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INTRODUCTION TO CALCULUS FOR BUSINESS AND ECONOMICS

Associate Professor of Statistics

Department of Statistics Eritrea Institute of Technology MAINEFHI, ASMARA, ERITREA

Assistant Professor of Mathematics & Head Department of Mathematics

G.L.A. College

Nilambar Pitambar University

Medininagar, Daltanganj, Jharkhand, India

Chapter I : | Functions | Page 1-53 |
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1.1. | Introduction | 1 |

1.2. | Functions | 1 |

1.3. | Intervals | 6 |

1.4. | Types of Functions | 6 |

1.4.1. | Constant Function | 6 |

1.4.2. | Identity Function | 7 |

1.4.3. | Absolute Value Function | 7 |

1.4.4. | Linear Functions | 7 |

1.4.5. | Quadratic Functions | 8 |

1.4.6. | Polynomial Functions | 9 |

1.4.7. | Rational Functions | 10 |

1.4.8. | One-to-one Function | 11 |

1.4.9. | Odd and Even Functions | 11 |

1.4.10. | Monotonic Functions | 13 |

1.4.11. | Composite Functions | 13 |

1.4.12. | Inverse Functions | 15 |

1.4.13. | Explicit and Implicit Functions | 17 |

1.4.14. | Exponential Functions | 17 |

1.4.15. | Logarithmic Functions | 21 |

1.4.16. | Power Functions | 23 |

1.4.17. | Homogeneous Functions | 25 |

1.4.18. | Homothetic Functions | 28 |

1.4.19. | Concave and Convex Functions | 31 |

1.4.20. | Periodic Functions | 32 |

1.5. | Functions in Business and Economics | 32 |

1.5.1. | Demand Function | 32 |

1.5.2. | Supply Function | 33 |

1.5.3. | Cost Function | 35 |

1.5.4. | Revenue Function | 35 |

1.5.5. | Profit Function | 35 |

1.5.6. | Consumption Function | 36 |

1.6. | The algebra of Functions | 36 |

1.7. | Vertical and Horizontal Translation of Functions | 37 |

1.8. | Applications of Linear Functions in Business and Economics | 39 |

1.9. | Applications of Non-linear Functions in Business and Economics | 45 |

Chapter II : | Limits and Continuity of Functions | 54-108 |
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2.1. | Introduction | 54 |

2.2. | The Concept of Limit | 54 |

2.3. | Properties of Limits and Evaluation of Limits | 56 |

2.4. | One Sided Limits | 69 |

2.5. | Limits at Infinity and Infinite Limit | 73 |

2.6. | The Concept of Continuity | 78 |

2.7. | One-Sided Continuity | 84 |

.8. | Continuity on Intervals | 85 |

2.9. | Types of Discontinuity | 90 |

2.10. | The Intermediate Value Theorem (IVT) | 93 |

2.11. | Asymptotes of Function | 95 |

2.12. | Applications of Limit and Continuity to Business and Economics. | 100 |

Chapter III : | Differentiation | 109-186 |
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3.1. | Introduction | 109 |

3.2. | The Slope of a Graph | 109 |

3.3. | The Derivative of a Function | 116 |

3.4. | Differentiability and Continuity | 120 |

3.5. | Differentiability and Linear Approximations | 122 |

3.6. | Rules of Differentiation | 125 |

3.7. | The Chain Rule and Composite Functions | 135 |

3.8. | Derivatives of Logarithmic and Exponential Functions | 143 |

3.9. | Implicit Differentiation | 152 |

3.10. | Derivative of Inverse of a Function | 159 |

3.11. | Derivative of a Function in Parametric Form | 161 |

3.12. | Derivative of a Function with respect to another Function | 165 |

3.13. | Logarithmic Differentiation | 166 |

3.14. | Successive Differentiation | 173 |

3.15. | nth Derivative of some Standard Functions | 179 |

3.16. | Leibnitz's Theorem. | 182 |

3.17. | Second Derivative in Parametric Form. | 185 |

Chapter IV : | Further Topics in Differentiation | 187-122 |
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4.1. | Introduction | 187 |

4.2. | Increasing and Decreasing Functions | 187 |

4.3. | Relative Maxima and Minima of a Function | 193 |

4.4. | Global Maxima and Minima of a Function | 204 |

4.5. | Concavity and Convexity of a Function | 209 |

4.6. | Rolle's and Lagrange's Mean Value Theorem | 219 |

Chapter V : | Applications of Differentiation to Business and Economics | 223-316 |
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5.1. | Introduction | 223 |

5.2. | Average and Marginal Functions | 223 |

.3. | Marginal Revenue Product | 232 |

5.4. | Marginal Propensity to Consume and Save | 233 |

5.5. | The Investment Multiplier | 236 |

5.6. | The Money Multiplier | 238 |

5.7. | The Elasticity of Functions | 239 |

5.8. | Rate of Change, Relative Rate of Change and Related Rates | 257 |

.9. | Univariate Utility Function and Risk Aversion | 264 |

5.10. | Monopoly Problems | 271 |

5.11. | Effect of Taxation under Pure Competition | 281 |

5.12. | Effects of Taxation and Subsidy on Monopoly | 284 |

5.13. | Law of diminishing Returns | 297 |

5.14. | Applied Optimization Problems | 300 |

Chapter VI : | Partial Differentiation | 317-358 |
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6.1. | Introduction | 317 |

.2. | Functions of Several Independent Variables | 317 |

.3. | Partial Differentiation | 318 |

6.4. | Rules of Partial Differentiation | 319 |

6.5. | Composite Functions and the Chain Rule | 324 |

6.6. | Second Order Partial Derivatives and Young's Theorem | 327 |

6.7. | Homogeneous Functions and Euler's Theorem | 330 |

6.8. |

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When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrov

When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrov