Description
Wiley Wiley Acing The Gate: Mechanical Engineering, 2Ed (Combo) by Ajay Kumar Tamrakar
This book is aimed to present the topics of Mechanical Engineering in a systematic, integrated and precise manner, primarily to meet the requirements of the aspirants of GATE (ME) and help them qualify the examination without unreasonable strain. The book is a self-explanatory and a fully-competent text for similar competitive examinations and undergraduate courses in mechanical engineering. The book helps to solve problems faced by aspirants in terms of extensive syllabus coverage, existing incongruity with syllabus, unavailability of a standard book, etc. Throughout the content, an intuitive and systematic approach is used to reinforce the fundamental concepts.
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
Ajay Kumar Tamrakar is currently serving Indian Railways as Senior Divisional Mechanical Engineer at Bhopal Division of West Central Railway
Table of Contents
Preface
Acknowledgments
About the Authors
Acing the GATE
Syllabus of GATE (Mechanical Engineering)
Trend of Topics (2014-17)
Methodological Concepts of Engineering Studies
Part I Applied Mechanics & Design
1 Engineering Mechanics
1.1 Force
1.2 Moment of a Force
1.3 Equivalent System of a Force
1.4 Single Resultant Force
1.5 Equilibrium of Rigid Bodies
1.6 Structural Analysis
1.7 Rectilinear Kinematics
1.8 Angular Motion
1.9 Motion Under Gravity
1.10 Dependent Motion of Particles
1.11 Newton’s Laws of Motion
1.12 Work and Energy
1.13 D’Alembert’s Principle
1.14 Impulse and Momentum
1.15 Law of Restitution
1.16 Principle of Virtual Work
2 Strength of Materials
2.1 Stress and Strain
2.2 Dynamic Loading
2.3 Bi-Axial Stress and Strain
2.4 Mohr’s Circle
2.5 Beam Loading
2.6 Theory of Bending
2.7 Beam Deflection
2.8 Torsion in Shafts
2.9 Combined Stresses
2.10 Thick-Walled Shells
2.11 Thin-Walled Shells
2.12 Struts and Columns
3 Theory of Machines
3.1 Mechanisms and Machines
3.2 Universal Joint
3.3 Kinematic Analysis
3.4 Cam Follower Mechanism
3.5 Gears
3.6 Dynamic Analysis of Slider Crank Mechanism
3.7 Flywheel
3.8 Belt Drive
3.9 Friction
3.10 Governor
3.11 Balancing of Masses
3.12 Gyroscopic Effects
4 Vibrations
4.1 Fundamentals
4.2 Undamped Free Vibration
4.3 Free Damped Vibration
4.4 Forced Vibration
5 Machine Design
5.1 Static Loading
5.2 Dynamic Loading
5.3 Riveted Joints
5.4 Welded Joints
5.5 Threaded Joints
5.6 Design of Shafts
5.7 Design of Keys
5.8 Design of Gears
5.9 Rolling Contact Bearing
5.10 Sliding Contact Bearing
5.11 Brakes and Clutches
Part II Fluid Mechanics & Thermal Sciences
6 Fluid Mechanics
6.1 Fluid Properties
6.2 Fluid Pressure
6.3 Buoyancy and Floatation
6.4 Solid Body Motions
6.5 Kinematics of Fluid Flow
6.6 Motion of Fluid Particles
6.7 Principles of Fluid Flow
6.8 Flow Measurements
6.9 Vortex Motion
6.10 Flow from a Line Source
6.11 Laminar Pipe Flow
6.12 Stokes’ Law
6.13 Boundary Layer Theory
7 Heat Transfer
7.1 Modes of Heat Transfer
7.2 Conduction
7.3 Convection
7.4 Radiation
7.5 Heat Exchanger
8 Thermodynamics
8.1 Basic Concepts
8.2 Zeroth Law of Thermodynamics
8.3 Energy Transfer
8.4 First Law of Thermodynamics
8.5 Second Law of Thermodynamics
8.6 Third Law of Thermodynamics
8.7 Exergy and Irreversibility
8.8 Properties of Gases
8.9 Thermodynamic Relations
8.10 Gas Compression
8.11 Brayton Cycle
9 Applications
9.1 Power Engineering
9.2 Internal Combustion Engines
9.3 Refrigeration and Air Conditioning
9.4 Turbomachinery
Part III Manufacturing & Industrial Engineering
10 Engineering Materials
10.1 Atomic Structure
10.2 Crystal Structure
10.3 Crystal Imperfections
10.4 Effects of Imperfections
10.5 Grain Formation
10.6 Grain Size Measurement
10.7 Grain Structure
10.8 Deformation
10.9 Multiphase Structure
10.10 Iron-Carbon Phase
10.11 Heat Treatment of Steel
10.12 Alloying of Steels
10.13 Mechanical Properties
10.14 Engineering Metals
10.15 Ceramics
10.16 Polymers
10.17 Composites
11 Metal Casting
11.1 Elements of Casting
11.2 Sand Casting
11.3 Pattern
11.4 Molding Sand
11.5 Gating System
11.6 Casting Methods
11.7 Casting Defects
11.8 Inspection of Casting
12 Forming
12.1 Rolling
12.2 Forging
12.3 Extrusion
12.4 Wire Drawing
12.5 Sheet Metal Forming
12.6 High-Energy Rate Forming
12.7 Powder Metallurgy
13 Joining
13.1 Welding
13.2 Brazing
13.3 Soldering
14 Machining
14.1 Mechanism of Metal Cutting
14.2 Cutting Heat
14.3 Tool Materials
14.4 Cutting Fluids
14.5 Cutting Tool Geometry
14.6 Machinability
14.7 Economics of Machining
14.8 Machining Processes
14.9 Finishing Operations
14.10 Modern Machining Processes
14.11 Jigs and Fixtures
15 Metrology and Inspection
15.1 Limits, Tolerances and Fits
15.2 Linear Measurement
15.3 Angular Measurement
15.4 Gauge Design
15.5 Interferometry
15.6 Surface Measurement
16 Computer Integrated Manufacturing
16.1 Computer Integrated Manufacturing
16.2 Computer Aided Design
16.3 Computer Aided Manufacturing
16.4 Integration of CAD and CAM Systems
16.5 Numerical Control
16.6 Group Technology
17 Production Planning & Control
17.1 Functions of PPC
17.2 Forecasting
17.3 Aggregate Planning
17.4 Disaggregation
17.5 Material Requirement Planning
17.6 Break-even Point Analysis
17.7 Lot Sizing Rules
17.8 Assembly Line Balancing
18 Inventory Control
18.1 Basic Concepts
18.2 EOQ Models
18.3 Probabilistic Inventory Models
18.4 Selective Approaches
18.5 Just-In-Time Production
19 Operations Research
19.1 Simplex Method
19.2 Transportation Problem
19.3 Assignment Problem
19.4 Sequencing
19.5 Queuing Theory
19.6 PERT and CPM
Important Formulas
Solved Examples
GATE Previous Years’ Questions
Multiple Choice Questions
Numerical Answer Questions
Answers
Explanations and Hints
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