# Investing and non inverting amplifier theory of relativity

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Topics covered include Boolean algebra, digital logic gates, combinational logic circuits, decoders, encoders, multiplexers. Asynchronous and synchronous counters. Registers, flip-flops, adders, Sequential circuit analysis and design. Simple computer architecture. APE Electronic Devices and Circuits I 3 credits P-N junction as a circuit element: Intrinsic and extrinsic semiconductors, operational principle of p-n junction diode, contact potential, current-voltage characteristics of a diode, simplified dc and ac diode models, dynamic resistance and capacitance.

Diode circuits: Half wave and full wave rectifiers, rectifiers with filter capacitor, characteristics of a zener diode, zener shunt regulator, clamping and clipping circuits. Bipolar junction transistor BJT as a circuit element: Basic structure. Single stage BJT amplifier circuits and their configuarations: Voltage and current gain, input and output impedances.

Prerequisite APE APE Electronic Devices and Circuits II 3 credits Frequency response of amplifiers: Poles, zeros and Bode plots, amplifier transfer function, techniques of determining 3 dB frequencies of amplifier circuits, frequency response of single-stage and cascade amplifiers, frequency response of differential amplifiers. Operational amplifiers Op-Amp : Properties of ideal Op-Amps, non-inverting and inverting amplifiers, inverting integrators, differentiator, weighted summer and other applications of Op-Amp circuits, effects of finite open loop gain and bandwidth on circuit performance, logic signal operation of Op-Amp, dc imperfections.

General purpose Op-Amp: DC analysis, small-signal analysis of different stages, gain and frequency response of Op-Amp. Negative feedback: properties, basic topologies, feedback amplifiers with different topologies, stability, frequency compensation. Active filters: Different types of filters and specifications, transfer functions, realization of first and second order low, high and bandpass filters using Op-Amps. Mechanical, electrical and electronic types of instruments, absolute and secondary instruments, analog and digital instruments, analog voltmeters and ammeters, AC transformer types, Flux gate magnetometer type.

Accuracy and error of analog voltmeters and ammeters. Different types of Digital voltmeters, digital multimeters, Automation in multimeters. Oscilloscopes, signal generators. Absorption and detection of radiation, Nucleonic instruments.

Prerequisite APE APE Plasma Physics with Industrial Applications 3 credits General introduction to plasma physics, plasma as a fourth state of matter, definition, screening and Debye shielding, plasma frequency, ideal plasma, temperature and pressure of plasma, magnetic pressure and plasma drifts, plasma waves, Landau damping, collisions in plasmas, hydrodynamic description of plasma, one fluid model, two fluid model, Chew-Goldberg theory, low waves in maneto-hydrodynamics, description of plasma, dielectric tensor, longitudinal and transverse waves, plasma instabilities, transport in plasmas, plasma kinetic theory, Vlasov equation, linear waves, waves in magnetized plasma, electromagnetic waves, waves in hot plasmas, nonlinear waves, Landau damping, quasi linear theory, plasmas in fusion research, plasmas in industrial applications.

Position control system, simulation diagrams, signal flow graphs, parallel state diagrams from transfer function. General frequency transfer function relationships, drawing the Bode plot, system type and gain as related to log magnitude curve, Nyquist's criterion and applications. Microprocessor interface ICs. Advanced microprocessor concept of microprocessor based system design. Microcomputer systems, representation of numbers and characters, introduction to IBMPC assembly language.

Prerequisite APE APE Computer Organization and Architecture 3 credits A systematic study of the various elements in computer design, including circuit design, storage mechanisms, addressing schemes, and various approaches to parallelism and distributed logic. Information representation and transfer; instruction and data access methods; CPU structure and functions processor and register organization, instruction cycles and pipe linings, the control unit; memory organisation.

The course includes a compulsory 3 hour laboratory work each week. Prerequisite APE APE Radar Engineering 3 credits The course is oriented towards the understanding and design of radar systems. Non-renewable energy sources-fossil fuels, coal, natural gas, petroleum, etc.

Energy, sustainability and environment, EIA. BI0 Introduction to Biology 3 credits An introduction to the cellular aspects of modern biology including the chemical basis of life, cell theory, energetics, genetics, development, physiology, behaviour, homeostasis and diversity, and evolution and ecology.

This course will explain the development of cell structure and function as a consequence of evolutionary process, and stress the dynamic property of living systems. CHE Introduction to Chemistry 3 credits The course is designed to give an understanding of basics in chemistry. Topics include nature of atoms and molecules; valence and periodic tables, chemical bonds, aliphatic and aromatic hydrocarbons, optical isomerism, chemical reactions.

