# Wiley Acing the GATE: Engineering Mathematics and General Aptitude, 2ed, 2021

ISBN: 9788126572267

984 pages

## Description

The book presents the subjects of Engineering Mathematics and General Aptitude in a systematic, structured and precise manner. It intends to offer GATE aspirants a self-study and do-it-yourself approach by providing comprehensive and step-by-step treatment of each and every aspect of the GATE examination. In addition, the book aims to solve problems faced by aspirants in terms of extensive syllabus coverage of major engineering branches and unavailability of a standard book.

1. Linear Algebra

Matrix

Determinants

Solutions of Simultaneous Linear Equations

Augmented Matrix

Gauss Elimination Method

Cayley—Hamilton Theorem

Eigenvalues and Eigenvectors

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

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

Limit and Continuity of Complex Functions

Derivative of Complex Variables

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

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

5. Probability and Statistics

Fundamentals of Probability

Statistics

Probability Distributions

Correlation and Regression Analyses

Hypothesis Testing

Hypothesis Testing Procedures for Some Common Statistical Problems

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

Numerical Solution of Algebraic and Transcendental Equations

Numerical Integration

Numerical Solution of Ordinary Differential Equation (O.D.E.)

Accuracy and Precision

Classification of Errors

Significant Figures

Measuring Error

Propagation of Errors

Method of Least Square Approximation

Lagrange Polynomials

Numerical Differentiation

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

7. Mathematical Logic

Introduction

Statements

Connectives

Well-Formed Formulas

Logical Identities

Propositional Calculus

Predicate Calculus

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

8. Set Theory and Algebra

Introduction to Set Theory

Operations on Sets

Important Laws and Theorems

Venn Diagrams

Application of Sets

Cartesian Product of Sets

Relations

Functions

Introduction to Algebra

Semigroups

Group

Residue Classes

Partial Ordering

Lattice

Boolean Algebra of Lattices

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

9. Combinatory

Introduction

Counting

Permutations

Combinations

Generating Functions

Recurrence Relation

Summation

Asymptotic Analysis

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

10. Graph Theory

Introduction

Fundamental Concepts of Graph

Walks, Paths and Connectivity

Subgraph

Types of Graphs

Cycle

Operations on Graphs

Matrix Representation of Graphs

Cuts

Spanning Trees and Algorithms

Binary Trees

Euler Tours

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

11. Transform Theory

Introduction

Laplace Transform

z -Transform

Fourier Transform

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Solved GATE Previous Years’ Questions

