LNCT University, Bhopal
BTech. III SEM
Branch-CSE
Mathematics III (LNBTC-301)
Module 1: Numerical Methods – 1: (8 hours): Solution of polynomial and transcendental equations – Bisection method, Newton-Raphson method and Regula-Falsi method. Finite differences, Relation between operators, Interpolation using Newton’s forward and backward difference formulae. Interpolation with unequal intervals: Newton’s divided difference and Lagrange’s formulae.
Module 2: Numerical
Methods – 2: (6 hours): Numerical Differentiation,
Numerical integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules.
Solution of Simultaneous Linear Algebraic Equations by Gauss’s Elimination,
Gauss’s Jordan, Crout’s methods, Jacobi’s, Gauss-Seidal, and Relaxation
method.,
Module 3: Numerical
Methods – 3: (10 hours): Ordinary differential
equations: Taylor’s series, Euler and modified Euler’s methods. RungeKutta method
of fourth order for solving first and second order equations. Milne’s and
Adam’s predicator-corrector methods. Partial differential equations: Finite
difference solution two dimensional Laplace equation and Poission equation,
Implicit and explicit methods for one dimensional heat equation (Bender-Schmidt
and Crank- Nicholson methods), Finite difference explicit method for wave
equation.
Module 4: Transform
Calculus: (8 hours): Laplace Transform, Properties
of Laplace Transform, Laplace transform of periodic functions. Finding inverse
Laplace transform by different methods, convolution theorem. Evaluation of
integrals by Laplace transform, solving ODEs by Laplace Transform method,
Fourier transforms.
Module 5: Concept of Probability: (8 hours): Probability Mass function, Probability Density Function, Discrete
Distribution: Binomial, Poisson’s, Continuous Distribution: Normal
Distribution, Exponential Distribution.
Textbooks / References :
1.
P. Kandasamy, K. Thilagavathy, K. Gunavathi, Numerical Methods, S. Chand & Company, 2nd Edition, Reprint 2012.
2. S.S. Sastry,
Introductory methods of numerical analysis, PHI, 4th Edition, 2005.
3. Erwin kreyszig,
Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
4. B.S. Grewal,
Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2010.
5.
N.P. Bali and Manish Goyal, A text
book of Engineering Mathematics, Laxmi Publications, Reprint, 2010.
6. Veerarajan T.,
Engineering Mathematics, Tata McGraw-Hill, New Delhi, 2008.
7.
P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability
Theory, Universal Book Stall, 2003 (Reprint).
8. S. Ross, A First
Course in Probability, 6th Ed.,
Pearson Education India, 2002.
9. W. Feller, An Introduction to Probability
Theory and its Applications, Vol. 1, 3rd Ed., Wiley,
1968. Statistics
LNCT University, Bhopal
BTech. III SEM
Branch-CSE
Discrete Structure III (LNCS-302)
UNIT-1: Propositional Logic and Proof Techniques:
Syntax, Semantics, valid, satisfiable and unsatisfied formula Proposition, First order logic, Basic logical operation, truth tables, tautologies, Contradictions, Algebra of Proposition, logical implications, logical equivalence, predicates, Normal Forms, Universal and existential quantifiers. Introduction to finite state machine Finite state machines as models of physical system equivalence machines, Finite state machines as language recognizer Theorem proving Techniques: Principles of Mathematical induction, Proof by contradiction, Forward proof, proof by contradiction.
UNIT-II: Basic Mathematical structures
Set Theory, Relation, Function, Theorem Proving Techniques Set Theory: Definition of sets, countable and uncountable sets, Venn Diagrams, proofs of some general identities on sets Relation: Definition, types of relation, composition of relations,Pictorial representation of relation, Equivalence relation, Partial ordering relation, Job-Scheduling problem.
UNIT-III: Function
Function: Definition, type of functions, one to one, into and onto function, inverse function, composition of functions, recursively defined functions, pigeonhole , Russels’s Paradox, principle, Po sets, Hasse Diagram and Lattices: Introduction, ordered set, Hasse diagram of partially, ordered set, counting techniques
UNIT-IV: Abstract algebra
Algebraic Structures: Definition, Properties, types: Semi Groups, Monoid, Groups, Abelian group, properties of groups, Subgroup, cyclic groups, Costs, factor group, Permutation groups, Normal subgroup, Homomorphism and isomorphism of Groups, example and standard results, Rings and Fields: definition and standard results. Applications to cryptography
UNIT-V: Graph Theory
Introduction and basic terminology of graphs, Planer graphs, Multigraphs and weighted graphs, Isomorphic graphs, Paths, Cycles and connectivity, Shortest path in weighted graph, Introduction to Eulerian graphs paths and characterization, Hamiltonian paths and circuits, Graph coloring and its applications, chromatic number, Isomorphism and Homomorphism of graphs. Applications to Computer Science
Books Suggested:
• C L Liu, Elements of Discrete Mathematics, Second Edition, Tata McGraw-Hill.
