Algebra of Matrices

Unit 1

Mathematical Logic

• Statements - Introduction in Logic
• Logical Connective, Simple and Compound Statements
• Statement Patterns and Logical Equivalence
• Algebra of Statements
• Venn Diagrams

Mathematical Logic

• Truth Value of Statement
• Logical Connective, Simple and Compound Statements
• Quantifier and Quantified Statements in Logic
• Statement Patterns and Logical Equivalence
• Algebra of Statements
• Venn Diagrams

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

• Integration
• Methods of Integration: Integration by Substitution
• Methods of Integration: Integration by Parts
• Methods of Integration: Integration Using Partial Fractions

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

• Introduction of Matrices
• Algebra of Matrices
• Inverse of Matrix
• Solution of Equations

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

• Continuous Function of Point

Differentiation

• Derivatives of Implicit Functions
• Logarithmic Differentiation
• Derivatives of Functions in Parametric Forms
• Second Order Derivative
• Derivative of Inverse Function

Applications of Derivative

• Increasing and Decreasing Functions
• Maxima and Minima

Indefinite Integration

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

Definite Integrals

• Properties of Definite Integrals
• Applications of Definite Integrals

Ratio, Proportion and Partnership

• Ratio, Proportion and Partnership

Commission, Brokerage and Discount

• 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

• Bivariate Frequency Distribution
• Karl Pearson’s Coefficient of Correlation
• Rank 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

• Random Variables and Its Probability Distributions
• Binomial Theorem and Binomial Distribution
• Poisson Distribution
• Normal Distribution
• Probability Distribution of a Discrete Random Variable
• Distribution Function of a Continuous Random Variable

Management Mathematics

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