Description
Wiley Wiley Acing The Gate: Electrical Engineering, 2Ed (Combo) by Dr.Debashis Chatterjee
Wiley’s Acing the GATE Examination in Electrical Engineering is intended to be the complete book for those aspiring to compete in the Graduate Aptitude Test in Engineering (GATE) in Electrical Engineering discipline. It comprehensively covers all the topics as prescribed in the latest GATE syllabus in terms of study material, quick reference material and an extensive question bank, complete with solutions. The book offers a number of useful features and the approach is logical concept building rather than only formula based, as offered by the other books generally published in this domain.
Wiley Acing the GATE: Engineering Mathematics and General Aptitude is intended to be the complete book for those aspiring to compete in the Graduate Aptitude Test in Engineering (GATE) in various engineering disciplines, including Electronics and Communication, Electrical, Mechanical, Computer Science, Civil, Chemical and Instrumentation, comprehensively covering all topics as prescribed in the syllabus in terms of study material and an elaborate question bank. The book presents the subjects of Engineering Mathematics and General Aptitude in a systematic, structured and precise manner.
About the Author
Dr. Debashis Chatterjee is Professor at the Department of Electrical Engineering
Table of Contents
Preface
About the Authors
Acing the GATE 2018
Syllabus for Electrical Engineering (EE)
Section 1: Electric Circuits
1. Electric Circuits
Circuit Concepts and Laws
Circuit Analysis Techniques
Topology
Network Theorems
Laplace Transform
Transient Response to DC and AC Networks
Sinusoidal Steady State Analyses Using Phasors
Magnetically Coupled Circuits
Resonance
Filters
Three-Phase Circuits
AC Power Analysis
Two-Port Network
Section 2: Electromagnetic Fields
2 Electromagnetic Fields
Coulomb’s Law
Electric Field Intensity
Electric Flux Density
Divergence and Curl
Divergence and Stokes’ Theorems
Gauss’ Law
Electric Field and Potential
Capacitance
Magnetic Flux and Magnetic Field
Biot—Savart Law
Ampere’s Law
Faraday’s Law and Lenz’s Law of Electromagnetic Induction
Lorentz Force
Maxwell’s Equations
Poynting Vector
Inductance
Self and Mutual Inductance for Simple Configurations
Magnetic Circuit and Magnetomotive Force
Important Formulas
Solved Examples
Practice Exercises
Answers to Practice Exercises
Solved GATE Previous Years’ Questions
Section 3: Signals and Systems
3 Signals and Systems
Elementary Signals
Classification of Signals
System
Time Domain Representation of Linear Time Invariant System
Continuous-Time Fourier Series
Discrete-Time Fourier Series
Continuous-Time Fourier Transform
Discrete-Time Fourier Transform
Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
Sampling Theorem for Continuous-Time Signal
Laplace Transform
Z-Transform and its Application to the Analysis of LTI System
Section 4: Electrical Machines
4 Electrical Machines
Transformer
DC Machines
Three Phase Induction Machines
Single-Phase Induction Motor
Synchronous Machines
Stepper and Servo Motors
Section 5: Power Systems
5 Power Systems
Power Generation Concepts
Transmission Line Parameters
Transmission Lines
AC and DC Transmission Concepts
Insulated Cables
Electric Line Insulators
Distribution Systems
PU (Per Unit System)
Bus Admittance Matrix
Voltage Control
Frequency Control
Power System Stability Concepts
Power Factor Correction
Symmetrical Components
Faults
Relays
Protection
Circuit Breakers
High Voltage Direct Current Transmission
Section 6: Control Systems
6 Control Systems
Fundamentals
Time-Response Analysis
Stability of Control Systems
Root Locus Technique
Frequency Response Analysis
Bode Plots
Compensators
State Space Representation
Section 7: Electrical and Electronic Measurements
7 Electrical and Electronic Measurements
Classification of Measuring Instruments
Types of Indicating Instruments
Bridges and Potentiometers
Measurement of Current and Voltage
Measurement of Power and Energy
Instrument Transformers
Digital Voltmeters and Multimeters
Cathode Ray Oscilloscope
Q-Meter
Transducers
Error Analysis
Section 8A: Analog Electronics
8 Analog Electronics
Semiconductor Physics
Semiconductor Diodes
Transistors