General Aptitude: VERBAL ABILITY

1. English Grammar

Articles

Noun

Pronoun

Adjective

Preposition

Verbs

Tenses

Adverbs

Practice Exercise

Answers

2. Synonyms

Tips to Solve Synonym Based Questions

Practice Exercise

Answers

3. Antonyms

Graded Antonyms

Complementary Antonyms

Relational Antonyms

Practice Exercise

Answers

4. Sentence Completion

Tips to Solve Sentence Completion Based Questions

Practice Exercise

Answers

5. Verbal Analogies

Types of Analogies

Tips to Solve Verbal Analogies Questions

Practice Exercise

Answers

Explanations and Hints

6. Word Groups

Practice Exercise

Answers

Explanations and Hints

7. Verbal Deduction

Tips and Tricks to Solve Verbal Deduction Questions

Practice Exercise

Answers

Explanations and Hints

General Aptitude: NUMERICAL ABILITY

Unit 1: Basic Arithmetic

1. Number System

Numbers

Progressions

Averages, Mean, Median and Mode

Some Algebraic Formulas

Base System

Inequations

Quadratic Equations

Even and Odd Numbers

Prime Numbers and Composite Numbers

HCF and LCM of Numbers

Cyclicity

Test for Divisibility

Solved Examples

Practice Exercise

Answers

Explanations and Hints

2. Percentage

Introduction

Some Important Formulae

Solved Examples

Practice Exercise

Answers

Explanations and Hints

3. Profit and Loss

Introduction

Some Important Formulae

Margin and Markup

Solved Examples

Practice Exercise

Answers

Explanations and Hints

4. Simple Interest and Compound Interest

Introduction

Some Important Formulae

Solved Examples

Practice Exercise

Answers

Explanations and Hints

5. Time and Work

Introduction

Important Formulas and Concepts

Solved Examples

Practice Exercise

Answers

Explanations and Hints

6. Average, Mixture and Alligation

Average

Mixture and Alligation

Solved Examples

Practice Exercise

Answers

Explanations and Hints

7. Ratio, Proportion and Variation

Ratio

Proportion

Variation

Solved Examples

Practice Exercise

Answers

Explanations and Hints

8. Speed, Distance and Time

Introduction

Some Important Formulas

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Unit 2: Algebra

1. Permutation and Combination

Permutation

Combination

Partitions

Counting

Fundamental Principle of Addition

Fundamental Principle of Multiplication

Solved Examples

Practice Exercise

Answers

Explanations and Hints

2. Progression

Arithmetic Progression

Geometric Progression

Infinite Geometric Progression

Harmonic Series

Relation between AM, GM and HM

Solved Examples

Practice Exercise

Answers

Explanations and Hints

3. Probability

Introduction

Some Basic Concepts of Probability

Some Important Theorems

Solved Examples

Practice Exercise

Answers

Explanations and Hints

4. Set Theory

Introduction

Venn Diagrams

Operation on Sets

Venn Diagram with Two Attributes

Venn Diagram with Three Attributes

Solved Examples

Practice Exercise

Answers

Explanations and Hints

5. Surds, Indices and Logarithms

Surds

Indices

Logarithm

Solved Examples

Practice Exercise

Answers

Explanations and Hints

Unit 3: Reasoning and Data Interpretation

1. Cubes and Dices

Cubes

Dices

Solved Examples

Practice Exercise

Answers

Explanations and Hints

2. Line Graph

Introduction

Solved Examples

Practice Exercise

Answers

Explanations and Hints

3. Tables

Introduction

Solved Examples

Practice Exercise

Answers

Explanations and Hints

4. Blood Relationship

Introduction

Standard Coding Technique

Solved Examples

Practice Exercise

Answers

Explanations and Hints

5. Bar Diagram

Introduction

Solved Examples

Practice Exercise

Answers

Explanations and Hints

6. Pie Chart

Introduction

Types of Pie Charts

Solved Examples

Practice Exercise

Answers

Explanations and Hints

7. Puzzles

Introduction

Types of Puzzles

Solved Examples

Practice Exercise

Answers

Explanations and Hints

8. Analytical Reasoning

Introduction

Solved Examples

Practice Exercise

Answers

Explanations and Hints

GENERAL APTITUDE: SOLVED GATE PREVIOUS YEARS’ QUESTIONS

APPENDIX — GATE 2018 PAPERS

Solved GATE (CS) 2018

Solved GATE (EC) 2018

Solved GATE (EE) 2018

Solved GATE (ME) 2018 Morning Shift

Solved GATE (ME) 2018 Afternoon Shift

Solved GATE (CE) 2018 Morning Shift

Solved GATE (CE) 2018 Afternoon Shift

APPENDIX — GATE 2019 PAPERS

Solved GATE (CS) 2019

Solved GATE (EC) 2019

Solved GATE (EE) 2019

Solved GATE (ME) 2019 Morning Shift

Solved GATE (ME) 2019 Afternoon Shift

Solved GATE (CE) 2019 Morning Shift

Solved GATE (CE) 2019 Afternoon Shift

APPENDIX — GATE 2020 PAPERS

Solved GATE (CS) 2020

Solved GATE (EC) 2020

Solved GATE (EE) 2020

Solved GATE (ME) 2020 Morning Shift

Solved GATE (ME) 2020 Afternoon Shift

Solved GATE (CE) 2020 Morning Shift

Solved GATE (CE) 2020 Afternoon Shift