MAT Basic Course in Mathematics No credit Topics including sets, relations and functions, real and complex numbers system, exponents and radicals, algebraic expressions; quadratic and cubic equations, systems of linear equations, matrices and determinants with simple applications; binomial theorem, sequences, summation of series arithmetic and geometric , permutations and combinations, elementary trigonometry; trigonometric, exponential and logarithmic functions; co-ordinate geometry; statics-composition and resolution of forces, equilibrium of concurrent forces; dynamics-speed and velocity, acceleration, equations of motion.

No credit. MAT Fundamentals of Mathematics 3 credits The real number system, exponents, polynomial, factoring, rational expression, radicals, complex number, linear equation, quadratic equation, variation, inequalities, coordinate system, functions, equations of line, equation of circle, exponential and logarithmic function, system of equations, system of inequalities properties of matrix, matrix solution of linear system, determinant, Cramer's rule, limit, rate of change, derivative.

Linear Equations, Solution, graphs and applications. Variation, Linear inequalities. Exponential and Logarithmic Functions, Exponential growth and decay, Ratios, proportions, percent, application of simple and compound interest. Population, Sample, Variable, Raw data, Frequency distribution table, Graphical presentation, Measures of central tendency and measures of dispersion. MAT Mathematics 2 credits Calculus, definition of limit, continuity and differentiability, successive and partial differentiation, maxima and minima.

Integration by parts, standard integrals, definite integrals. Solid geometry, system of coordinates. Distance between two points. Coordinate Transformation, Straight lines sphere and ellipsoid. Indeterminate forms. Partial differentiation. Tangent and normal. Subtangent and subnormal. Pair of straight lines. General equation of second degree. System of circles. Conics section. Set of Natural numbers, Integers, Rational numbers, Irrational numbers and Real numbers alongwith their geometrical representation, Idea of Open and Closed interval,.

Idea of absolute value of real number, Variables and Constants, Product of two sets: Idea of product of sets, Product set of real numbers and their geometric representation, Axioms of real number system and their application in solving algebraic equations. Equation and Inequality, Laws of inequality, Solution of equations and inequalities.

Variable and Functions: Variable of a set, Functions of single variable, Polynomial, Graph of Polynomial functions in single variable. Exponential, Logarithmic, Trigonometric functions and their graphs, Permutation and Combination. Binomial theorem. Integration by the method of substitution. Integration by parts.

Standard integrals. Integration by method of successive reduction. Definite integrals, its properties and use in summing series. Walli's formula. Improper integrals. Beta function and Gamma function. Area under a plane curve in Cartesian and polar coordinates. Area of the region enclosed by two curves in Cartesian and polar coordinates.

Trapezoidal rule. Simpson's rule. Arc lengths of curves in Cartesian and polar coordinates, parametric and pedal equations. Intrinsic equations. Volumes of solids of revolution. Volume of hollow solids of revolutions by shell method. Area of surface of revolution. Ordinary Differential Equations: Degree of order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solutions of general linear equations of second and higher order with constant coefficients.

Solution of homogeneous linear equations. Solution of differential equations of the higher order when the dependent and independent variables are absent. Solution of differential equations by the method based on the factorisation of the operators. The concept of sets: Sets and subsets, Set operations, Family of Sets. Relations and functions: Cartesian product of two sets, Relations, Order relation, Equivalence relations, Functions, Images and inverse images of sets, Injective, surjective, and bijective functions, Inverse functions.

Real number system: Field and order properties, Natural numbers, integers and rational numbers. Absolute value, Basic inequalities. Including inequalities of means, powers, Weierstrass, Cauchy Complex number system: Field of complex numbers, De Moivre's theorem and its applications.

Elementary number theory: Divisibility, Fundamental theorem of arithmetic, Congruence. Summation of finite series: Arithmetic-geometric series, Method of difference, Successive differences, Use of mathematical induction. Theory of equations: Synthetic division, Number of roots of polynomial equations, Relations between roots and coefficients, Multiplicity of roots, Symmetric functions of roots, Transformation of equations.

Reduction of second degree equations to standard forms, Pairs of straight lines, Circles, Identification of conics, Equations of conics in polar Coordinates. Three dimensional geometry Coordinates in three dimensions, Direction cosines, and Direction ratios.

