Introduction – Formulation of optimization problems – Linear programming – duality - Non- linear programming – unconstrained optimization: optimality conditions, range elimination methods, gradient method, quasi-newton method, conjugate gradient method – Constrained optimization: Lagrange multiplier theorem, Kuhn Tucker condition, penalty function methods, projected gradient methods, Quadratic programming, sequential quadratic programming – Non-traditional optimization techniques for single and multi-objective optimization – Applications in Engineering.

Machine learning basics: capacity, overfitting and under fitting, hyper parameters and validation sets, bias & variance; PAC model; Rademacher complexity; growth function; VC- dimension; fundamental concepts of artificial neural networks; single layer perceptron classifier; multi-layer feed forward networks; single layer feed-back networks; associative memories; introductory concepts of reinforcement learning, Markhov decision process.

Introduction – approximate solutions to governing differential equations (GDE) – finite element formulations starting from GDE – finite element formulations based on stationarity of a functional – one-dimensional finite element analysis; shape functions, types of elements and applications – two and three-dimensional finite elements – numerical integration – applications to structural mechanics and fluid flow.

Review of basic equations of elasticity – state of stress at a point – analysis of strain, constitutive relations – generalized Hook’s law – formulation of boundary value problems – solution of 2D problems – energy methods in elasticity – bending, shear and torsion – thin walled beams – applications.

Analysis of LTI system: Phase and Magnitude response of the system, Minimum phase, maximum phase, Allpass. MultiMate Signal Processing: Interpolation, Decimation, sampling rate conversion, Filter bank design, Poly phase structures. Time-frequency representation; frequency scale and resolution; uncertainty principle, short-time Fourier transform. Multi-resolution concept and analysis, Wavelet transform (CWT, DWT). Optimum Linear Filters: Innovations Representation of a Stationary Random Process, Forward and Backward linear prediction, Solution of the Normal Equations.

Wireless Communications and Diversity: Introduction to Wireless Channel and Fading - Rayleigh/Rician Fading, Broadband Wireless Channel Modeling: Introduction to LTV Systems, Channel Delay Spread, Coherence Bandwidth, BER Comparison of Wired and Wireless Communication Systems. Introduction to Diversity, Multi-antenna Maximal Ratio Combiner, BER with Diversity, Spatial Diversity and Diversity Order. ISI and Doppler in Wireless Communications, Doppler Spectrum and Jakes Model. Spread spectrum: PN Sequences, DSSS with BPSK, Signal space dimensionality and processing gain, Frequency-Hop SS.

Motivating examples of digital communications. Spectrum availability and channels. Channel modeling base band and pass band channels. Digital modulation schemes for base band and pass band channels. Line coding, Pulse amplitude modulation, Phase modulation, CPFSK, Frequency shift keying, QAM.

Nature of Radar and Applications, Simple form of Radar Equation, Radar Block Diagram and Operation, Prediction of Range Performance, Minimum Detectable Signal, Radar Receivers, Transmitter Power, CW and Frequency Modulated Radar, MTI and Pulse Doppler Radar, Tracking Radar, Detection of Radar Signals in Noise, Airborne Radar, Space borne Radar, Synthesis aperture radar, SHAR and MST radar.

Optical properties of semiconductor materials -Optical absorption and emission-Diode lasers-edge emitting, vertical cavity surface emitting lasers, direct modulation-frequency chirping-steady state characteristics-noise. Dielectric waveguides, perturbation and coupled mode theory, Photonic crystals, metamaterials, plasmonics, Integrated optics and photonic integrated circuits. Optical modulators-Electrooptic, Electro absorption, Photodetectors. Optical delay lines, Optical based true time delays. Optoelectronic integrated circuits, Silicon photonics.