Topics
Unit 1
Introduction to Micro and Macro Economics
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
- Properties of Transpose of a Matrix
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)`