Planes, straight lines, shortest distance, sphere, orthogonal projection and conicoids. Vector geometry Vectors in plane and space, Algebra of vectors, scalar and vector products, Triple scalar products, its applications to Geometry. MAT Calculus I 3 credits Differential Calculus: Real number system and its geometrical representation, real variable, function of single real variable, parametric equations, limit, continuity and differentiability, derivatives of different types of functions, geometrical significance of derivative, Rolle's Theorem, Mean Value Theorem, Taylor's Theorem; maxima, minima, point of inflexion, concavity and convexity, sketching of curves using concepts of calculus; Indeterminate Form, L'Hospital Rule, Successive Differentiation, Leibnitz's Theorem, tangent, normal and related formulas, curvature.

Integral Calculus: Indefinite integrals of different types of functions, various methods of integrations, definite integrals, Fundamental Theorems of Definite Integrals, properties of definite integrals, Reduction formulas, Arc Length, Area under the curves, Surface area and Volume of a 3-D objects. Improper Integrals and applications. Linear Algebra: System of linear equations, vector space; 2D- space, 3D- space, Euclidean nD- space, sub space, linear dependence, basis and dimension, row space, column space, rank and nullity, linear transformation, eigen value and eigen vector, matrix diagonalization and similarity, application of linear algebra.

Ordinary Differential Equations: Introduction to differential equations, first-order differential equations and applications, higher order differential equations and applications, series solutions of linear equations, systems of linear first-order differential equations.

Cauchy's integral theorem, Cauchy's integral formula, Liouville's theorem, Taylor's and Laurent's theorem, singular points, residue, Cauchy's residue theorem, evaluation of residues, contour integration and conformal mapping. Fourier analysis: Real and complex form, finite Fourier transform, Fourier integrals, Fourier transforms and their use in solving boundary value problems. Prerequisite MAT MAT Calculus II 3 credits Functions of several variables, concept of surface, sketching of , contour sketch for surface, limit and continuity, partial derivative and its geometrical significance, chain rule of partial differentiation, concept of gradient, divergence and curl, directional derivative and tangent plane, concept of differential and perfect differential, linear approximation and increment estimation, maxima, minima and saddle point, Lagrange multiplier, higher order derivatives, Taylor's theorem of function of several variables.

Multiple integrals: Double integrals, Double integrals in Polar coordinates, Triple integrals, Triple integrals in Cylindrical and Spherical coordinates, Change of variables in Multiple integrals, Jacobian, Line integrals, Green's theorem, Surface integrals, Applications of Surface integrals, Divergence theorem, Stoke's theorem.

Prerequisite: MAT MAT Linear Algebra 3 credits Introduction to matrix, different types of matrices, equivalent matrices, determinants, properties of determinants, minors, cofactors, evaluation of determinants, adjoint matrix, inverse matrix, method for finding inverse matrix, elementary row operations and echelon form of matrix, system of linear equations homogeneous and non-homogeneous equations and their solutions; Vector, vector spaces and subspaces, linear independence and dependence, basis and dimension, change of bases, rank and nullity, linear transformation, kernel and images of a linear transformation and their properties, eigenvalues and eigenvectors, diagonalization, Cayley Hamilton theorem, MAT MATH III Complex Variables and Laplace Transformations 3 credits Complex Variables: Complex number systems.

General functions of a complex variable. Limits and continuity of a function of complex variables and related theorems. Complex differentiation and Couchy-Riemann equations. Mapping by elementary functions. Line integral of a complex function. Cauchy's integral theorem. Cauchy's integral formula. Liouville's theorem.

Taylor's and Laurent's theorem. Singular points. Cauchy's residue theorem. Evaluation of residues. Contour integration. And conformal mapping Laplace Transforms: Definition. Laplace transforms of some elementary functions. Sufficient conditions for existence of Laplace transforms. Inverse Laplace transforms. Laplace transforms of derivatives.

The unit step function. Periodic function. Some special theorems on Laplace transforms. Solutions of differential equations by Laplace transformations. Evaluation of improper integrals. Fourier Analysis: Real and complex form. Finite transform. Fourier integral. Fourier transforms and their uses in solving boundary value problems. Multiple integrals; surface and volume integrals, divergence and Stoke's theorem.

Sequences of Real Numbers: Infinite sequence, Convergent sequences, Monotone sequences, subsequences, Cauchy sequence, Cauchy criteria for convergence of sequences. Infinite Series: Concept of sum and convergence, series of positive terms, alternating series, absolute and conditional convergence, test for convergence, Convergence of sequences and series of functions.

