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.Differential Equations: first order ordinary differential equations – classification of differential equations – existence and uniqueness of solutions of initial value problem – higher order linear differential equations wi

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 bodyPlanetary motion:  central force motion of two bodies – relative coordinates – reduction to one dimensional problem – spherical symmetry and conservation of angular momentum, consequences – planetary motion an

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.Differential Calculus: functions of one variable – limits, continuity and derivatives – Taylor’s theorem – applications of derivatives – curvature and asymptotes – functions of two variables – limits and continuity – partial d

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.Adaptive control theory: System Identification – Frequency – Impulse – Step Response methods – Off-line – on line methods – Least square – Recursive least square – fixed memo

Classical scaling in CMOS, Moore’s Law, Clean room concept, Material properties, crystal structure, lattice, characterization of material based on band diagram and bonding, conductivity, resistivity, sheet resistance, phase diagram and solid solubility.Growth of single crystal Si, Wafer Cleaning and etching-Wet etch, Dry etch, Plasma etching, RIE etching, etch selectivity/selective etch, Lithography (Photolithography, EUV lithography, X-ray lithography, e-beam lithography etc.) Next generation technologies: Immersion lithography, Phase shift mask, ion lithography, SCALPEL.Thermal oxidation-Kin