## Saturday, July 25, 2009

### Second Year Syllabus - SNDT University Mumbai

Applied Mathematics - III

Semester: III Lect: 4Hr
Branch:ENC/CST/IT Credit: 04

SECTION - A

1. LAPLACE TRANSFORM

Definition, properties with regards to summation, differentiation and integration. Laplace transform of standard functions. Theorems on Laplace transform, Shifting properties. Laplace transform of t f(t), f(t) / t.
Laplace transform of derivative of a function, integral of a function.
Evaluation of inverse Laplace transform (by standard formulae and partial fraction method)
Laplace transform of periodic functions, step functions and its derivatives.
Convolution integral and its application in finding the inverse Laplace transform.
Solving differential equation by Laplace transform. Applications in Engg.

2. FOURIER SERIES
3.
Orthogonal functions, expression of a function in a series of orthogonal functions.
Fourier series, definition and condition for its existence, Evaluation of Fourier Coefficients.
Even and Odd functions, Evaluation of Fourier series of even and odd functions
Half range sine and cosine series. Parseval’s theorem and its relations.
Complex form of Fourier series, Introduction to Fourier integrals, Fourier transform, Sine transform, Cosine transform-properties and its elementary applications.
Parseval’s identity and evaluation of definite integrals by using it. Applications in Engg.

SECTION – B

3. COMPLEX VARIABLES

Complex number, representation in Cartesian, Polar and exponential forms. De Moiver’s Theorem and its application to complex numbers. Complex variable (and variables). Continuity, Differentiability of functions of complex variables. Necessary and sufficient conditions for a function to be analytic (Cauchy Riemann Equations in cartesian and polar co-ordinates with proof). Determining the function of a complex variable f(z) from its real and imaginary parts using Cauchy Riemann Equations. Applications in Engg.

4. MAPPING

Conformal mapping and bilinear mapping Geometrical interpretations of mapping. Concept of line integral and its relation with Riemann integral. Concept of point function and path independent functions. Contour integral. Cauchy’s theorem for analytic functions and its applications for multiply connected domains. Cauchy’s integral formula and nth derivative of a complex function Morera’s theorem, maximum modulus theorem (Statements and proof’s). Taylor’s and Lorents development of a functions of a complex variable. Singularities – isolated essential singularity and non isolated singularity. Poles, evaluation of residues. Residue theorem and its application to evaluate real integrals. Applications in Engg.

TEXT BOOKS / REFERENCE BOOKS

1. B. S. Grewal, Higher Engineering Mathematics, 34th edition, Khanna Publishers, 1998. (Rs. 170).
2. Edwin Kreyszig, Advance Engg. Mathematics, 5th Edition, New Age International (P) Ltd; 1997. (Rs. 295/-)
3. P.N.Wartikar & J. N. Wartikar, Elements of Applied Mathematics, 1st edition, Pune Vidyarthi Griha Prakashan, 1995. (rs. 110/-)

Discrete Structures and Combinatorics

Semester: III Lect: 4 Hr
Branch: CST Credit: 04

• Logic: Introduction, statement and notations.
Connectives: conjunction, disjunction, negation, statement formulas and truth table, conditional, bi-conditional, well formed formulas, tautology, contradiction, laws of logic’s, equivalence of formulas, duality law, tautological implication, formulas with distinct truth table, other connectives such as XOR, NAND, NOR.
Normal forms: disjunctive normal form, conjunctive normal form, principal disjunctive normal form, principal conjunctive normal form, ordering and uniqueness of normal forms. Principle of mathematical induction.
Predicate calculus: predicates, the statement functions, variables, universal and existential quantifiers, predicate formulas, free and bound variables, the universe of discourse.

• Set Theory: Introduction, basic concept of set theory, set notation and description, inclusion and equality of sets, finite and infinite set, null set, power set.
Basic set operations such as intersection, union, relative and absolute complement, Cartesian product, and symmetric difference. Disjoint sets, partitions of a set, Venn diagram.
Methods of proof for sets: by using example, by using Venn diagram, by using set membership tables, by using definitions. Laws of set theory, proof using previously proven theorem, proofs using indirect method.