Field-Effect Transistor (JFET and MOSFET)
Simple Diode Circuits
Stability and Biasing
Amplifiers
Frequency Response
Active Filters
Oscillators
Multivibrators
Section 8B: Digital Electronics
9 Digital Electronics
Number Systems
Boolean Algebra
Logic Gates
Logic Families
Combinational Logic Circuits
Memory
Sequential Logic Circuits
D/A and A/D Converters
Microprocessors
8085 Microprocessors
Memory Interfacing
Section 9: Power Electronics
10 Power Electronics
Power Semiconductor Devices
Bipolar Junction Transistor
Thyristors
TRIAC
Gate Turn-OFF Thyristor (GTO)
Power Metal Oxide Semiconductor Field Effect Transistors (MOSFETS)
Insulated Gate Bipolar Transistor (IGBT)
Performance Parameters
Converters: AC-DC Rectifiers
DC to DC Conversion
Important Formulas
Solved Examples
Practice Exercises
Answers to Practice Exercises
Solved GATE Previous Years’ Questions
Index
Preface
Engineering Mathematics
1 Linear Algebra
Matrix
Determinants
Solutions of Simultaneous Linear Equations
Augmented Matrix
Gauss Elimination Method
Cayley—Hamilton Theorem
Eigenvalues and Eigenvectors
2 Calculus
Limits
Properties of Limits
Continuity and Discontinuity
Differentiability
Mean Value Theorems
Fundamental Theorem of Calculus
Differentiation
Applications of Derivatives
Partial Derivatives
Integration
Methods of Integration
Definite Integrals
Improper Integrals
Double Integration
Change of Order of Integration
Triple Integrals
Applications of Integrals
Fourier Series
Vectors
Line Integrals
Surface Integrals
Stokes’ Theorem
Green’s Theorem
Gauss Divergence Theorem
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
3 Differential Equations
Introduction
Solution of a Differential Equation
Linear Differential Equation
Particular Integrals
Homogeneous Linear Equation
Bernoulli’s Equation
Euler—Cauchy Equations
Solving Differential Equations Using Laplace Transforms
Variation of Parameters Method
Separation of Variables Method
One-Dimensional Diffusion (Heat Flow) Equation
Second Order One-Dimensional Wave Equation
Two-Dimensional Laplace Equation
Solved Examples
Practice Exercises
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
4 Complex Variables
Introduction
Complex Functions
Exponential Function of Complex Variables
Circular Function of Complex Variables
Hyperbolic Functions of Complex Variables
Logarithmic Function of Complex Variables
Limit and Continuity of Complex Functions
Derivative of Complex Variables
Cauchy—Riemann Equations
Integration of Complex Variables
Cauchy’s Theorem
Cauchy’s Integral Formula
Taylor’s Series of Complex Variables
Laurent’s Series of Complex Variables
Zeros and Poles of an Analytic Function
Residues
Residue Theorem
Calculation of Residues
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
5 Probability and Statistics
Fundamentals of Probability
Types of Events
Approaches to Probability
Axioms of Probability
Conditional Probability
Geometric Probability
Rules of Probability
Statistics
Arithmetic Mean
Median
Mode
Relation between Mean, Median and Mode
Geometric Mean
Harmonic Mean
Range
Mean Deviation
Standard Deviation
Coefficient of Variation
Probability Distributions
Random Variable
Properties of Discrete Distribution
Properties of Continuous Distribution
Types of Discrete Distribution
Types of Continuous Distribution
Correlation and Regression Analyses
Correlation
Lines of Regression
Hypothesis Testing
Hypothesis Testing Procedures for Some Common Statistical Problems
Hypothesis Testing of a Proportion
Hypothesis Testing of a Mean
Hypothesis Testing of Difference Between Proportions
Hypothesis Testing of Difference Between Means
Bayes’ Theorem
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
6 Numerical Methods
Introduction
Numerical Solution of System of Linear Equations
Gauss Elimination Method
Matrix Decomposition Methods (LU Decomposition Method)
Gauss—Jordan Method
Iterative Methods of Solution
Numerical Solution of Algebraic and Transcendental Equations
Bisection Method
Regula—Falsi Method (Method of False Position Method)
Newton—Raphson Method
Secant Method
Jacobian
Numerical Integration
Newton—Cotes Formulas (General Quadrature)
Rectangular Rule
Trapezoidal Rule
Simpson’s Rule
Numerical Solution of Ordinary Differential Equation (O.D.E.)
