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# «VISVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAUM III SEMESTER ENGINEERING MATHEMATICS – III CODE: 10 MAT 31 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 ...»

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B.E

Computer Science and Engineering

## ENGINEERING MATHEMATICS – III

CODE: 10 MAT 31 IA Marks: 25

Hrs/Week: 04 Exam Hrs: 03

Total Hrs: 52 Exam Marks:100 PART-A Unit-I: FOURIER SERIES Convergence and divergence of infinite series of positive terms, definition and illustrative examples* Periodic functions, Dirichlet’s conditions, Fourier series of periodic functions of period and arbitrary period, half range Fourier series. Complex form of Fourier Series. Practical harmonic analysis. [7 hours] Unit-II: FOURIER TRANSFORMS Infinite Fourier transform, Fourier Sine and Cosine transforms, properties, Inverse transforms [6 hours] Unit-III: APPLICATIONS OF PDE Various possible solutions of one dimensional wave and heat equations, two dimensional Laplace’s equation by the method of separation of variables, Solution of all these equations with specified boundary conditions.

D’Alembert’s solution of one dimensional wave equation.

[6 hours] Unit-IV: CURVE FITTING AND OPTIMIZATION Curve fitting by the method of least squares- Fitting of curves of the form y = ax + b, y = a x 2 + b x + c, y = a e, y = ax bx b Optimization: Linear programming, mathematical formulation of linear programming problem (LPP), Graphical method and simplex method.

[7 hours] PART-B Unit-V: NUMERICAL METHODS - 1 Numerical Solution of algebraic and transcendental equations: Regula-falsi method, Newton - Raphson method. Iterative methods of solution of a system of equations: Gauss-seidel and Relaxation methods. Largest eigen value and the corresponding eigen vector by Rayleigh’s power method.

[6 hours] Unit-VI: NUMERICAL METHODS – 2 Finite differences: Forward and backward differences, Newton’s forward and backward interpolation formulae. Divided differences - Newton’s divided difference formula, Lagrange’s interpolation formula and inverse interpolation formula.

Numerical integration: Simpson’s one-third, three-eighth and Weddle’s rules (All formulae/rules without proof) [7 hours] Unit-VII: NUMERICAL METHODS – 3 Numerical solutions of PDE – finite difference approximation to derivatives, Numerical solution of two dimensional Laplace’s equation, one dimensional heat an

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Note: * In the case of illustrative examples, questions are not to be set.

Text Books:

1. B.S. Grewal, Higher Engineering Mathematics, Latest edition, Khanna Publishers

2. Erwin Kreyszig, Advanced Engineering Mathematics, Latest edition, Wiley Publications.

Reference Book:

1. B.V. Ramana, Higher Engineering Mathematics, Latest edition, Tata Mc. Graw Hill Publications.

2. Peter V. O’Neil, Engineering Mathematics, CENGAGE Learning India Pvt Ltd.Publishers

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UNIT - 2 6 Hours Field Effect Transistors: Bipolar Junction Transistors versus Field Effect Transistors, Junction Field Effect Transistors, Metal Oxide Field Effect Transistors, Differences between JFETs and MOSFETs, Handling MOSFETs, Biasing MOSFETs, FET Applications, CMOS Devices, Insulated Gate Bipolar Transistors (IGBTs) UNIT - 3 6 Hours Optoelectronic Devices: Introduction, Photosensors, Photoconductors, Photodiodes, Phototransistors, Light-Emitting Diodes, Liquid Crystal Displays, Cathode Ray Tube Displays, Emerging Display Technologies, Optocouplers UNIT - 4 7 Hours Small Signal Analysis of Amplifiers: Amplifier Bandwidth: General Frequency Considerations, Hybrid h-Parameter Model for an Amplifier, Transistor Hybrid Model, Analysis of a Transistor Amplifier using complete h-Parameter Model, Analysis of a Transistor Amplifier Configurations using Simplified h-Parameter Model (CE configuration only), Small-Signal Analysis of FET Amplifiers, Cascading Amplifiers, Darlington Amplifier, Low-Frequency Response of Amplifiers (BJT amplifiers only).

PART - B UNIT - 5 6 Hours Large Signal Amplifiers, Feedback Amplifier: Classification and

characteristics of Large Signal Amplifiers, Feedback Amplifiers:

Classification of Amplifiers, Amplifier with Negative Feedback, Advantages of Negative Feedback, Feedback Topologies, Voltage-Series (Series-Shunt) Feedback, Voltage-Shunt (Shunt-Shunt) Feedback, Current-Series (SeriesSeries) Feedback, Current-Shunt (Shunt-Series) Feedback.

UNIT - 6 7 Hours Sinusoidal Oscillators, Wave-Shaping Circuits: Classification of Oscillators, Conditions for Oscillations: Barkhausen Criterion, Types of Oscillators, Crystal Oscillator, Voltage-Controlled Oscillators, Frequency Stability.

