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Wiley's Decoding Mathematics For JEE, Vol II

ISBN: 9788126572441

984 pages

INR 1099

Description

Fundamentals of Mathematics, Volume – II (as per Class 12 syllabus) offers a compelling solution for all CBSE students preparing for JEE and other engineering entrance examinations. The content has been organized to provide a more structured approach to meet the requirements of both JEE and CBSE syllabi. The book offers multidimensional approach of the subject through clear and engaging explanation of concepts aided with interesting coloured figures. Also, the book deals with application-based approach through qualitative problem sets. This book empowers students’ concept building and enhances critical thinking skills in mathematics and its fundamentals.

Chapter 1 Functions

1.1 Introduction

1.2 Defining a Function

1.3 Domain, Codomain and Range of a Function

1.4 Some Useful Types of Functions

1.5 Domain of a Function

1.6 Range of a Function

1.7 Finding Range of a Function

1.8 Classification of Functions

1.9 One–One and Many–One Functions

1.9.3 Methods to Identify One–One or Many–One Functions

1.10 Onto and Into Functions

1.11 Nature of Functions

1.12 Odd and Even Nature of Function

1.13 Periodic Function

1.14 Inverse of a Function

1.15 Inverse Sine Function

1.16 Inverse Cosine Function

1.17 Some Standard Functions along with Their Inverse Functions

1.18 Properties of Inverse Function

1.19 Composite Functions

1.20 Graphical Transformation

1.21 Sequences of Transformations

Chapter 2 Limits, Continuity and Differentiability

2.1 Introduction

2.2 Defining Limits

2.3 Fundamental Theorems of Limits

2.4 Different Strategies to Evaluate Limits

2.5 Continuity of a Function

2.6 Types of Discontinuity

2.7 Theorems on Continuity

2.8 Properties of Function Continuous in [a, b]

2.9 Differentiability of Functions

Chapter 3 Application of Derivatives

3.1 Introduction

3.2 Derivative as Slope of Tangents

3.3 Derivative of a Function

3.4 Theorems of Differentiation

3.5 Chain Rule of Differentiation

3.6 Implicit Differentiation

3.7 Higher Order Derivatives

3.8 Tangent and Normal

3.9 Angle of Intersection of Two Curves

3.10 Length of Tangent, Normal, Subtangent and Subnormal

3.11 Approximation and Differentials

3.12 Monotonicity of a Function

3.13 Greatest Value and Least Value of a Function

3.14 Establishing Inequalities

3.15 Maxima and Minima of a Function

3.16 Rolle’s Theorem

3.17 Lagrange’s Mean Value Theorem (LMVT)

Chapter 4 Indefinite Integrals

4.1 Introduction

4.2 Anti-Derivatives

4.3 Some Standard Integration Formulas

4.4 Integration using Substitution

4.5 Integration by Parts

4.6 Few Useful Trigonometric Formulas

4.7 Some Standard Substitutions Used in Integration

4.8 Integration of Rational Functions

4.9 Some Standard Forms of an Integral

4.10 Integration of Trigonometric Functions

Chapter 5 Definite Integration

5.1 Introduction

5.2 Properties of Definite Integral

5.3 Advanced Properties of Definite Integral

5.4 Definite Integral as the Limit of a Sum

5.5 Method to Express the Infinite Series as Definite Integral

Chapter 6 Area Under the Curve

6.1 Introduction

6.2 Area Bounded by Single Curve

6.3 Area Bounded between Two Curves

Chapter 7 Differential Equations

7.1 Introduction

7.2 Introduction of a Differential Equation

7.3 Order and Degree of a Differential Equation

7.4 Formation of Differential Equation

7.5 Solution of a Differential Equation

7.6 General Solution

7.7 Particular Solution

7.8 Differential Equations in Variables Separable Form

7.9 Differential Equation Reducible to Variables Separable Form

7.10 Homogeneous Differential Equation

7.11 Solution of Homogeneous Differential Equation

7.12 Linear and Non-Linear Differential Equations

7.13 Procedure to Find the Orthogonal Trajectory of a Curve

7.14 Solution by Inspection

7.15 First-Order Differential Equations – Real-Life Applications

Chapter 8 Matrices

8.1 Introduction

8.2 Definition of Matrix

8.3 Types of Matrices

8.4 Operations on Matrices

8.5 Addition and Subtraction of Matrices

8.6 Scalar Multiplication of Matrices

8.7 Multiplication of Two Matrices

8.8 Types of Matrices Based on Operations

8.9 Determinants of a Matrix

8.10 Minor, Cofactor and Adjoint of Matrices

8.11 Inverse of a Matrix

8.12 Consistent System of Equations

8.13 Homogeneous System of Equations

Chapter 9 Determinants

9.1 Introduction

9.2 Determinants

9.3 Properties of Determinants

9.4 Area of a Triangle in Determinant Form

9.5 Product of Two Determinants

9.6 Differentiation of a Determinant

9.7 Summation of Determinants

9.8 Determinants Involving Integrations

9.9 Special Determinants

9.10 Solution of Equations Using Determinant Method

Chapter 10 Vectors

10.1 Introduction

10.2 Geometric Description of Vectors

10.3 Types of Vectors

10.4 Properties of Vectors

10.5 Vectors in Three-Dimensions

10.6 Dot Product

10.7 Cross Product of Vectors

10.8 Scaler Triple Product

10.9 Vector Triple Product

10.10 Geometrical Applications

10.11 Application of Vectors in Mechanics

10.12 Equations of Lines and Planes

Chapter 11 Three-Dimensional Geometry

11.1 Introduction to Three-Dimensional Rectangular Coordinate System

11.2 Direction Cosines of a Straight Line

11.3 Direction Ratios

11.4 Area of a Triangle

11.5 Equations of Straight Lines

11.6 Angle between Two Lines

11.7 Shortest Distance between Two Lines

11.8 The Plane

11.9 Equation of Plane in Different Forms

11.10 Angle between Two Planes

11.11 Plane and Line

11.12 Point and Plane

11.12.3 Perpendicular Distance between a Point and a Plane

11.13 Sphere

Chapter 12 Probability

12.1 Introduction

12.2 Basic Terminology

12.3 Probability Experiment

12.4 Classical Approach to Probability

12.5 Notation in Probability

12.7 Dependent and Independent Events

12.8 Conditional Probability

12.9 Multiplication Rule

12.10 Pairwise and Mutually Independent Events

12.11 Law of Total Probability

12.12 Bayes’ Theorem

12.13 Probability Distribution of a Random Variable

12.14 Geometrical Application and Mixed Approach Problems

Chapter 13 Principle of Mathematical Induction

13.1 Introduction

13.2 Principle of Mathematical Induction

Chapter 14 Mathematics Reasoning

14.1 Introduction

14.2 Sentence

14.3 Statement

14.4 Basic Logical Connectives or Logical Operators

14.5 Negation

14.6 Conditional or Implication Statements

14.7 Bi-Conditional or Equivalence Statement

14.8 Negation of Conditional Statement

14.9 Special Types of Compound Statements

14.10 Logical Equivalence

14.11 Quantifiers

Chapter 15 Statistics

15.1 Introduction

15.2 Variables

15.3 Frequency Distribution

15.4 Statistical Terms

15.5 Average of Discrete Data

15.6 Measure of Dispersion

15.7 Relative Frequency

15.8 Relation between Mean, Median and Mode

Solved Examples

Practice Questions

Important Formulas

Chapter Exercise

Previous Years’ JEE Main Questions (2008–2018)

Concept Map

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