**Description:**

The use of mathematical
techniques has been gaining popularity in social and biological sciences as
well as in the field of commerce and management for the last two decades. The
exactness and precision of mathematical language and methods have made it possible
to explore large areas of research in these subjects which remains hidden so
far from the keen eyes of the researchers. Today one could say that mathematics
is probably the most convenient shoulder to lean on for not only pure sciences
but subjects like commerce and economics.

The present exposition is
intended as a textbook keeping in view the needs of the undergraduate students
of commerce and economics. This book is divided into thirteen chapters which
are as follows:

Functions, Limits and Continuity;
Differentiation of Functions; Partial Differentiation; Differentiation and
Partial Differentiation (Applications); Integration; Definite Integrals;
Matrices and Determinants; Matrices (Continued); Linear Programming
(Mathematical Formulation & Graphical Method); Linear Programming (Simplex
Algorithm & Duality); Transportation and Assignment Problem; Financial
Mathematics (Compound Interest & Annuity); Differential Equations
(Separation of Variables, Homogeneous & Linear Differential Equations of
Order one & Degree one).

Contents:

*Preface to the Second Edition*

*Preface to the First Edition*

**Chapter 1. Basic Preliminaries** • Sets • Subsets • Functions • Algebra of Functions • Some
Special Types of Functions • Composite Functions • Limit of a Function •
Geometrical Interpretation of Definition • Methods of Finding out the Limits •
Dome Theorems on Limits • Evaluation of Limits • Direct Substitution Method •
Factorization Method • Rationalization Method • Using Standard Forms • Method
of Evaluating Limits • Evolution of Limits of Exponential and Logarithmic
Functions • Continuity and Discontinuity of Functions • Continuity at a Point •
Continuity in an Interval • Properties of Continuous Functions •
Differentiability of a Function • Theory of Logarithm • Fundamental Laws of
Logarithm • To Determine Characteristic of a Common Logarithm • To Determine
Mantissa of a Common Logarithm • Antilogarithm • To Find Logarithm of Numbers
when the Logarithms of some numbers are given

**Chapter 2. Differentiation of
Functions** • Introduction • Derivative of a Function •
Derivative at a Point • Geometrical Interpretation of Derivative •
Differentiation from the First Principles • Differentiation of Exponential
Functions • Differentiation of Logarithmic Functions • Theorems on Differentiation
• Product and Quotient Rules for Differentiation • Derivative of the Function
of a Function (Chain Rule) • Logarithmic Differentiation • Derivative of
Parametric Equations • Differentiation of Implicit Functions • Derivatives of
Higher Order

**Chapter 3. Partial
Differentiation** • Introduction • Partial
Derivatives • Partial Derivatives of Higher Order • Homogeneous Functions •
Total Differentiation • Derivative of an Implicit Function • Chain Rule
(Approximation by Total Differential)

**Chapter 4. Differentiation and
Partial Differentiation (Applications)** • Introduction
• Increasing and Decreasing Functions • Test for Increasing and Decreasing
Functions • Convex and Concave Functions • Points of Inflexion • Maximum and
Minimum Values • Conditions for Existence of Maximum or Minimum Value • Method
of Finding Maxima or Minima • Second Derivative Test for Maxima and Minima •
Marginal Analysis • Marginal Cost and Average Cost Function • Relation between
Average and Marginal Cost Curves • Marginal Product and Marginal Cost •
Equipment Replacement • Marginal Revenue and Average Revenue Function •
Marginal Revenue Product • Profit Function • Profit Maximization under Perfect
Competition • Profit Maximization under Monopoly • Monopoly Problem in Economic
Theory • Effect of Taxation and Subsidy on Monopoly • Maxima and Minima of
Functions of Two Variables • Method of Finding Maxima and Minima • Lagrange’s
Multipliers and Constrained Optimization

**Chapter 5. Integration** • Introduction • Indefinite Integrals as Antiderivatives • Some
Properties of Indefinite Integral • Integration by Substitution Method •
Integration of the Type • Integration by Parts • Some Standard Integrals •
Integration by Partial Fractions • When The Denominator Contains Non-repeated
Linear Factors • When Denominator Contains Repeated Linear Factors • When
Denominator Contains Non-repeated Quadratic Factors • When Denominator Contains
Repeated Quadratic Factors

**Chapter 6. Definite Integrals** • Introduction • Definite Integral • Evaluation of Definite
Integrals • Properties of Definite Integrals • Definite Integral as an Area •
Area Between two Curves • Applications of Integration to Marginal Analysis •
Determination of Cost Function from Marginal Cost Function • Derivative of
Total Revenue Function and Demand Function from a Given Marginal Revenue
Function • Maximization of Profit Over Time • Rate of Sales (or Growth •
Consumer’s and Producer’s Surplus • The Learning Curves