• Counting: permutations and combinations, the pigeonhole principle, elements of probability, recurrence relations.

• Relations: Basic definition, relation notation, and set arising from relations.
Properties of relation: reflexive, irreflexive, symmetric, asymmetric, anti-symmetric, transitive.
Relation matrix and graphs of relation: paths in relation and digraph, composition of paths, identification of properties of relations from relation matrix and graph.
Equivalence relation: definition, determination of equivalence relation from partitions, equivalence classes, properties of equivalence classes.
Manipulation of relations: Boolean product of relation matrices, inverse of a relation, composition of a relation, inverse of a composite relation, complementary relation.
Closures: reflexive, symmetric and transitive closure of a relation, transitive closure by Warshall’s algorithm.

• Functions: definition, image of a function, and restriction of function to a set.
Special types of functions: injective, surjective, bijective, invertible, identity, floor, ceiling, and characteristic function of a set, composition of functions.
Permutation function: definition, different properties.
Growth of a function: Big O notation, big  relation and rules of determining  classes of a function.

• Algebraic structure: binary and n-ary operations on a set, representation of binary operation by composite table, properties of binary operations.
Algebraic system: definition, some simple algebraic system, and properties of algebraic system such as homomorphism, epimorphism, monomorphism, isomorphism, and endomorphism. Direct product of algebra, congruence relation.
Semigroups and monoids: definition, notation, product of partition, cyclic monoid, different properties of semigroup and monoid such as homomorphism, epimorphism, monomorphism, isomorphism, endomorphism, automorphism implications of homomorphism.
Product and quotient of Semigroups: congruence relation, quotients of semigroups, and direct product of semigroups, Subsemigroup and submonoid.
Groups: definition, notation, order of a group, abelian group, cyclic group, subgroup, proper subgroup, group homomorphism, kernel of the homomorphism, Cosets and LaGrange’s Theorem, normal subgroups, product of groups, quotients of groups.
Ring: definition, properties, ring homomorphism, field.

• Lattice and Boolean algebra: Partial order relation, poset, comparable and incomparable elements, linear ordering, totally order set or chain, lexicographic order, cover of an element, Hasse diagram, different features of Hasse diagram, topological sorting, isomorphism between two poset, extremal elements of posets such as minimal, maximal, least, greatest, upper bound, lower bound, least upper bound, greatest lower bound.
Lattice: Definition, properties of lattice, sublattice, direct product of lattices, lattice homomorphism, isomorphism, endomorphism, automorphism, order preserving, order isomorphism, complete lattice, bounded lattice, complemented lattice, distributive lattice.
Boolean algebra: definition, properties of Boolean algebra, sub algebra, direct product of Boolean algebra, Boolean functions as Boolean polynomials.

• Graphs and Trees: Introduction, definition, applications of graph, finite and infinite graph, incidence and degree, isolate vertex, pendant vertex, null graph.
Paths and Circuits: isomorphism, subgraphs, and coloring of a graph, component of a graph, Euler graph, and operation on graphs, Hamiltonian paths and circuits.
Trees and fundamental circuits: definition, properties of trees, pendant vertices in tree, distance and centers in tree, rooted and binary tree, on counting tree, undirected tree, spanning tree, fundamental circuits, finding all spanning trees of a graph, spanning trees in a weighted graph (Prim’s and Kruskal’s algorithm).