Integration: Necessary and sufficient conditions for integrability, Darboux Sums and Riemann Sums, Improper integral and their tests for convergence. Inhomogeneous linear difference equations variation of parameters, reduction of order, Series solutions of second order linear equations: Taylor series solutions about an ordinary point.

Frobenious series solutions about regular singular points. Series solutions of Legendre, Bessel, Laguerre and Hermite equations. Systems of linear first order differential equations: Elimination method. Matrix method for homogeneous linear systems with constant coefficients. Variation of parameters. Matrix exponential. Interpolation: Interpolating polynomials for equispaced and nonequispaced nodes, Lagrange's polynomial, Newton-Gregory's Interpolating polynomials, curve fitting with Least Square method, Iterated interpolation, Extrapolation.

Groups and subgroups, Cyclic groups, Symmetric groups. Integral Domain, Field of fractions. Prime Fields, characteristic of Fields. Part A: Theory Solutions of linear system of equations: Gaussian Elimination method with pivoting, Matrix inversion, Direct factorization of matrices, Iterative Techniques for solving linear system of equations: Jacobi's and Gauss-Seidel Method.

Solution of tridiagonal system, Eigen values and Eigen vectors Power Method. Numerical solution of Nonlinear system: Fixed point for functions of several variables, Newton's method, Quasi-Newton's method. Boundary Value problem involving elliptic, parabolic and hyperbolic equations, explicit and implicit Finite Difference method. There will be at least 15 lab assignments.

Prerequisite: MAT MAT Differential Geometry 3 credits Curves in space: Vector functions of one variable, space curves, unit tangent to a space curve, equation of a tangent line to a curve, Osculating plane or plane of curvature , vector function of two variables, tangent and normal plane for the surface , Principal normal, binormal and fundamental planes, curvature and torsion, Serret Frenet's formulae, theorems on curvature and torsion, Helices and its properties, Circular helix.

Spherical indicatrik, Curvature and torsion. Curvature and torsion for spherical indicatrices. Involute and Evolute of a given curve, Bertrand curves. Surface: Curvilinear coordinates, parametric curves, Metric first fundamental form , geometrical interpretation of metric, relation between coefficients E, F, G. Derivatives of surface normal M Weingarten equations , Third fundamental form, Principal sections, Principal sections, direction and curvature, first curvature, mean curvature, Gaussian curvature, normal curvature, lines of curvature, centre of curvature, Rodrigues's formula, condition for parametric curves to be line of curvature, Euler's Theorem, Elliptic, hyperbolic and parabolic points, Dupin Indicatrix.

MAT Complex Analysis 3 credits Introduction to complex numbers and their properties, complex functions, limits and continuity of complex functions, Analytic functions, Cauchy Riemann equations, harmonic functions, Rational functions, Exponential functions, Trigonometric functions, Logarithmic functions, Hyperbolic functions.

Contour integration: Cauchy's Theorem, Simply and Multiply connected domain, Cauchy integral formula, Morera's theorem, Liouville's theorem. Convergent series of analytic functions, Laurent and Taylor series, Zeroes , Singularities and Poles, residues, Cauchy's Residue theorem and its applications, Conformal Mapping.

Prerequisite: MAT MAT History of Mathematics 3 credits A Survey of the development of mathematics beginning with the history of numeration and continuing through the development of the calculus. The study of selected topics from each field is extended to the 20th century. Biographical and historical aspects will be reinforced with studies of procedures and techniques of earlier mathematical cultures. MAT Operations Research I 3 credits Convex sets and related theorems, Introduction to linear programming, Formulation of linear programming problems, Graphical solutions, Simplex method, Duality of linear programming and related theorems, Sensitivity.

Unconstrained optimization: Newton's method, Trust region algorithms, Least Squares and zero finding. Linear programming: Simplex method, primal dual interior point methods. Connected set: Compact sets, locally compact sets and related theorems, connected sets, locally connected sets, continuity and compactness. Sequence in metric space: Convergent and Cauchy sequence, Completeness, Banach Fixed Point theorem with applications, sequence and series of functions, pointwise and uniform convergence, differentiation and integration of series.

Continuous function on metric space: Boundedness, Intermediate Value Theorem, uniform continuity. Dependence of solutions on initial conditions and equation parameters. Existence and uniqueness theorems for systems of equations and higher order equations. Eigen value problems and Strum-Liouville boundary value problems: Regular Strum-Liouville boundary value problems. Solution by eigenfunction expansion.

