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Module-2 Numerical Methods: Numerical solution of second order ordinary differential equations, Runge-Kutta method and Milnes method. Special Functions: Series solution-Frobenious method. Series solution of Bessels differential equation leading to Jn x -Bessels function of first kind.

Basic properties and orthogonality. Series solution of Legendres differential equation leading to Pn x -Legendre polynomials.

Rodrigues formula, problems. Module-3 Complex Variables: Review of a function of a complex variable, limits, continuity, differentiability. Analytic functions-Cauchy-Riemann equations in cartesian and polar forms. Properties and construction of analytic functions.

Complex line integrals-Cauchys theorem and Cauchys integral formula, Residue, poles, Cauchys Residue theorem without proof and problems. Transformations: Conformal transformations, discussion of. Binomial distribution, Poisson distribution. Exponential and normal distributions, problems.

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation, covariance, correlation coefficient. Module-5 Sampling Theory: Sampling, Sampling distributions, standard error, test of hypothesis for means and proportions, confidence limits for means, students t-distribution, Chi-square distribution as a test of goodness of fit.

Stochastic process: Stochastic processes, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probability-simple problems. Solve first and second order ordinary differential equations arising in flow problems using single step and multistep numerical methods. Understand the analyticity, potential fields, residues and poles of complex potentials in field theory and electromagnetic theory.

Describe conformal and bilinear transformation arising in aerofoil theory, fluid flow visualization and image processing. Solve problems of quantum mechanics, hydrodynamics and heat conduction by employing Bessels function relating to cylindrical polar coordinate systems and Legendres polynomials relating to spherical polar coordinate systems.

Solve problems on probability distributions relating to digital signal processing, information theory and optimization concepts of stability of design and structural engineering. Draw the validity of the hypothesis proposed for the given sampling distribution in accepting or rejecting the hypothesis. Determine joint probability distributions and stochastic matrix connected with the multivariable correlation problems for feasible random events.

Define transition probability matrix of a Markov chain and solve problems related to discrete parameter random process. Each full Question consisting of 16 marks There will be 2 full questions with a maximum of four sub questions. Publishers,7th Ed. Rajnish Verma: "Higher Engineering Mathematics",. Solve second and higher order differential equations. Understand Laplace and inverse Laplace transforms and elementary probability.

Module-1 Linear Algebra: Introduction - rank of matrix by elementary row operations - Echelon form. Consistency of system of linear equations - Gauss elimination method. Eigen values and Eigen vectors of a square matrix.

Application of Cayley-Hamilton theorem without proof to compute the inverse of a matrix-Examples. Module-2 Higher order ODEs: Linear differential equations of second and higher order equations with constant coefficients. Inverse differential operators. Solutions of initial value problems. Method of undetermined coefficients and variation of parameters.

Module-3 Laplace transforms: Laplace transforms of elementary functions. Transforms of derivatives and integrals, transforms of periodic function and unit step function-Problems only.

Inverse Laplace transforms: Definition of inverse Laplace transforms. Evaluation of Inverse transforms by standard methods. Application to solutions of Linear differential equations and simultaneous differential equations. Module-5 Probability: Introduction. Sample space and events. Axioms of probability. Addition and multiplication theorems. Conditional probability illustrative examples. Bayess theorem-examples. Recall basic concepts of elementary probability theory and, solve problems related to the decision theory, synthesis and optimization of digital circuits.

Each full Question consisting of 16 marks. Addressing modes, Machine language instruction formats, Machine coding the program 2. Module -2 Logical Instructions, String manipulation instructions, Flag manipulation and Processor control instructions, Illustration of these instructions with example programs. Other Architectures: Architecture of refer 1. Each full Question consisting of 16 marks There will be 2 full questions with a maximum of Three sub questions from.

Ray and K. Understand the basic features, configurations and application of control systems. Understand various terminologies and definitions for the control systems. Learn how to find a mathematical model of electrical, mechanical and electro-. Know how to find time response from the transfer function. Find the transfer function via Masons rule. Analyze the stability of a system from the transfer function.

Block diagrams and signal flow graphs: Transfer functions, Block diagram algebra and Signal Flow graphs. Time response specifications, Time response specifications of second order systems, steady state errors and error constants. Module -3 Stability analysis: Concepts of stability, Necessary conditions for Stability, Routh stability criterion, Relative stability analysis: more on the Routh stability criterion, Introduction to Root-Locus Techniques, The root locus concepts, Construction of root loci.