References:

1. J. P. Tremblay, and R. Manohar, Discrete mathematical structures with applications to computer science, Tata McGraw Hill,
2. Bernard Kolman, Robert C. Busby, and Sharon Ross, Discrete mathematical structures, 4th edition, PHI, 2002. (Rs. 195/-)
3. Narsing Deo, Graph theory and applications to engineering and computer science, PHI, 1999. (Rs. 150/-)
4. Alan Doerr and Kenneth Levasseur, Applied discrete structures for computer science, Galgotia Publication, 1998. (Rs- 176/-)
5. C. L. Liu, Elements of Discrete Mathematics, 2nd edition, Tata McGraw Hill, 2000. (Rs. 175/-)
6. Frank Harary, Graph theory, Narosa Publication, 1998. (Rs. 135/-)
7. Douglas B. West, Introduction to graph theory, PHI, 1999. (Rs- 195/-)

Digital Logic Circuits

Semester: III Lect: 4 Hr
Branch: ENC / CST / IT Credit: 04

Concept of Digital & Analog Circuit

Diodes & Transistors as ‘Switch’ in Digital Circuits, Applications of Digital Logic Circuits, Positive Logic & Negative Logic.

Number Systems & Conversions

Decimal, Binary, Octal & Hexadecimal, Double – Dabble, Hex-Dabble, Octal Dabble & Streamlined Methods of Interconversions.

Representation of Negative Numbers

Signed – Magnitude Method
1’s Complement Method
2’s Complement Method
Arithmetic operations on binary number system, addition, subtraction, multiplication & division. Hexadecimal addition & subtraction. Octal addition & subtraction. 9’s complement & 10’s complement methods.

Special Codes

Weighted & non-weighted codes. Standard 8421 code, XS-3 code & gray code. XS-3 code numbers addition, gray to binary & binary to gray conversions. Concept of parity, odd & even parity. Error detecting methods: parity & forbidden group.

Logic Gates

OR, AND, NOT, NOR, NAND, X-OR gates EX-NOR. Truth-tables & their equivalent Ckts. Using switches diodes & transistors.
NAND & NOR as universal gates.
N-OR gate as parity checker & parity generator. Realization of Boolean expression using gates.
De Morgan’s Theorems
Realization of De Morgan’s theorems using gates.
Reduction Techniques
1) Laws of Boolean algebra
2) K-map reduction techniques
SOP & POS using universal gates.
(concept of minterms & maxterms)
K-map using two, three, four & five variables.
Duality Theorem
K-map reduction techniques : pairs, quads, octets, rolling, overlapping etc.
Quine-Maclusky method .

Combinational Circuits (Data Processing Circuits)

Encoders & Decoders
2 : 4, 3 : 8 encoder BCD to decimal
decoder, IC7445, IC74154
Decoder drivers: 7-segment display (MAN-72)
IC 7446, IC 7447 & IC 7448.
Encoders: Decimal to BCD encoder IC 74147.

Multiplexers & Demultiplexes

IC 74150, IC 74151 & IC 74155
Their applications (Boolean function simplification using mux & demux)

Arithmetic Circuits

Sequential Circuits

Flip-flops R-S, ƒƒ, ƒK ƒƒ, D ƒƒ, T ƒƒ, master slave JK ƒƒ their properties & truth tables conversion of one type of ƒƒ into another without using K-maps. Timing diagrams IC 7474, IC 7446.

Applications of flip-flops:
Counters
Principles of working of a 3-bit ripple counter, synchronous counter, preset table counter, mod-3,mod-6,mod-5,mod-7, mod-10, and mod-12, using decoding gates.
Ring counter,Twisted ring counter.Glitch and gating of a counter.
IC 7490, IC 7493, IC 7495, IC 74193.

Shift Registers
Principle of working of buffer register, shift-left, shift-right register.
Four types of register: SISO, SIPO, PISO, PIPO,Typical shift register.Mode controlled shift register.

Memories
Classification and characteristics of memories.
Methods of address decoding, memory cells.
RAM memories:-TTL RAM,NMOS RAM,Dynamic RAM.

TTL Logic family.
Their principles of working, critical values for I/P, O/P vtg. Levels, curr. Sinking & sourcing, fan-out, noise immunity.
Study of basic 2-i/p TTL NAND gate and its transfer characteristics..