Wave-Shaping Circuits: Basic RC Low-Pass Circuit, RC Low-Pass Circuit as Integrator, Basic RC High-Pass Circuit, RC High-Pass Circuit as Differentiator, Multivibrators, Integrated Circuit (IC) Multivibrators.

UNIT - 7 7 Hours Linear Power Supplies, Switched mode Power Supplies: Linear Power Supplies: Constituents of a Linear Power Supply, Designing Mains Transformer; Linear IC Voltage Regulators, Regulated Power Supply Parameters.

Switched Mode Power Supplies: Switched Mode Power Supplies, Switching Regulators, Connecting Power Converters in Series, Connecting Power Converters in Parallel UNIT - 8 6 Hours Operational Amplifiers: Ideal Opamp versus Practical Opamp, Performance Parameters, Some Applications: Peak Detector Circuit, Absolute Value Circuit, Comparator, Active Filters, Phase Shifters, Instrumentation Amplifier, Non-Linear Amplifier, Relaxation Oscillator, Current-To-Voltage Converter, Voltage-To-Current Converter, Sine Wave Oscillators.

Text Book:

1. Anil K Maini, Varsha Agarwal: Electronic Devices and Circuits, Wiley, 2009.

(4.1, 4.2, 4.7, 4.8, 5.1 to 5.3, 5.5, 5.6, 5.8, 5.9, 5.13, 5.14, 6.1, 6.3,

7.1 to 7.5, 7.10 to 7.14, Listed topics only from 8, 10.1, 11, 12.1, 12.2, 12.3, 12.5, 13.1 to 13.6, 13.9, 13.10, 14.1, 14.2, 14.6, 14.7, 15.1, 15.5 to 15.7. 16.3, 16.4, 17.12 to 17.22)

Reference Books:

1. Jacob Millman, Christos Halkias, Chetan D Parikh: Millman’s Integrated Electronics – Analog and Digital Circuits and Systems, 2nd Edition, Tata McGraw Hill, 2010.

2. R. D. Sudhaker Samuel: Electronic Circuits, Sanguine-Pearson, 2010.

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UNIT – 1 7 Hours Digital Principles, Digital Logic: Definitions for Digital Signals, Digital Waveforms, Digital Logic, 7400 TTL Series, TTL Parameters The Basic Gates: NOT, OR, AND, Universal Logic Gates: NOR, NAND, Positive and Negative Logic, Introduction to HDL.

UNIT – 2 6 Hours Combinational Logic Circuits Sum-of-Products Method, Truth Table to Karnaugh Map, Pairs Quads, and Octets, Karnaugh Simplifications, Don’t-care Conditions, Product-of-sums Method, Product-of-sums simplifications, Simplification by Quine-McClusky Method, Hazards and Hazard Covers, HDL Implementation Models.

UNIT – 3 6 Hours Data-Processing Circuits: Multiplexers, Demultiplexers, 1-of-16 Decoder, Encoders, Exclusive-or Gates, Parity Generators and Checkers, Magnitude Comparator, Programmable Array Logic, Programmable Logic Arrays, HDL Implementation of Data Processing Circuits UNIT – 4 7 Hours Clocks, Flip-Flops: Clock Waveforms, TTL Clock, Schmitt Trigger, Clocked D FLIP-FLOP, Edge-triggered D FLIP-FLOP, Edge-triggered JK FLIP-FLOP, FLIP-FLOP Timing, JK Master-slave FLIP-FLOP, Switch Contact Bounce Circuits, Various Representation of FLIP-FLOPs, Analysis of Sequential Circuits, HDL Implementation of FLIP-FLOP

–  –  –

UNIT – 6 7 Hours Counters: Asynchronous Counters, Decoding Gates, Synchronous Counters, Changing the Counter Modulus, Decade Counters, Presettable Counters, Counter Design as a Synthesis problem, A Digital Clock, Counter Design using HDL UNIT – 7 7 Hours Design of Synchronous and Asynchronous Sequential Circuits: Design of Synchronous Sequential Circuit: Model Selection, State Transition Diagram, State Synthesis Table, Design Equations and Circuit Diagram, Implementation using Read Only Memory, Algorithmic State Machine, State Reduction Technique.

Asynchronous Sequential Circuit: Analysis of Asynchronous Sequential Circuit, Problems with Asynchronous Sequential Circuits, Design of Asynchronous Sequential Circuit, FSM Implementation in HDL UNIT – 8 6 Hours D/A Conversion and A/D Conversion: Variable, Resistor Networks, Binary Ladders, D/A Converters, D/A Accuracy and Resolution, A/D ConverterSimultaneous Conversion, A/D Converter-Counter Method, Continuous A/D Conversion, A/D Techniques, Dual-slope A/D Conversion, A/D Accuracy and Resolution

Text Book:

1. Donald P Leach, Albert Paul Malvino & Goutam Saha: Digital Principles and Applications, 7th Edition, Tata McGraw Hill, 2010.