Frequency domain analysis and stability: Correlation between time and frequency response, Bode Plots, Experimental determination of transfer function. Introduction to Polar Plots, Inverse Polar Plots excluded Mathematical preliminaries, Nyquist Stability criterion, Systems with transportation lag excluded Introduction to lead, lag and lead-lag compensating networks excluding design.

Develop the mathematical model of mechanical and electrical systems Develop transfer function for a given control system using block diagram. Determine the stability of a system in the frequency domain using Nyquist and. Build basics for understanding of courses such as signal processing, control. Introduction and Classification of signals: Definition of signal and systems, communication and control systems as examples.

Sampling of analog signals, Continuous time and discrete time signal, Classification of signals as even, odd, periodic and non-periodic, deterministic and non-deterministic, energy and power. Operations on signals: Amplitude scaling, addition, multiplication, differentiation, integration Accumulator for DT , time scaling, time shifting and time folding. Systems: Definition, Classification: linear and non-linear, time variant and invariant, causal and non- causal, static and dynamic, stable and unstable, invertible.

Module -2 Time domain representation of LTI System: System modeling: Input-output relation, definition of impulse response, convolution sum, convolution integral, computation of convolution integral and convolution sum using graphical method for unit step to unit step, unit step to exponential, exponential to exponential, unit step to rectangular and rectangular to rectangular only.

Properties of convolution. System interconnection, system properties in terms of impulse response, step response in terms of impulse response 4 Hours. Impulse sampling and reconstruction: Sampling theorem only statement and reconstruction of signals 2 Hours.

Determine the linearity, causality, time-invariance and stability properties of continuous and discrete time systems. Compute the response of a Continuous and Discrete LTI system using convolution integral and convolution sum. Determine the spectral characteristics of continuous and discrete time signal using Fourier analysis. The question paper will have ten questions. Learn the concepts of random process and various types of noise. Evaluate the performance of the communication system in presence of noise.

Chapter 3 of Text. The Superheterodyne Receiver refer Chapter 4 of Text. Characterize analog signals in time domain as random processes and in frequency domain using Fourier transforms. Characterize the influence of channel on analog modulated signals Determine the performance of analog communication systems.

Understand the characteristics of pulse amplitude modulation, pulse position modulation and pulse code modulation systems. Ltd, , ISBN 81 7.

Lathi, Oxford University Press. Discuss the effects of Input and Output voltage ranges upon Op-Amp circuits. Impedances and other performance parameters. Sketch and Explain typical Frequency Response graphs for each of the Filter circuits.

Describe and Sketch the various switching circuits of Op-Amps and analyze its. Module -2 Op-Amps as AC Amplifiers: Capacitor coupled voltage follower, High input impedance Capacitor coupled voltage follower, Capacitor coupled non inverting amplifiers, High input impedance Capacitor coupled Non inverting amplifiers, Capacitor coupled inverting amplifiers, setting the upper cut-off frequency, Capacitor coupled difference amplifier.

OP-Amp Applications: Voltage sources, current sources and current sinks, current amplifiers, instrumentation amplifier, precision rectifiers.

Text 1 Log and antilog amplifiers, Multiplier and divider. Other IC Application: timer, Basic timer circuit, timer used as astable and monostable multivibrator. Impedances and Slew Rate.

Instrumentation and Precision Amplifiers. Test circuits of Op-Amp based linear and non-linear circuits comprising of. Linear Integrated Circuits, D. Roy Choudhury and Shail B. Course objectives: This course will enable students to: Get familiarize with instructions and DOS 21H interrupts and function.

Develop and test assembly language programs to use instructions of Get familiarize with interfacing of various peripheral devices with Data transfer instructions like: i Byte and word data transfer in different addressing Modes ii Block move with and without overlap iii Block interchange. Programs involving:. Bit manipulation instructions like checking: i Whether given data is positive or negative ii Whether given data is odd or even iii Logical 1s and 0s in a given data iv 2 out 5 code v Bit wise and nibble wise palindrome 4.

String manipulation like string transfer, string reversing, searching for a string. Programs involving. Interfacing Experiments:. Matrix keyboard interfacing 2. Seven segment display interface 3.

Logical controller interface 4. Stepper motor interface 5. Write and execute assembly level programs to perform data transfer, arithmetic and logical operations. Write and execute assembly level programs to sort and search elements in a.