Reference Books:

1. William Gotmann, “Digital Electronics – An Introduction to theory & Practice”, 2nd edition, Rs.110/-
2. Malvino Leach, “Digital Principles & Applications”, 4th edition.
3. R. P. Jain, “Modern Digital Electronics” 2nd edition, Rs.150/-.

Electrical Network Theory

Semester: III
Lect: 4 Hr
Branch:ENC Credit: 04
NETWORK TOPOLOGY
Graph- oriented, planer, subgraph, concept of tree, Incidence matrix, reduced incidence matrix, Tie- set / fundamental loops of graph, KVL equations for f-loops, rank, Cut-set & its orientation, KCL equations for cut-set, Cut-set matrix, Formulations network equations, Networks with mutual inductances & controlled sources, Duality Concept.Maximum, mini-cut Theorem & Properties.

TIME & FREQUENCY DOMAIN APPROACH TO ELECTRICAL NETWORKS
Transient responses to networks, General & particular solution, R-L & R-C network, Time constant, DC forcing function response, Initial conditions in networks.
RLC network.

State Variable Analysis-
State equations and their formulations, Equivalent source method & topological method, Time-Domain solution of State-Equations.
Laplace Transform and their application to networks.

TWO PORT NETWORKS
Z, Y, H, G, ABCD or Transmission parameters, Interconversion of parameters, Condition of reciprocity & Symmetry.

TRANSFER FUNCTIONS
Network functions of some typical networks, Pole- Zero Plot of network functions, restrictions on Pole- Zero locations.

ELEMENTS OF FILTER THEORY
Filter classifications, Mathematical representations of Attenuation, Characteristics Impedance, Attenuation & Phase Constants, Cut-off Frequency.

DISTRIBUTED PARAMETERS (TRANSMISSION LINES)
Equivalent Circuit of transmission lines, Line equations, VSWR, Measurement of various parameters, Transmission line Matrices, Distortions in Transmission Lines, Distortion less line, Characteristics Impedance, Impedance transformation & matching- - single and Double Stub Matching.

Reference Books

1) Gopal Bhise, Prem Chadha, Durgesh Kulshreshta Engineering Network Analysis & Filter Design, 1st Edition, Umesh Publications, 1999. (Rs. 250/-)
2) M.E. Van Valkenberg, Network Analysis, 3rd Edition, PHI, 1997 (Rs 150/-)
3) D Roy Choudhury, Networks & Systems, Fourth Reprint, Wiley Eastern Publications, 1994. (Rs-200/-)
4) Hayt, Kemmerly, Engineering Circuit analysis, Fifth Edition, Tata McGraw Hill 2000. (Rs.275/-)

Electronics Measurement and Instruments

Semester: IV Lect: 4 Hr
Branch: ENC Credit: 04

1. Measurement and Error
• Definition, Significance, Methods of Measurements
• Accuracy and Precision
• Significant Figures
• Types of Error
• Statistical Analysis
• Probability of Errors
• Phases of Instruments (Mechanical Instruments, Electrical Instruments, Electronics Instruments)

2. Standards of Measurements
• Classification of Standards
• Standards for Mass, Length, and Volume
• Time and Frequency Standards
• Electrical Standards
• Standards of Temperature and Luminous Intensity
• IEEE Standards

3. Bridge Measurements
• Introduction
• Whetstone Bridge
• Kelvin Bridge
• AC Bridge and Their Application
• Maxwell Bridge
• Hay Bridge
• Schering Bridge
• Unbalance Condition
• Wein Bridge

4.
• Electronic DC Voltmeter
• RMS Voltmeter
• Electronic Multimeter
• Ohm-Meter
• Series Type Ohm-Meter
• Shunt Type Ohm-Meter
• DC Ammeters
• Suspension Galvanometer (D’ Arsonval Galvanometer
• Permanent Magnet Moving Coil Instrument (PMMC Galvanometer)
5. Q-Meter
• Basic Q-Meter Circuit
• Measurement Methods
• Direct Connection
• Series Connection
• Parallel Connection
• Sources of Errors