Reference Books:

1. Stephen Brown, Zvonko Vranesic: Fundamentals of Digital Logic Design with VHDL, 2nd Edition, Tata McGraw Hill, 2005.

2. R D Sudhaker Samuel: Illustrative Approach to Logic Design, Sanguine-Pearson, 2010.

3. Charles H. Roth: Fundamentals of Logic Design, Jr., 5th Edition, Cengage Learning, 2004.

4. Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss: Digital Systems Principles and Applications, 10th Edition, Pearson Education, 2007.

5. M Morris Mano: Digital Logic and Computer Design, 10th Edition, Pearson Education, 2008.

## DISCRETE MATHEMATICAL STRUCTURES

(Common to CSE & ISE)

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Text Book:

1. Ralph P. Grimaldi: Discrete and Combinatorial Mathematics,, 5th Edition, Pearson Education, 2004.

(Chapter 3.1, 3.2, 3.3, 3.4, Appendix 3, Chapter 2, Chapter 4.1, 4.2, Chapter 5.1 to 5.6, Chapter 7.1 to 7.4, Chapter 16.1, 16.2, 16.3, 16.5 to 16.9, and Chapter 14.1, 14.2, 14.3).

Reference Books:

1. Kenneth H. Rosen: Discrete Mathematics and its Applications, 7th Edition, McGraw Hill, 2010.

2. Jayant Ganguly: A Treatise on Discrete Mathematical Structures, Sanguine-Pearson, 2010.

3. D.S. Malik and M.K. Sen: Discrete Mathematical Structures: Theory and Applications, Cengage Learning, 2004.

4. Thomas Koshy: Discrete Mathematics with Applications, Elsevier, 2005, Reprint 2008.

–  –  –

Text Book:

1. Horowitz, Sahni, Anderson-Freed: Fundamentals of Data Structures in C, 2nd Edition, Universities Press, 2007.

(Chapters 1, 2.1 to 2.6, 3, 4, 5.1 to 5.3, 5.5 to 5.11, 6.1, 9.1 to 9.5, 10)

Reference Books:

1. Yedidyah, Augenstein, Tannenbaum: Data Structures Using C and C++, 2nd Edition, Pearson Education, 2003.

2. Debasis Samanta: Classic Data Structures, 2nd Edition, PHI, 2009.

3. Richard F. Gilberg and Behrouz A. Forouzan: Data Structures A Pseudocode Approach with C, Cengage Learning, 2005.

4. Robert Kruse & Bruce Leung: Data Structures & Program Design in C, Pearson Education, 2007.

–  –  –

UNIT 2 7 Hours Classes & Objects – I: Class Specification, Class Objects, Scope resolution operator, Access members, Defining member functions, Data hiding, Constructors, Destructors, Parameterized constructors, Static data members, Functions UNIT 3 7 Hours Classes & Objects –II: Friend functions, Passing objects as arguments, Returning objects, Arrays of objects, Dynamic objects, Pointers to objects, Copy constructors, Generic functions and classes, Applications Operator overloading using friend functions such as +, -, pre-increment, post-increment, [ ] etc., overloading,.

–  –  –

Text Books:

1. Herbert Schildt: The Complete Reference C++, 4th Edition, Tata McGraw Hill, 2003.

Reference Books:

1. Stanley B.Lippmann, Josee Lajore: C++ Primer, 4th Edition, Pearson Education, 2005.

2. Paul J Deitel, Harvey M Deitel: C++ for Programmers, Pearson Education, 2009.

3. K R Venugopal, Rajkumar Buyya, T Ravi Shankar: Mastering C++, Tata McGraw Hill, 1999.

–  –  –

1. Using circular representation for a polynomial, design, develop, and execute a program in C to accept two polynomials, add them, and then print the resulting polynomial.

2. Design, develop, and execute a program in C to convert a given valid parenthesized infix arithmetic expression to postfix expression and then to print both the expressions. The expression consists of single character operands and the binary operators + (plus), minus), * (multiply) and / (divide).

3. Design, develop, and execute a program in C to evaluate a valid postfix expression using stack. Assume that the postfix expression is read as a single line consisting of non-negative single digit operands and binary arithmetic operators. The arithmetic operators are + (add), - (subtract), * (multiply) and / (divide).

–  –  –

5. Design, develop, and execute a program in C++ based on the

following requirements:

An EMPLOYEE class is to contain the following data members and

member functions:

Data members: Employee_Number (an integer), Employee_Name (a string of characters), Basic_Salary (an integer), All_Allowances (an integer), IT (an integer), Net_Salary (an integer).

Member functions: to read the data of an employee, to calculate Net_Salary and to print the values of all the data members.

(All_Allowances = 123% of Basic; Income Tax (IT) = 30% of the gross salary (= basic_Salary _ All_Allowance); Net_Salary = Basic_Salary + All_Allowances – IT)

6. Design, develop, and execute a program in C++ to create a class called STRING and implement the following operations. Display the results after every operation by overloading the operator.

i. STRING s1 = “VTU” ii. STRING s2 = “BELGAUM” iii. STIRNG s3 = s1 + s2; (Use copy constructor)

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