• J P Tremblay and R Manohar, Discrete mathematical structures with applications to Computer Science, Tata McGraw-Hill.
• Kenneth H Rosen (Editor-in-chief), Handbook of Discrete and Combinatorial Mathematics, CRC Education 2002.
LNCT University, Bhopal
BTech. III SEM
Branch-CSE
Object Oriented Programming System (LNCS-303)
UNIT-1:
Introduction to Object Oriented Programming: Object Oriented Concepts, Merits of Object Oriented Technology. Abstraction, Encapsulation, Information Hiding. Object Model: definition, State, behavior, Identity and messages. Concept of object initialization, constructors, constructor overloading. Access modifiers: Class attributes and methods. Introduction to object model of software development.
UNIT-II:
Introduction to classes and Objects: Java features: Java syntax, data types, data type conversions, control statements, operators and their precedence. Introduction to Class: Instance members and member functions. String Handling, Wrapper classes: Arrays and Vectors.
UNIT-III:
Inheritance and Polymorphism: Structure, Class Relationships, Merits and Demerits. Inheritance, Types of Inheritance, Polymorphism: Dynamic method dispatch, Runtime polymorphism, Abstract classes.
UNIT-IV:
Exception Handling and Multithreading : Exceptions: Need for exceptions, Checked Vs Unchecked exceptions, creating custom exceptions. Multithreading: Introduction, Priorities and scheduling, Inter-thread communication, Thread Synchronization and its life cycle.
UNIT-V:
Java I/O, and C++ case study : Basic concept of streams I/O stream & reader-writer classes. File handling. In C++ and Java.
Books Suggested:
👉 Cay S.Horstmann, Core JAVA Vol-1, 9/e, Pearson Education 2012.
👉 Herbert Schildt, The complete Reference, 9/e, Tata McGraw Hill 2014.
👉 Scott W Amber, The Object Primer, 3/e, Cambridge 2004.
👉 Timothy Budd, Object Oriented Programming, 3/e, Pearson Education 2002.
LNCT University, Bhopal
BTech. III SEM
Branch-CSE
Digital Electronics (LNCS-304)
UNIT-1:
Foundation: Number system, Arithmetic operations using 1's,2's complement, various codes, Review of basic gates, universal gate application, Logic Families: - RTL, DTL, TTL &MOS, CMOS families for NOR/NAND gate, characteristics of Digital IC's - speed of operation, power dissipation, Fan-in, Fan-out, Noise margin, Current and Voltage parameters.
UNIT-II:
Combinational Circuits: Boolean laws & algebra , Sum Of Product & Product Of Sum expression, K-Map and Tabular method of minimization, Combinational devices like Multiplexer, Demultiplexer, Decoders, Encoders,Tri-state Devices, Combinational circuit design for Adder, Subtractor, Comparator, Code converters.
UNIT-III:
Sequential Circuits: Latches and Flip-Flops SR, D, T, JK, Master-slave , Flip- Flop conversions, Synchronous counter, Asynchronous counter, Up-Down Counter.
UNIT-IV:
Registers: Shift Registers, serial in parallel out, serial in serial out, parallel in serial out, parallel in parallel out, Universal Shift Register, Sequence Generators, Designing of Synchronous & Asynchronous sequential circuits.
UNIT V:
A/D Conversion and Microprocessor: Digital to Analog Conversion Technique as Binary Weighted DAC, R-2R Ladder, Conversions as Flash type, Counter type , Successive Approximations type A/D converter, Clock generation through IC555, Memory- Types ROM, RAM, Introduction to Microprocessor, Microprocessor Evaluation, Programming and hardware model of Microprocessor, 8/16/32/64 bit Series of Microprocessors.
Books Suggested
👉 Morris Mano, Digital Circuits & Logic Design, PHI
👉 Gothman, Digital Electronics, PHI
👉 Tocci, Digital Electronics, PHI
👉 Mavino& Leach, Digital Principles & Applications, PHI
👉 Taub and schilling, Digital Integrated electronics.
👉 Simon Haykin, Introductionto Analog& Digital Communication, Wil
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