#### Topics

##### Mathematical Logic

##### Mathematical Logic

##### Matrices

- Determinant of a Matrix
- Types of Matrices
- Algebra of Matrices
- Properties of Matrices
- Elementary Transformations
- Inverse of Matrix
- Application of Matrices

##### Differentiation

- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative

##### Applications of Derivatives

- Introduction of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima
- Application of Derivatives to Economics

##### Integration

##### Definite Integration

- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals

##### Applications of Definite Integration

- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves

##### Differential Equation and Applications

- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations

##### Matrices

##### Commission, Brokerage and Discount

- Commission and Brokerage Agent
- Discount

##### Insurance and Annuity

- Concept of Insurance
- Fire Insurance
- Accident Insurance
- Marine Insurance
- Annuity

##### Linear Regression

- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients

##### Time Series

- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend

##### Index Numbers

- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number

##### Linear Programming

- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem

##### Assignment Problem and Sequencing

- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence

##### Probability Distributions

- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
- Expected Value and Variance of a Random Variable

##### Continuity

##### Differentiation

##### Applications of Derivative

##### Indefinite Integration

- Definition of an Integral
- Integral of Standard Functions
- Rules of Integration
- Methods of Integration
- Integration by Parts

##### Definite Integrals

##### Ratio, Proportion and Partnership

##### Commission, Brokerage and Discount

##### Insurance and Annuity

- Insurance and Annuity

##### Demography

- Concept of Demography
- Uses of Vital Statistics in Demography
- Measurements of Mortality
- Life Tables

##### Bivariate Data and Correlation

##### Regression Analysis Introduction

- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Regression Coefficient of X on Y and Y on X
- Regression Propertise

##### Random Variable and Probability Distribution

##### Management Mathematics

- Inequations in Management Mathematics
- Linear Programming Problem in Management Mathematics
- Assignment Problem
- Sequencing in Management Mathematics

## Definition

Suppose f is a real valued function and a is a point in its domain of definition. The derivative of f at a is defined by

`lim_(h -> 0 ) [ f(a+h) - f(a)]/ h`

provided this limit exists. Derivative of f (x) at a is denoted by f ′ (a).

**Defination -**

Suppose f is a real valued function, the function defined by

`lim_(h -> 0 ) [f(x + h) - f(x)]/h`

wherever the limit exists is defined to be the derivative of f at x and is denoted by f ′ (x). This definition of derivative is also called the first principle of derivative.

Thus f ' (x) = `lim _( h -> 0) [f( x + h) - f(x)]/h`

Clearly the domain of definition of f ′ (x) is wherever the above limit exists. There are different notations for derivative of a function. Sometimes f ′ (x) is denoted by `d/(dx) f(x)` or if y = f(x) , it is denoted by `(dy)/(dx)`. This is referred to as derivative of f(x) or y with respect to x.

It is also denoted by D (f (x) ). Further, derivative of f at x = a is also denoted by

`d/(dx) f(x) |_a` or `(df)/(dx)|_a`or even `((df)/(dx))_(x=a)`