Introduction to linear vector spaces, bases and dimension, inner product, orthogonality, Fourier series,orthogonal polynomials, Cauchy Schwartz inequality, eigenvalues, eigenvectors, Hermitian operators,unitary operators, discrete Fourier transform.

Quantum Theory of Atomic Energy Levels – Radiative and Nonradiative decay of excited state atoms –Emission Broadening and linewidth – Radiation and Thermal equilibrium – Conditions for laser action –Laser Oscillation above threshold - Laser Amplifiers – Requirements for obtaining population inversion –Rate Equations for three and four level systems – Laser pumping requirements – Laser Cavity modes –Stable resonators – Gaussian beams– Special Laser Cavities – Q-switching and Mode locking –Generation of ultra fast Optical pulses– Pulse compression.

Optical materials: Glasses, IR materials, Optical, mechanical and thermal properties of optical materials,Fabrication of lenses, mirrors and flats: spherical curve generation, polishing and figuring of “Curved Surfaces” of glass materials, Aspheric surface polishing/figuring, Polishing and figuring of IR materials:Ge, ZnSe and Zns, Advanced computer controlled polishing: Techniques, MRF polishing, Ion polishing,Micro-optics fabrication techniques, Large Mirrors fabrication techniques.

Introduction to Kinematic Mount Design (Basics).

Optical and Mechanical Materials: Material properties, Need for mechanical mounts. Stress Transfer Mechanism: Mechanical Design for minimum stress transfer. Design of Mechanical Mounts for Lenses and Mirrors: Gimbal Mount, Closed form solutions. Different categories of Mechanical Mounts, Fine Mechanics design, Linear and nonlinear movements; CAMS.

Ray optics, Postulates of ray optics, Simple optical components, Matrix optics, The Ray-transfer matrix and Gaussian ray Optics, Wave and Electromagnetic optics, Elementary waves, Paraxial approximation, Effects of simple optical components on optical waves, Specular and diffuse reflection, refraction, transmission, absorption and scattering.

Basic stability and device stabilization techniques (BJT). Small signal low & high frequency models for

(BJT, FET, MOSFET), Large signal amplifiers, Differential Amplifier, Instrumental amplifiers, Integrated

circuits, Tuned amplifiers, Feedback amplifiers, Oscillators, Multivibrators, Wave shaping circuits, Filter

design.

Basic stability and device stabilization techniques (BJT). Small signal low & high frequency models for

(BJT, FET, MOSFET). Large signal amplifiers - Multistage amplifiers - Differential amplifier - Tuned

• Liquid lens

• Diffraction –single slit and circular aperture

• Michelson interferometer

• Faraday optic effect

• Beam profile of a laser diode

• Fabry-Perot etalon

• Rayleigh scattering

• Diffraction – wavelength of a He-Ne laser

• Birefringence

Module 1: Exploring the subject matter of Economics

What is Economics? Definitions – Importance of Economics for Engineers – Schools of thought The Economic Problem – Scarcity and Choice – Resource allocation – the question of What to produce, How to Produce and How to Distribute Output – its nature and Importance in developing countries – Economic Systems – Basics of Capitalism, Socialism, Mixed Economy, Market Economy and Third World Economies. Is Economics a Science? Distinction between Micro and Macro Economics.

Sketching functions, Gaussian integrals, Stirling's formula, Generalised functions: Step function, Dirac delta function, properties of delta function,

Vectors and Tensors: Cartesian tensors, covariant and contravariant components of a vector, covariant and contravariant tensor, mixed tensor, metric tensor, contraction, rotations and index notation, Isotropic tensors: Kronecker delta, Levi-Civita symbol, Gram determinant. Rotations in three dimensions, Proper and improper rotations, scalars and pseudoscalars; polar and axial vectors.