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**ISBN:**
9789387925649

**Bind:**
Paperback

**Year: **
2020

**Pages:**
596

**Size:**
6.75 x 9.5 Inch

**Publisher:**
Viva Books Originals

**Sales Territory:**
Worldwide

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).

**Target Audience:**

Undergraduate students of Commerce and Economics.

**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.

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