Mathematical Introduction: Linear vector spaces, inner products, linear operators, eigenvalue problem, generalization to infinite dimensions.

Towards quantum mechanics: relevant experiments, wave particle duality, uncertainty principle, postulates of quantum mechanics, Schrodinger equation, probability current and conservation.

Simple one-dimensional potential problems: Free particle, particle in a box; scattering in step-potentials, transmission and reflection coefficients.

Brief survey of the Newtonian mechanics of a particle and systems of particles; Constraints , generalised coordinates, D'Alembert's principle and Lagrange's equation, velocity dependent potential and dissipation function.

Variational principles and Lagrange's equations, Lagrange multipliers,conservation theorems and symmetry properties.

Central force motion, Kepler's laws,orbital dynamics, stability of circular orbits, precession of equinoxes and of satellite orbits.

Rigid body motion, Euler angles, inertia tensor and moment of inertia.

Electricity: curvilinear coordinates– conservative vector fields and their potential functions Gauss’ theorem, Stokes’ theorem – physical applications in electrostatics – electrostatic potential and field due to discrete and continuous charge distributions – dipole and quadrupole moments– energy density in an electric field– dielectric polarization – conductors and capacitors– electric displacement vector – dielectric susceptibility.

Vector Calculus: scalar and vector fields – level surfaces – directional derivatives, gradient, curl, divergence

–  Laplacian – line and surface integrals – theorems of Green, Gauss, and Stokes.

Sequences and Series of Functions: complex sequences – sequences of functions – uniform convergence of series – test for convergence – uniform convergence for series of functions.

Introduction to vectors: linear independence – completeness – basis – dimensionality – inner product – orthogonality – displacement – derivatives of a vector – velocity – acceleration – plane polar coordinates.

Angular momentum: angular momentum and torque on a single particle – angular momentum and torque on a system of particles – moment of inertia – angular momentum of a rigid body

Sequence and Series of Real Numbers: sequence – convergence – limit of sequence – non-decreasing sequence theorem – sandwich theorem (applications) – L'Hopital's rule – infinite series – convergence – geometric series – tests of convergence (nth term test, integral test, comparison test, ratio and root test) – alternating series and conditional convergence – power series.

Review of Embedded Hardware: Gates - Timing Diagram - Memory – microprocessors. Interrupts Microprocessor Architecture - Interrupt Basics - Shared Data Problem - Interrupt latency. Software Development: Round-Robin, Round robin with Interrupts, function-Queue- Scheduling Architecture, Algorithms. Introduction to - Assembler - Compiler - Cross Compilers and Integrated Development Environment (IDE). Object-Oriented Interfacing, Recursion, Debugging strategies, Simulators. Embedded Microcomputer Systems - Motorola MC68H11: Motorola MC68H11 Family Architecture, Interfacing methods.

State space Approach: State space modeling of physical systems – diagonal and Jordan canonical forms – Solution of Linear Time Invariant (LTI) state equation – Cayley Hamilton theorem – Controllability and Observability Tests – Kalman decomposition technique – Controller design by state feedback – Full order/reduced order observer design – observer-based state feedback control – stability definitions in state space domain.