Contents. Set Theory. Functions and its Applications CHAPTER 1 CHAPTER 2. Preface... (v)

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1 (vii) Preface... (v) CHAPTER 1 Set Theory Definition of Set... 1 Roster, Tabular or Enumeration Form... 1 Set builder Form... 2 Union of Set... 5 Intersection of Sets... 9 Distributive Laws of Unions and Intersections Complement of a Set Difference of Sets De Morgan s Law Some Important results on Difference, Union and Intersection Symmetric Difference of Two Sets Cardinal Number of a Set Ordered Pairs Cartesian Products Summary Self Practice Exercises Answers CHAPTER 2 Functions and its Applications Brief History and Introduction Definition of a Function or Mapping Types of Mapping One One Mapping (or Injection) (vii)

2 (viii) One Many Mapping Many One Mapping Into Mapping Onto Mapping Some Functions Graph of Functions General Condition for Market Equilibrium in an Economic System Market Equilibrium Break Even Analysis Summary Self Practice Exercises Answers CHAPTER 3 Limits and Continuity Brief Overview and Introduction Limit of a Function Some Other Types of Limits Some Important Theorem Some Important Results Methods of Evaluation of Limits Rationalization Method Substitution Method The Concept of Right and Left hand Limit Difference between Limit and Value of a Function Continuity

3 (ix) Application of Limits and Continuity in Business and Economics Brief Summary Self Practice Exercises Answers Appendix CHAPTER 4 Derivatives and its Applications Concept and Definition Meaning of Increment Some Important Rules Some Important Standard Derivative Some Solved Illustrations using 1 st principle Some Important Standard Derivatives of Trigonometric Functions Some Standard Derivative of Inverse Trigonometric Functions Application of Concepts of Differentiation to Business and Economics Elasticity of Demand Some Important cases of ed Elasticity of Supply Concept of Total Cost, Average Cost and Marginal Cost Concept of Total Revenue, Average Revenue and Marginal Revenue Summary Self Practice Exercises Answers Appendix

4 (x) CHAPTER 5 Maxima and Minima and its Application Introduction Increasing Function Decreasing Function Maxima and Minima of a Function First Order Derivative test for Maxima and Minima Second Order Derivative test for Maxima and Minima Convexity and Concavity Point of Inflexion Application of Theory of Maxima and Minima in Business and Economics Effect of Taxation and Subsidy on Profitability Effect of Taxation Effect of Subsidy Summary Self Practice Exercises Answers CHAPTER 6 Partial Derivatives and its Application Concept and Definition The Concept of Successive Partial Derivatives The Concept of Cross Partial Derivatives Total Differentials Second Order Total Differential Euler s Theorem Euler s Theorem on Homogenous Functions of Two Variables Derivative of Implicit Functions

5 (xi) Application of the Concepts of Partial Derivatives to Business and Economics Demand Analysis Nature of Commodities whether substitutes (competitive) or Complementary Partial Elasticity of Demand Utility Analysis Marginal Rate of Substitution Constrained Utility Maximization Production Analysis The Concept of Maxima and Minima of a function of two variables Summary Self Review Questions Answers Appendix CHAPTER 7 Integration and its Application Definition Some Standard Fundamental Integrals Methods of Integration Integration by Parts Some Important Rule Some Standard Integrals Integration by Partial Fraction Definite Integrals Fundamental Theorem of Integral Calculus Valuation of Definite Integral Application of Integration in Business and Economics Consumer and Producer Surplus

6 (xii) Learning Curve Summary Self Practice Exercises Answers CHAPTER 8 Differential Equations and its Application Definitions Order of a Differential Equation Degree of the Differential Equation Solution of a Differential Equation Solution of First Order and First degree Differential Equation Equation with Variables are Separable Homogenous Differential Equation An Equation Reducible to Homogenous Form Linear Differential Equation Equations Reducible to Linear Form (Bernoulli s Equation) Exact Differential Equation Equations Reducible to Exact Differential Equation Form Solving Second Order Differential Equations Application of Differential Equation to Business and Economics Summary Self Practice Questions Answers CHAPTER 9 Theory of Matrices-I Brief History Forms of Matrix

7 (xiii) Rules of Matrix s Operation Some of the Properties of Matrix Addition Scalar Multiplication of Matrix Some of the Properties of Scalar Multiplication Multiplication Rule Some of the Properties of Matrix Multiplication Transpose of a Matrix Application of Theory of Matrix to Business and Economics Summary Self Practice Exercises Answers CHAPTER 10 Determinants of Matrices Definition Minor and Cofactor of the Elements of a Determinant Cofactors of the Elements Some Important Properties of Determinants Summary Self Practice Exercises Answers CHAPTER 11 Theory of Matrices - II Definition Singular Matrix Non singular Matrix Adjoint of a Square Matrix Properties of Inverse of a Matrix Orthogonal Matrix