**Chapter 7. Matrices and
Determinants** • Introduction • Matrices • A
General Form of a Matrix • Types of Matrices • Operations on Matrices •
Addition of Matrices • Properties of Matrix Addition • Scalar Multiplication of
Matrices • Properties of Scalar Multiplication • Subtraction of Matrices •
Multiplication of Matrices • Properties of Matrix Multiplication • Determinant
of a Square Matrix • Rule for Expanding the Determinants of Order • Sarrus
Diagram for the Expansion of a Determinant of Third Order • Minors and
Cofactors of Elements of Determinant • Properties of Determinants • Product of
two Determinants • Rules to Find the Product of Two Determinants • Applications
of Determinants in Solving a System of Linear Equations • System of Linear
Equations in Three Unknowns • Conditions for Consistency

**Chapter 8. Matrices (Continued)** • Transpose of a Matrix • Properties of Transpose of a Matrix •
Symmetric and Skew Symmetric Matrices • Adjoint of a Square Matrix • Inverse of
a Square Matrix • Singular and Non-Singular Matrices • Expression for Finding
the Inverse of a Matrix A • Steps Involved in Finding the Inverse of a Matrix A
• Properties of the Inverse of a Matrix • Solution of a System of Linear
Equations • Steps Involved in Solving a System of Linear Equations •
Homogeneous System of Linear Equations • Elementary Transformations • Elementary
Row Transformation • Elementary Column Transformation

**Chapter 9. Linear Programming
(Mathematical Formulation & Graphical Method)** • Introduction • Basic Requirements • Linear Programming Model •
Formulation of Linear Programming Problem • Linear Inequalities and their
Graphs in Two Variables • System of Linear Inequalities • Some Important
Definitions • Graphical Method

**Chapter 10. Linear Programming
(Simplex Algorithm & Duality)** • Introduction
• Few Important Definitions and Notations • Slack Variables • Surplus Variables
• To Determine Initial Basic Feasible Solution • Computational Procedure of
Simplex Method for the Solution of a Maximization Problem • Artificial
Variables Technique • Two Phase Method • Big M-Method (Method of Penalties) •
Duality in Linear Programming • Symmetric Dual Problem • The Dual of a Mixed
System • Standard Form of the Primal • To Read the Solution to the Dual From
the Final Simplex Table the Primal and Vice-Versa

**Chapter 11. Transportation and
Assignment Problems** • Introduction • General
Transportation Problem • Mathematical Formulation • Few Important Definitions •
Finding an Initial basic Feasible Solution • Test for Optimality •
Computational Procedure of Optimality Test • Transportation Algorithm or Modi
Method • Degeneracy in Transportation Problems • Unbalanced Transportation
Problem • Assignment Problem • Mathematical Formulation of the Problem • The
Assignment Algorithm

**Chapter 12. Financial Mathematics** • Introduction • Some Basic Definitions • Simple Interest • Different
Types of Interest Rates • Compound Interest • Difference between Simple and
Compound Interest • Expression for Amount and Compound Interest • To Find
Compound Interest and Amount • Computation of Compound Interest when the Number
of Conversion Periods are not Integer • Computation of Compound Interest when
Interest is compounded Monthly, Quarterly, Half Yearly • Problems on
Depreciation and Population • Annuity • Difference between Compound Interest
and Annuity • Objectives of an Annuity • Characteristics of an Annuity •
Classification of Annuities • Amount of an Ordinary Annuity • Present Value of
an Annuity • Deferred Annuity • Amount of Deferred Annuity • Present Value of
Deferred Annuity • Perpetual Annuity or Perpetuity • Continuous Compounding •
Amount and Present value of an Annuity in Case of Continuous Compounding •
Sinking Funds

**Chapter 13. Differential
Equations** • Introduction • Method of Separation of
Variables • Transformation of Some Equations in the Form in which Variables are
Separable • Homogeneous Differential Equations • Equations Reducible to
Homogeneous Form • Exact Differential Equations • Integrating Factor • Linear
Differential equations • Equations Reducible to Linear Form

*Answers • Logarithmic Table •
Antilogarithmic Table • References*

About the Author:

**Dr Mohd. Shadab Khan **completed his M.Phil. and Ph.D. degrees in Mathematics from
Department of Mathematics, Aligarh Muslim University, Aligarh. During his
research programme of five years he has been very actively engaged in teaching
of undergraduate classes in the Department of Mathematics. Dr Khan is presently
working as Assistant Professor in the Department of Commerce, Aligarh Muslim
University and is teaching undergraduate and postgraduate students in the
Department of Commerce for the last fifteen years and also guiding many Ph.D.
students. Dr Khan has attended many national/international conferences and
published several research papers in journals of national and international
repute.

Target Audience:

Undergraduate students of Commerce and
Economics.