Picard’s Method
Euler’s Method
Runge—Kutta Method
Euler’s Predictor—Corrector Method
Accuracy and Precision
Classification of Errors
Significant Figures
Measuring Error
Propagation of Errors
Method of Least Square Approximation
Lagrange Polynomials
Numerical Differentiation
Newton’s Forward Formula
Newton’s Backward Formula
Stirling’s or Bessel’s Formula
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
7 Mathematical Logic
Introduction
Statements
Atomic Statements
Molecular Statements
Truth Table
Truth Values
Connectives
Types of Connectives
Well-Formed Formulas
Duality Law
Equivalent Well-Formed Formula
Logical Identities
Normal Form
Disjunction Normal Form
Conjunctive Normal Form
Propositional Calculus
Rules of Inference
Predicate Calculus
Predicates
Quantifier
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
8 Set Theory and Algebra
Introduction to Set Theory
Subsets and Supersets
Equal Sets
Comparable Sets
Universal Set
Power Set
Types of Sets
Operations on Sets
Important Laws and Theorems
Venn Diagrams
Operations on Sets Using Venn Diagrams
Application of Sets
Cartesian product of Sets
Relations
Types of Relations
Properties of Relation
Functions
Types of Functions
Compositions of Functions
Introduction to Algebra
Semigroups
Some Important Theorems
Group
Some Important Theorems
Residue Classes
Residue Class Addition
Residual Class Multiplication
Partial Ordering
Hasse Diagram
Lattice
Sublattice
Bounds
Boolean algebra of Lattices
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
9 Combinatory
Introduction
Counting
Fundamental Principle of Addition
Fundamental Principle of Multiplication
Permutations
Conditional Permutations
Permutations when all Objects are not Distinct
Circular Permutations
Combinations
Properties of Combinations
Conditional Combinations
Generating Functions
Ordinary Generating Function
Exponential Generating Function
Poisson Generating Function
Recurrence Relation
Logistic Map
Fibonacci Numbers
Binomial Coefficients
Summation
Asymptotic Analysis
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
10 Graph Theory
Introduction
Fundamental Concepts of Graph
Common Terminologies
Degree of a Vertex
Multigraph
Walks, Paths and Connectivity
Subgraph
Types of Graphs
Complete Graph
Regular Graph
Bipartite Graph
Tree Graph
Trivial Graph
Cycle
Operations on Graphs
Matrix Representation of Graphs
Adjacent Matrix
Incidence Matrix
Cuts
Spanning Trees and Algorithms
Kruskal’s Algorithm
Prim’s Algorithm
Binary Trees
Euler Tours
Konigsberg Bridge Problem
Hamiltonian Graphs
Closure of a Graph
Graph Isomorphism
Homeomorphic Graphs
Planar Graphs
Matching
Covering
Independent Set
Graph Coloring
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
Chapter 11 Transform Theory
Introduction
Laplace Transform
Laplace Transform of Common Signals
Properties of Laplace Transform
Inverse Laplace Transform
z -Transform
z -Transform of Common Sequences
Properties of z -Transform
Inverse z-Transform
Relationship between z-Transform and Laplace Transform
Fourier Transform
Convergence of Fourier Transforms