6. Cathode Ray Oscilloscope
• Introduction
• Oscilloscope Block Diagram
• Cathode Ray Tube
• Electrostatic Focusing
• Electrostatic Deflection (Derivation for D-LldEd/2dEa)
• Deflection Sensitivity, Deflection Factor
• Post Deflection Acceleration of Electrostatic Beam
• Screens for CRT
• Vertical Deflection System
• Horizontal Deflection System
• Types of Sweeps
• Dual Trace Oscilloscope
• Sampling Oscilloscope
• Storage Oscilloscope
Principle of Secondary Emission
Variable Persistence Storage
Bistable Storage Oscilloscope
• Digital Storage Oscilloscope
• Comparison Between Analog and Digital Storage Oscilloscope

7. Signal Generation
• Sine Wave Generator
• Frequency Synthesized Signal Generator
• Sweep Frequency Generator
• Function Generator

8. Spectrum Analysis
• Wave Analyzers
• Frequency Selective Wave Analyzers
• Heterodyne Wave Analyzers
• Harmonic Distortion Analyzers
Tuned-Circuit Harmonic Analyzer
Heterodyne Harmonic Analyzer or Wave Meter
• Spectrum Analyzer
• Basic Spectrum Analyzer
• Fourier Transform Spectrum Analyzer
• Applications of the Spectrum Analyzers

9. Transducers
• Introduction
• Structure and Classification
• Piezoelectric Transducers
• Thermocouple
• Photo-Electric Transducer

Text Book
W. D. Cooper," Electronic Instrumentation & Measurement Technique", Prentice Hall India, 1982

References
1. B. H. Oliver & J.M. Cage (ed.), "Electronic Measurement & Instrumentation", McGraw Hill , 1971
2. A. M. Rudkin , "Electronic Test Equipment", 1981
3. M. L. Meade," Lock-in amplifiers", Peter Peregnius, 1983
Prentice Hall, 1987.
5. J. A. Alloca," Electronic Instrumentation", Prentice Hall, 1987
6. A. K. Sawani, “Electronic Measurement & Instrumentation”.

Microprocessor – I

Semester: V Lect: 4 Hr
Branch: ENC / CST / IT Credit: 04

Introduction of Microprocessor
Brief history of Microprocessors, Basic building blocks of microcomputer systems.

8085 Microprocessor
Pin diagram and pin description
Internal architecture with functional block diagram.
Register organization inside 8085

Interfacing devices ---- tri state buffer, decoder, and latch.
Instruction set of 8085: study of instructions from instruction set
of 8085. Grouping of instructions.
Addressing modes of 8085 – their types with suitable examples.
Programming of 8085 - Program development for 8085 using inst. set
Stacks and subroutines – concept of stack and stack pointer, use of PUSH, POP and other stack related instructions, subroutines, their types and execution of subroutines.
I/O data transfer techniques- programmed I/O, interrupt driven I/O, DMA, data transfer with handshake signals and ready signals.
Interrupts - hardware and software interrupts, maskable and Nonmaskable interrupts, vectored and nonvectored interrupts, interrupt structure of 8085,
Instructions related to interrupt like EI, DI, RIM and SIM.
I/O device interfacing – I/O mapped I/O and memory mapped
I/O techniques.
Programmable I/O devices – study of 8155, 8355/8755, block diagram, pin functions and modes of operation.
Programmable Peripheral Interface (PPI) 8255-block diagram, pin functions, features, modes of operations, interfacing with 8085.
Programmable Interval Timer 8253/54- block diagram, pin function, features, modes of operations, interfacing with 8085.
Programmable interrupt controller 8259-block diagram, pin function, features, modes of operation, interfacing with 8085.
DMA Controller 8257- block diagram, pin function, features, modes of operation, interfacing with 8085.
ADC/DAC interfacing – study of ADC/DAC IC’S – 0800, 0808,0809,generation of various waveforms
Debugging tools: Assemblers, Logic Analyzers.
8085 Microprocessor based system Design.