Green's functions. Singular Strum-Liouville boundary value problems. Oscillation and comparison theory. Nonlinear differential equations: Phase plane, paths and critical points. Critical points and paths of linear systems. PDE: First order equations: complete integral, General solution.

Cauchy problems. Method of characteristics for linear and quasilinear equations. Charpit's method for finding complete integrals. Methods for finding general solutions. Second order equations: Classifications, Reduction to canonical forms. Boundary value problems related to linear equations. Applications of Fourier methods Coordinates systems and separability. Homogeneous equations. Boundary value problems involving special functions.

Transformation methods for boundary value problems, Applications of the Laplace transform. Application of Fourier sine and cosine transforms. Roger, A. Recommended References 2. Section B Application of Laplace transformation to linear circuits, Impulse function, convolution integral and its application, superposition integral; Z-Transformation and its application; Introduction to topological concepts in electrical and magnetic circuit networks Recommended References 1.

Transpose of matrices and inverse of matrix and Rank of matrices. Harmonic: Solution of Laplace equation, Cylindrical harmonics, spheriacal harmonics. Section B Complex Variable: Complex number system, General functions of a complex variable; Limits and continuity of a function of complex variable and related theorems; Complex differentiation and the Cauchy-Riemann equations.

Section B Product costing-cost sheet under job costing; Operating costing and process costing system; Marginal cost analysis-cost-volume-profit relationship; Relevant costs and special decial decisions; Accounting for planning and control-capital budgeting; Master budgets, flexible budgets and variance analysis.

ECE Control Theory 3 hrs per week 3. ECE Analog Communication 3 hrs per week 3. CSE Microprocessors 3 hrs per week 3. Gaonkar, Microprocessors and System Design 3. Barry b. BA Industrial Management and Law 3 hrs per week 3. Koontz and H. Stevenson W. Nath and Co.

ECE Digital Communication 3 hrs per week 3. Synchronization of PAM. PTM: Method of generation and demodulation of pulse duration modulated and pulse position modulated signals. Cross talk in PTM systems. Taub and Schilling. Recommended References 4. Rectangular, Cylindrical and spherical co-ordinates, Solutions to static field problems. Rectangular, Cylindrical and spherical harmonics with applications. Retarded potentials. Relation between circuit theory and field theory: Circuit concepts and the derivation from the field equations.

High frequency circuit concepts, Circuit radiation resistance. Skin effect and circuit impedance. Concept of good and perfect conductors and dielectrics. Current distribution in various types of conductors, Depth of penetration, Internal impedance, Power loss, Calculation of inductance and capacitance.

Transmission line analogy, Reflection from conducting and conducting dielectric boundary. Display lines ion in dielectrics, Liquids and solids, Plane wave propagation through the ionosphere. Introduction to radiation. William H. The telephone system, multiplexiers, Concentrators and front-end processors, Circuit switching, Packet switching, Computer to terminal handling.

Section B Capacity assignment for terminal networks and distributed networks, Concentration and buffering for finite and infinite buffers, Dynamic buffers and blocked storage. Section B Proximity, Closest pair problem, Intersections, Voronoi and Delaunay diagrams, arrangements of lines and points, Geometry of rectangles, hidden surface removal, polygon triangulation, art gallery theorems, shortest paths, and lower-bounds.

Shamos, Computational Geometry 2. Robert Sedgewick, Algorithms 3. The Project and thesis topic selected in this course is to be continued in the ECE course, but students must pass individually in both courses. ECE Industrial Electronics 3 hrs per week 3. Solid state motor speed controllers: single transistor speed control, Op-amp and Darlington pair amplifier speed control.

DC-DC chopper control: basic Jones chopper circuit. Stepper motors: stepper motor drive circuit using transistors. Speed control of AC motors: variable frequency converter block diagram, simplified single phase cycloconverter, Single phase inverter, three phase six step inverter, Voltage multipliers, Magnetic amplifiers, Resistance welder controls, Induction heating, Di- electric heating. Douglas A. ECE Microwave Engineering 3 hrs per week 3.

David M. Section B Modern transmission systems; Signaling techniques; Network traffic load and parameters; Grade of service and blocking probability; Modeling switching systems; Incoming traffic and service time characterization; Blocking model and loss estimates; Delay systems; Integrated services digital network ISDN ; Electronic mail; Videotext.

Viswanathan, Telecommunication switching systems and network, Prentice-Hall, Flow graph and matrix representation of digital filters.

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