann),numerical computation and mechanical computing devices; General overview of: computer architecture, hardware, software and liveware, programming languages, application packages, the present day use of computers and its future; Introduction to Linux Operating System: UNIX commands, directory structure, text editors, user accounts and file permissions, text editors, virtual terminals in text mode. programming with C on Unix system – editing (with emacs), compilation, debugging etc,. ; Formatted input-output, control structures, loops, C-functions, pointers, File input/output, command-line arguments (the above shall be discussed with mathematical applications); Introduction to X-Windows system.

*Method of assessment:Practical examination/assignments/project report and end of semester oral examinatin and/orpresentation.*

Level I – Semester II

**IMT121β: Classical Mechanics-II (Statics) (30 lecture hrs + 15 tutorial hrs) -(Credit Value 2.5)**

Theory of Forces and Couples: Force acting at a point, Resultant of a system of Forces acting at a point, Condition for equilibrium of a system of Forces acting at a point, Vector moment of a Force, Couple, Moment of a Couple, Resultant of a system of Forces in 3D, Invariants, Wrench, Coplanar Systems of Forces, Varignon’s Theorem of Moments, Parallel Systems, Conjugate forces. Bending of Beams: Shear and Bending moment in a beam, Relations among Load, Shear and Bending Moment, Thin Elastic Beams, Bernoulli-Euler Law, Macaulay’s Notation, Clapeyron’s equation for three moments. The Catenary: Flexibility, The common catenary, Parabolic chain, suspension bridge, Catenary of uniform strength, General equations of equilibrium of a string in one plane under given forces, Strings on rough curves, Variable chain hanging under gravity.

*Method of assessment: end of semester examination*

IMT1b2β: Mathematical Computing (15 lecture hrs + 60 practical hrs) -( Credit Value 2.5)

Level I – Semester II

**IMT122β : Mathematical Modelling I (30 lecture hrs + 15 tutorial hrs) -(Credit Value 2.5)**

Introduction: General Introduction to Modelling, concepts of system identification, Deterministic vs Stochastic, classification of models. Modelling via First Order Differential Equations: Modelling Through First Order and Simple Higher Order Differential Equations, Linear Differential Equations (LDEs), systems of Ordinary Differential Equations (ODEs). Analysis of Solutions: Existence and uniqueness of solutions, continuation of solutions, dependence on initial conditions and parameters, linear systems of equations with constant and variable coefficients, autonomous systems, phase space, and stability, Interpretation of solutions in modelling. Applications: Population ecology, chemical kinetics, traffic dynamics, Mechanics, Biology and Medicine, Pharmokinetics, Economics, Engineering, Special topics in modelling.

*Method of assessment: end of semester examination*