Probability and statistics: Joint and conditional probabilities and densities. Moments, cumulants, generating functions, characteristic function. Binomial, Poisson, Gaussian d
Theorems of Picard, Casorati-Weierstrass and Riemann on Removable Singularities:Properties of the Image of an Analytic Function:Introduction to the Picard Theorems,Recalling S
Structure of present day electronic products - Analog signal conditioning and processing functions in instrumentation and control and communication - One-port networks for ana
Vectors and Elementary linear algebra - Linear vector space and matrices - Determinants, trace and special matrices - Linear first order differential equations - First and sec
Theorems of Rouche and Hurwitz:Fundamental Theorems Connected with Zeros of Analytic Functions - The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theore
Symmetry and Physical Properties of Crystals Point groups, Bravais lattices, Space groups, Neumann�s Principle and tensor properties of crystalline solids, elements of group
Introduction to digital system - Number Systems - Complement Numbers - Complement Subtraction and codes - Review of First Four Lectures and Introduction to logic Gates - Basic
Introduction to Indian Philosophy:Brief Discussion on Veda and Upanishads - Origin of Indian Philosophy;Charvaka Philosophy:Epistemology - Metaphysics;Samkhya Philosophy:Metap
Analytic functions of a complex variable:Complex numbers. Equations to curves in the plane in terms of z and z* - The Riemann sphere and stereographic projection. Analytic fu
Introduction - Compressibility of Fluids; Compressible and Incompressible Flows; Perfect Gas Equation of State; Calorically Perfect Gas - One Dimensional Flows � Basics Gove
Mechanics of a system of particles in vector form. Conservation of linear momentum, energy and angular momentum - Degrees of freedom, generalized coordinates and velocities. L
Governing Equations: Continuity, Momentum and Energy Equations and their derivations in different coordinate systems, Boundary layer Approximations to momentum and energy - La
Introduction and mathematical preliminaries:What is Pattern recognition; Applications and Examples - Clustering vs. Classification; Supervised vs. unsupervised - Relevant basi
Basics of magnetic circuits - Analysis of magnetic circuits with airgap and permanent magnets - Analysis of singly excited electromechanical system with linear magnetics - Non
Introduction to the course; Current and Voltage; Kirchhoff's Current and Voltage laws - Electrical circuit elements: Voltage and current sources; R, C, L, M - Elements in se
Introduction to chemical bonding and development of band gap - Introduction and types of semiconductors. Explanation of density of states, Fermi energy, and band occupancy - P
Thermodynamics and the Chemical Industry - James Prescot Joule and the first law - Sadi Carnot and the second law - Equilibrium and Extrema in work - Illustrative Calculation
Basics:Prologue � Introduction to the course - Science, Engineering and Technology of Materials;Microstructure:Atomic Bonding - Structure of Solids - Movement of Atoms - Dev
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