# Wiley Acing the GATE: Engineering Mathematics and General Aptitude, 2ed (Reprint 2019)

ISBN: 9788126573622

898 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. The emphasis on fundamental concepts helps in developing the aptitude required for success in GATE. The book has all the three important 'C' qualities, that is Conciseness, Completeness and Correctness.

Preface

Engineering Mathematics

1 Linear Algebra

- Matrix
- Determinants
- 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

3 Differential Equations

- 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

4 Complex Variables

- 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

5 Probability and Statistics

- Fundamentals of Probability
- Statistics
- Probability Distributions
- Correlation and Regression Analyses
- Hypothesis Testing
- Hypothesis Testing Procedures for Some Common Statistical Problems

6 Numerical Methods

- 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

7 Mathematical Logic

- Statements
- Connectives
- Well-Formed Formulas
- Logical Identities
- Propositional Calculus
- Predicate Calculus

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

9 Combinatory

- Counting
- Permutations
- Combinations
- Generating Functions
- Recurrence Relation

10 Graph Theory

- 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

Chapter 11 Transform Theory

- Introduction
- Laplace Transform
- z -Transform
- Fourier Transform

General Aptitude: Verbal Ability

1 English Grammar

- Articles
- Noun
- Pronoun
- Adjective
- Preposition
- Verbs
- Tenses

2 Synonyms

3 Antonyms

4 Sentence Completion

5 Verbal Analogies

6 Word Groups

7 Verbal Deduction

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

3 Profit and Loss

4 Simple Interest and Compound Interest

5 Time and Work

6 Average, Mixture and Alligation

7 Ratio, Proportion and Variation

8 Speed, Distance and Time

Unit 2: Algebra

1 Permutation and Combination

2 Progression

3 Probability

4 Set Theory

5 Surds, Indices and Logarithms

Unit 3: Reasoning and Data Interpretation

1 Cubes and Dices

2 Line Graph

3 Tables

4 Blood Relationship

5 Bar Diagram

6 Pie Chart

7 Puzzles

8 Analytical Reasoning

General Aptitude: Solved Gate Previous Years’ Questions

Solved GATE 2018 paper.