Properties of Fourier Transform
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
General Aptitude: Verbal Ability
1 English Grammar
Articles
Noun
Use of Nouns in Singular Form
Use of Nouns in Plural Form
Conversion of Nouns from Singular to Plural
Collective Nouns
Pronoun
Personal Pronoun
Reflexive and Emphatic Pronoun
Demonstrative Pronoun
Indefinite Pronoun
Distributive Pronoun
Relative Pronoun
Interrogative Pronoun
Use of Pronouns
Adjective
Use of Adjectives
Preposition
Preposition of Time
Preposition of Position
Preposition of Direction
Other Uses of Preposition
Verbs
Use of Verb
Use of Infinitives
Use of Gerunds
Tenses
Use of Tenses
Adverbs
Practice Exercise
2 Synonyms
Tips to Solve Synonym Based Questions
3 Antonyms
Graded Antonyms
Complementary Antonyms
Relational Antonyms
Practice Exercise
4 Sentence Completion
Tips to Solve Sentence Completion Based Questions
5 Verbal Analogies
Types of Analogies
Tips to Solve Verbal Analogies Questions
6 Word Groups
7 Verbal Deduction
Tips and Tricks to Solve Verbal Deduction Questions
General Aptitude: Numerical Ability
Unit 1: Basic Arithmetic
1 Number System
Numbers
Classification of Numbers
Progressions
Arithmetic Progressions
Geometric Progressions
Infinite Geometric Progressions
Averages, Mean, Median and Mode
Relation between AM, GM and HM
Some Algebraic Formulas
The Remainder Theorem
The Polynomial Factor Theorem
Base System
Counting Trailing Zeros
Inequations
Quadratic Equations
Even and Odd Numbers
Prime Numbers and Composite Numbers
HCF and LCM of Numbers
Cyclicity
Test for Divisibility
2 Percentage
Introduction
Some Important Formulae
3 Profit and Loss
Introduction
Some Important Formulae
Margin and Markup
4 Simple Interest and Compound Interest
Introduction
Some Important Formulae
5 Time and Work
Introduction
Important Formulas and Concepts
6 Average, Mixture and Alligation
Average
Weighted Average
Mixture and Alligation
7 Ratio, Proportion and Variation
Ratio
Proportion
Variation
8 Speed, Distance and Time
Introduction
Some Important Formulas
Unit 2: Algebra
1 Permutation and Combination
Permutation
Combination
Partitions
Counting
Fundamental Principle of Addition
Fundamental Principle of Multiplication
2 Progression
Arithmetic Progression
Geometric Progression
Infinite Geometric Progression
Harmonic Series
Relation between AM, GM and HM
3 Probability
Introduction
Some Basic Concepts of Probability
Some Important Theorems
4 Set Theory
Introduction
Venn Diagrams
Operation on Sets
Venn Diagram with Two Attributes
Venn Diagram with Three Attributes
5 Surds, Indices and Logarithms
Surds
Logarithm
Unit 3: Reasoning and Data Interpretation
1 Cubes and Dices
Cubes
Dices
2 Line Graph
Introduction
3 Tables
Introduction
4 Blood Relationship
Introduction
Standard Coding Technique
5 Bar Diagram
Introduction
6 Pie Chart
Introduction
Types of Pie Charts
3-D Pie Chart
Doughnut Chart
Exploded Pie Chart
Polar Area Chart
Ring Chart/Multilevel Pie Chart
7 Puzzles
Introduction
Types of Puzzles
8 Analytical Reasoning
Introduction
General Aptitude: Solved Gate Previous Years’ Questions