8 (xiv) Matrix Inversion Method Gauss Jordan Elimination Method Rank of Matrix Application of Theory of Matrix to Business and Economics Summary Self Practice Exercises Answers CHAPTER 12 Input Output Analysis Brief History The Alternate Explanation Simon Hawkins Conditions Solution for a 2 Sector Model with Primary Inputs In Case of 2 Primary Inputs Utilized Determination of Equilibrium Prices (2 Sector Model) Importance of Input Output Analysis Practical Issues Theoretical Issues Review Questions Self Practice Exercises Answers CHAPTER 13 Theory of Equation and Inequation Introduction The Nature of the Roots of the Quadratic Equation Relation between Roots and Coefficients of a Quadratic Equation Formulation of an Equation using given Roots

9 (xv) Solving Simultaneously Linear Equation Having Two Variables Cubic and Biquadratic Equations Inequalities Graphs of Linear Inequations or Inequalities in Two variables Graphs of System of Linear Equations Summary Self Practice Exercises Answers CHAPTER 14 Progression Arithmetic Progression Properties of an Arithmetic Progression Arithmetic Mean (A. M) Representation of Terms in A.P Geometric Progression Geometric Means Relationship between A.M and G.M Harmonic Progression Summary Self Practice Exercises Answers CHAPTER 15 Permutation and Combination A Brief Historical Background The Fundamental Principles of Counting Multiplication Rule Corollary Permutations when some of the objects are Similar

10 (xvi) Combination Brief Summary Self Practice Questions Answers CHAPTER 16 Theory of Probability-I Introduction A Brief Historical Background Different Approaches to Probability Emphirical or Statistical Approach (Von Mises) Axiomatic Approach Addition Theorems Corollary Solved Exercises Compound Probability Conditional Probability Multiplication Theorem Bayes Theorem Brief Summary Review Questions Self Practice Exercises Answers CHAPTER 17 Theory of Probability - II Random Variable Probability Function (or Density Function) of a Random Variable Expectation of Random Variable

11 (xvii) Binomial Distribution Mean (or expectation) and Variance of the Binomial Distribution Fitting of a Binomial Distribution Poissons Distribution Fitting of a Poisson Distribution Solved Exercises Normal Approximation to Binomial Distribution Brief Summary Review Questions Self Practice Questions Answers Appendix CHAPTER 18 Linear Programming Formulation and Graphical Method Brief History Introduction Basic Requirement of Linear Programming Assumptions of Linear Programming Problems Business Application of Linear Programming Problem Guidelines for Formulation of Linear Programming Problem Graphical Method of Solving Linear Programming Problem The Corner or Extreme Point Method Iso-Profit or Iso-Cost Method Special Cases of Linear Programming Summary Self Practice Exercises Answers

12 (xviii) CHAPTER 19 The Simplex Method and Duality Brief Introduction The Simplex Method (Maximization Case) Simplex Method for Minimization Case (all constraint type) Using Charne s Big M Method Some Typical Problems Encounter in Simplex method Duality Some of the Advantages of Duality Summary Self Practice Exercises Answers CHAPTER 20 Decision Theory and Decision Tree Introduction General Characteristics of Decision Making Some of the Steps in Decision Making Process Different Categories of Decision Making Models Maximin or Minimax Criterion (Pessimism Criterion) Maximax or Minimin Criterion (Optimism Criterion) Hurwicz Alpha Criterion Regret Criterion Decision Making Under Risk (Stochastic Models) Expected Opportunity Loss (EOL) Expected Value of Perfect Information (EVPI) Bayesian Analysis and Posterior Probabilities

13 (xix) Decision Tree Analysis Summary Review Questions Self Practice Exercises Answers CHAPTER 21 Game Theory Brief History Introduction Key Terminology Saddle Point Types of Games Dominance Rule Arithmetic Method Algebraic Method Matrix Method Graphical Method Solution of Two Person Zero Sum Game by Linear Programming Method Summary Self Practice Exercises Answers Appendix CHAPTER 22 Mathematics of Finance Introduction What is Time Value? Some Key Terminology

14 (xx) Concept of Simple and Compound Interest Compound Interest Nominal vs Effective Rate Future Value of a Single Sum Present Value of a Single Sum Annuities Calculation of Future Value of an Ordinary Annuity (Using Time line Analysis) Calculation of Present Value of an Ordinary Annuity (Using Time line Analysis) Sinking Fund, Amortization and Capital Recovery Future Value of an Annuity Due Present Value of an Annuity Due Bond Basics Bond Valuation Summary Review Questions Self Practice Exercises Answers Logarithms Tables Index

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