Perform string transfer, string reversing, searching a character in a string with string. Utilize procedures and macros in programming Demonstrate the interfacing of with 7 segment display, matrix keyboard, logical.

Conduct of Practical Examination: All laboratory experiments are to be included for practical examination. For examination, one question from software and one question from hardware. Change of experiment is allowed only once and Marks allotted to the procedure. Course objectives: This laboratory course enables students to: Design, Demonstrate and Analyze instrumentation amplifier, filters, DAC, adder,.

Design 4 bit R 2R Op-Amp Digital to Analog Converter i using 4 bit binary input from toggle switches and ii by generating digital inputs using mod counter. Understand basic skills of Management Understand the need for Entrepreneurs and their skills Understand Project identification and Selection.

Identify the Management functions and Social responsibilities Distinguish between management and administration. Entrepreneurship: Definition of Entrepreneur, Importance of Entrepreneurship, concepts of Entrepreneurship, Characteristics of successful Entrepreneur, Classification of Entrepreneurs, Myths of Entrepreneurship, Entrepreneurial Development models, Entrepreneurial development cycle, Problems faced by Entrepreneurs and capacity building for Entrepreneurship Selected topics from Chapter 2, Text 2.

Module-5 Projects Management: AProject. Match case Limit results 1 per page. E …vtu. Author hacong View Download 9. Solve algebraic and transcendental equations, vector integration and calculus of variations. L3 Module-4 Finite differences: Forward and backward differences, Newtons forward and backward interpolation formulae. L3 8 Module-5 Vector integration: Line integrals-definition and problems, surface and volume integrals-definition, Greens theorem in a plane, Stokes and Gauss-divergence theorem without proof and problems.

L3, L4 L2, L4 Course outcomes: On completion of this course, students are able to: Know the use of periodic signals and Fourier series to analyze circuits and system communications. Explain the general linear system theory for continuous-time signals and digital signal processing using the Fourier Transform and z-transform. Employ appropriate numerical methods to solve algebraic and transcendental equations.

Each full Question consisting of 16 marks There will be 2 full questions with a maximum of four sub questions from each module. Chand publishing, 1st edition, Solve first order differential equations. L1 Module-2 Differential Calculus: Review of successive differentiation. L1, L2 Module-3 Integral Calculus: Statement of reduction formulae for sinnx, cosnx, and sinmx cosnx and evaluation of these with standard limits-Examples. L1, L2 Module-5 Ordinary differential equations ODEs : Introduction-solutions of first order and first degree differential equations: homogeneous, exact, linear differential equations of order one and equations reducible to above types.

L1, L2 10 Course outcomes: On completion of the course, students are able to: Understand the fundamental concepts of complex numbers and vector algebra to analyze the problems arising in related area.

Use derivatives and partial derivatives to calculate rates of change of multivariate functions. Evaluate the efficiency of Class A and Class B power amplifiers and voltage regulators. There will be 2 full questions with a maximum of Three sub questions from each module.

Text Book: Robert L. ISBN 4. Develop state diagrams Synchronous Sequential Circuits. Modules RBT Level Module 1 Principles of combination logic: Definition of combinational logic, canonical forms, Generation of switching equations from truth tables, Karnaugh maps-3,4,5 variables, Incompletely specified functions Dont care terms Simplifying Max term equations, Quine-McCluskey minimization technique, Quine-McCluskey using dont care terms, Reduced prime implicants Tables.

Text 1, Chapter 3 L1, L2, L3 Module -2 Analysis and design of combinational logic: General approach to combinational logic design, Decoders, BCD decoders, Encoders, digital multiplexers, Using multiplexers as Boolean function generators, Adders and subtractors, Cascading full adders, Look ahead carry, Binary comparators. Explain the operation of decoders, encoders, multiplexers, demultiplexers, adders, subtractors and comparators.

Apply the knowledge gained in the design of Counters and Registers. L1, L2, L3,L4 Module -5 16 Two port network parameters: Definition of Z, Y, h and Transmission parameters, modeling with these parameters, relationship between parameters sets.

Describe functional concepts and operation of various Analog and Digital measuring instruments. Describe basic concepts and operation of Digital Voltmeters and Microprocessor based instruments. Recognize and describe significance and working of different types of transducers. Text 1 L1, L2, L3 Course Outcomes: After studying this course, students will be able to: Describe instrument measurement errors and calculate them.

