1.

Relations and Functions

3

 

1.1

Introduction

1

 

1.2

Types of Relations

1

 

1.3

Types of Functions

2

 

1.4

Composition of Functions and Invertible Function

2-3

 

1.5

Binary Operations

3

2.

Inverse Trigonometric Functions

1

 

2.1

Introduction

1

 

2.2

Basic Concepts

1

 

2.3

Properties of Inverse Trigonometric Functions

1

3.

Matrices

4

 

3.1

Introduction

1

 

3.2

Matrix

1

 

3.3

Types of Matrices

1

 

3.4

Operation on  Matrices

2

 

3.5

Transpose of a  Matrix

3

 

3.6

Symmetric and Skew Symmetric  Matrices

3

 

3.7

Elementary Operations (Transformation) of a Matrix

4

 

3.8

Invertible  Matrices

4

4.

Determinants

3

 

4.1

Introduction

1

 

4.2

Determinant

1

 

4.3

Properties of  Determinant

1

 

4.4

Area of a Triangle

2

 

4.5

Minors and Cofactors

2

 

4.6

Adjoint and Inverse of a Matrix

3

 

4.7

Applications of  Determinant and Matrices

3

5.

Continuity and Differentiability

4

 

5.1

Introduction

1

 

5.2

Continuity

1

 

5.3

Differentiability

2

 

5.4

Exponential and Logarithmic Functions

3

 

5.5

Logarithmic Differentiation

3

 

5.6

Derivatives of Functions in Parametric Forms

4

 

5.7

Second Order Derivatives

4

 

5.8

Mean Value Theorem

4

6.

Application of Derivatives

3

 

6.1

Introduction

1

 

6.2

Rate of Change of Quantities

1

 

6.3

Increasing and Decreasing Functions

1

 

6.4

Tangents and Normal

2

 

6.5

Approximations

3

 

6.6

Maxima and Minima

3

7.

Integrals

6

 

7.1

Introduction

1

 

7.2

Integration as an Inverse Process of Differentiation

1

 

7.3

Methods of Integration

1-2

 

7.4

Integrals of some Particular Functions

2

 

7.5

Integration by Partial Fractions

3

 

7.6

Integration by Parts

4

 

7.7

Define Integral

5

 

7.8

Fundamental Theorem of Calculus

5

 

7.9

Evaluation of Define Integrals by Substitution

6

 

7.10

Some Properties of Definite Integrals

6

8.

Application of Integrals

1

 

8.1

Intro

1

 

8.2

Area under curve

1

 

8.3

Area between curves

1

9.

Differential Equations

4

 

9.1

Intro

1

 

9.2

Basic concepts

1

 

9.3

General and particular solution of a DE

1-2

 

9.4

Formation of DE whose general solution is given

2

 

9.5

Methods of solving first order, first degree DE

3+4

10.

Vector Algebra

2

 

10.1

Intro

1

 

10.2

Basics concepts

1

 

10.3

Types of vectors

1

 

10.4

Addition of vectors

1

 

10.5

Multiplication of vector by a scalar

2

 

10.6

Product of two vectors

2

11.

Three Dimensional Geometry

4

 

11.1

Intro

1

 

11.2

Direction cosines and ratios of a line

1

 

11.3

Equation of line

1-2

 

11.4

Angle between lines

2

 

11.5

Shortest distance between lines

2-3

 

11.6

Plane

3

 

11.7

Co-planarity in planes

3

 

11.8

Angle between planes

4

 

11.9

Distance of a point from a plane

4

 

11.10

Angle between line and a plane

4

12.

Linear Programming

1-2

 

12.1

Intro

1

 

12.2

LP problems and its mathematical foundation

1

 

12.3

Different types of LPP

1

13.

Probability

5

 

13.1

Intro

1

 

13.2

Conditional Probability

1

 

13.3

Multiplication theorem

2

 

13.4

Independent events

2

 

13.5

Bayes theorem

3

 

13.6

Random variables and probability distribution

4

 

13.7

Bernoulli Trails and binomial distribution

5

 

 

Total Sessions

43