Microcontroller 8051
Architecture of 8051, hardware, of 8051, oscillator & clock, Register organization inside 8051,Special function Registers, Internal memory, internal RAM.
Pin Configuration & functions of pins.
Modes for serial I/O operation- mode 0, mode 1, mode 2, mode 3. Modes for interrupt- operation interrupt structure external
interrupt control and priority.
Timer/ counter modes - mode 0, mode 1, mode 2, mode 3.
Power Saving modes -power down mode, idle mode
Instruction set & Addressing modes of 8051
Programming of 8051- programs for addition,subtraction,
multiplication and division.
Interfacing of external memory to 8051
Interfacing of external peripherals to 8051.

Text Books and Reference Books

1. R. S. Gaonkar, “Microprocessor”, 3rd edition, Penram International Publications. (RS. 225/-)
2. Borole and Vibhute, “Microprocessor”, 2nd edition, Technova Publications. (Rs. 220/-)
3. A. P. Godse , “Microprocessor”, 1st edition, Nirali Publications. (Rs. 275/-)
4. A .P. Godse, Gilmore , “Microprocessor”, 2nd edition, McGraw Hill International. (Rs. 765/- )
5. Kenneth J. Ayala, ‘The 8051Microcontroller”, 2nd edition, Penram International. (Rs. 225/-)

Electromagnetic Wave Theory

Semester: IV Lect: 4 Hr
Branch: ENC
Credit: 04

Electrostatics:
Fundamental relations, Guass’s law, electric potential, continuous charge distribution, equipotential surfaces,Divergence theorem, Poissons & Laplace equations, capacitace, elctrostatic energy, boundary conditions, Uniquness theorem, Dirac delta representation.

Magnetostatics:
Magnetic field, Faraday’s law, Lenz’s law, Flux density, field strength, Ampere’s law, Permeability, Magnetostatic energy, Lornetz force equation, Ampere’s force law, Magnetic potential, analogies between electric & magnetic field.Maxwell’s equations: Continuity equation for time varying fields, Maxwell’s equations, Boundary conditions.

Electromagnetic waves:
Waves in free space, Uniform plane waves, Waves in conducting medium, sinusoidal time variations.
Conductors & Dielectrics: Polarization in dielectrics, Normal & oblique incidence, surface impedance, Poynting theorem, poynting vector, interpretation of E*H, power loss in plane conductor.
Guided Waves: TE & TM waves, characteristics of TE & TM waves, TEM waves, velocities of propagation, wave impedance, current flow through conductor.

Transmission lines: Parallel plane transmission line, radio & UHF transmission line, Transmission line charts, Impedance matching by stubs.

Wave Guides: Rectangular guides, TE & TM waves in rectangular wave-guides, nonexistence of TEM waves in wave-guides, Bessel’s function, circular wave-guides, wave & characteristics impedance, attenuation factor & Q of wave-guides.

Radiation & Antenna: Basic antenna parameters, general solution of Maxwell’s equations. Retarded vector potential, electric dipole, current element & dipole, power radiated from Quarter wave monopole or half wave dipole, antenna properties- Radiation pattern, radiation intensity, gain, directive gain, directivity, effective length, efficiency & effective area, relation between radiation resistance, directive gain & effective length, antenna arrays- broad side, end-fire, binomial array, Principle of pattern multiplication

References:
1. Edward Jordan & Kieth Balmain, Electromagnetic waves & radiating systems, 2nd Edition, PHI, 1998. (Rs-175/-)
2. John D. Kraus, Electromagnetics, 4th Edition, McGraw-Hill, 1991. (Rs- 300/-)
3. K. D. Prasad, Antenna & Wave Propagation, 3rd Edition, Satya Prakashan New Delhi, 2001. (Rs. 250/-)

Analog Circuits

Semester: IV Lect: 4 Hr
Branch:ENC/CST/IT Credit: 04

Differential Amplifiers:
Diff. Amp. Circuit configurations- dual/single i/p balanced output, dual/single i/p unbalanced output, DC & AC analysis, swamping resistors, constant current bias, current mirror, level shifter.