Describe and discuss functioning and types of Oscilloscopes, Signal generators and Transducers. Utilize AC and DC bridges for passive component and frequency measurements. Know the physical interpretation of Maxwell equations and applications for Plane waves for their behaviour in different media Acquire knowledge of Poynting theorem and its application of power flow.

L1, L2, L3 Module -4 21 Magnetic Forces Force on a moving charge, differential current elements, Force between differential current elements. L1, L2, L3 Module -5 Time-varying fields and Maxwells equations Fardays law, displacement current, Maxwells equations in point form, Maxwells equations in integral form.

L1, L2, L3 Course Outcomes: After studying this course, students will be able to: Evaluate problems on electric field due to point, linear, volume charges by applying conventional methods or by Gauss law. Calculate magnetic field, force, and potential energy with respect to magnetic materials.

Apply Maxwells equation for time varying fields, EM waves in free space and conductors. Evaluate power associated with EM waves using Poynting theorem. BJT characteristics and Amplifiers. NOTE: The experiments are to be carried using discrete components only. Laboratory Experiments: 1. Design and set up the following rectifiers with and without filters and to determine ripple factor and rectifier efficiency: a Full Wave Rectifier b Bridge Rectifier 2.

Conduct an experiment on Series Voltage Regulator using Zener diode and power transistor to determine line and load regulation characteristics. Realize BJT Darlington Emitter follower with and without bootstrapping and determine the gain, input and output impedances. Design and set up the BJT common emitter amplifier using voltage divider bias with and without feedback and determine the gain- bandwidth product from its frequency response.

Plot the transfer and drain characteristics of a JFET and calculate its drain resistance, mutual conductance and amplification factor.

Plot the transfer and drain characteristics of n-channel MOSFET and calculate its parameters, namely; drain resistance, mutual conductance and amplification factor.

Set-up and study the working of complementary symmetry class B push pull power amplifier and calculate the efficiency. Design and set-up the following tuned oscillator circuits using BJT, and determine the frequency of oscillation. Design and set-up the crystal oscillator and determine the frequency of oscillation. Course Outcomes: On the completion of this laboratory course, the students will be able to: Test circuits of rectifiers, clipping circuits, clamping circuits and voltage regulators.

Strictly follow the instructions as printed on the cover page of answer script for breakup of marks. Change of experiment is allowed only once and Marks allotted to the procedure part to be made zero. For experiment No. Verify a Demorgans Theorem for 2 variables. Design and implement a Full Adder using basic logic gates.

Realize a Multiplexer using gates. Realize Demux and Decoder using IC Simulate Full- Adder using simulation tool. Course outcomes: On the completion of this laboratory course, the students will be able to: Demonstrate the truth table of various expressions and combinational circuits using logic gates. Design and test various combinational circuits such as adders, subtractors, comparators, multiplexers and demultiplexers.

L3 Module-3 Complex Variables: Review of a function of a complex variable, limits, continuity, differentiability. L3 27 Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation, covariance, correlation coefficient. L3 L1 Course Outcomes: On completion of this course, students are able to: Solve first and second order ordinary differential equations arising in flow problems using single step and multistep numerical methods.

Understand Laplace and inverse Laplace transforms and elementary probability theory. L1,L3 Module-3 Laplace transforms: Laplace transforms of elementary functions. L1,L2 Module-5 Probability: Introduction. L1,L2 Course Outcomes: On completion of this course, students are able to: Solve systems of linear equations in the different areas of linear algebra.

L1, L2, L3 Module -2 Logical Instructions, String manipulation instructions, Flag manipulation and Processor control instructions, Illustration of these instructions with example programs. Write Assembly level programs using the instruction set Write modular programs using procedures and macros.

Each full Question consisting of 16 marks There will be 2 full questions with a maximum of Three sub questions from each module.

Liu and A. Gibson, 2nd edition, PHI Learn how to find a mathematical model of electrical, mechanical and electro- mechanical systems. Definition Gradient, Divergence, Curl- problems. Solenoidal and Irrotational vector fields.

Applications- orthogonal trajectories in Cartesian and polar forms. Linear Algebra Rank of a matrix by elementary transformations, solution of system of linear equations — Gauss- elimination method, Gauss- Jordan method and Gauss-Seidel method. Linear transformation, diagonalisation of a square matrix, Quadratic forms, reduction to Canonical form. Tags engineering mathematics 1 engineering mathematics 1 lecture notes pdf engineering mathematics 1 notes engineering mathematics 1 pdf.

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