Operational Amplifiers:
Block diagram of typical Op-Amp, schematic symbol, Ideal Op-Amp, Op-Amp equivalent circuit, Transfer characteristics, Op- Amp parameters- DC – offset voltage & current, compensation for offset voltage, AC parameters- CMRR, slew rate, gain bandwidth product. Thermal drift, Noise.

Closed loop Op-Amp:
Feedback configurations- Inverting, non-inverting & Differential Op-Amp, effect of f/b on different parameters

Frequency Response:
Frequency response, Compensation for frequency, Op-Amp at high frequency, effects of slew rate.
Linear Applications:
Peaking amplifier, summing, scaling, averaging amp, Instrumentation amplifier, Integrator & Differentiator, Log & Antilog amplifier.

Oscillators:
Oscillator principles, Barkhausen criterion, Types- Phase shift, Wien Bridge, Quadrature oscillators. Waveform generators- Square, triangular & sweep generator, Voltage controlled oscillator.

Non-linear applications:
Basic comparator, zero crossing detector, Schmitt trigger, window detector, V/F & F/V converters, sample & hold circuits.

Specialized IC applications:
IC555 timer - monostable & astable multivibrators, applications.

Phase locked loop:
Operating principle, monolithic PLLs, IC565 PLL applications.

Voltage regulators:
Fixed & variable voltage regulators, IC723 voltage regulators.

Power Amplifiers:
Monolithic power amplifiers, LM 380 power amplifier.

References:
1. Ramakant Gayakwad, “Op-Amps and Linear Integrated circuits”, 3rd edition, PHI, 2000. (Rs 195/-)
2. K.R. Botkar, “Integrated Circuits”, 9th Edition, Khanna Publication, 1996. (Rs –150/-)
3. Graeme Tobey, “Operational Amplifier, Design & applications”, 1985.

Numerical Methods

Semester: IV Lect: 4 Hr
Branch: ENC/ CST / IT Cedit: 04

Computer Arithmetic:
Floating-point representation of numbers, arithmetic operations with normalized floating point numbers, consequences, and errors in numbers, Binary representation of numbers, conversions and conclusions.

Iterative Methods:
Introduction, starting an iterative method, method of successive bisection, False-position method, Newton Raphson method, Secant method, Successive approximation method, comparison of iterative methods, solution of non-linear equations
(By Newton Raphson method)

Solution Of Simultaneous Algebraic Equations:
Introduction, Gauss-elimination method, pivoting, Gauss-seidel iterative method, comparison of direct and iterative methods.
Interpolation: Introduction, Lagrange’s interpolation, difference tables, and truncation error in interpolation.

Least Squares Approximation Of Functions:
Introduction, fitting a straight line, polynomial regression, fitting geometric and exponential functions, multiple linear regressions.

Approximation Of Functions:
Introduction, Taylor series representation

Differentiation:
Introduction, formulae for numerical differentiation, numerical integration, Trapezoidal rule, Simpson’s 1/3 rd and 3/8 th rules, Gaussian quadrature formulae, comparison of integration formulae.

Numerical Solution Of Differential Equations:
Introduction, Euler’s method, Taylor series method, Runge-kutta (R-K) second & fourth order formulae, Predictor-corrector (P-C) method, higher order differential equations, comparison of R-K and P-C methods.

Linear Programming:
Transportation problems, PERT/CPM

References:
1. E. Balagurusamy, Numerical Methods, Tata McGraw- Hill, 2001. (Rs.150/-)
2. S. S. Sastry, Introductory Methods of Numerical Analysis, 2nd Edition, PHI, 1997. (Rs. 75/-)
3. V. Rajaraman, Computer Oriented Numerical Methods, 3rd Edition, PHI, 1997. (Rs. 59/-)
4. John H. Mathews, Numerical Methods for Mathematics, Science & Engineering, 2nd Edition, PHI, 1998. (Rs. 175/-)

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