What is included with this book?
Hiroyuki Kojima received his PhD in Economics from the Graduate School of Economics, Faculty of Economics, at the University of Tokyo. He has worked as a lecturer and is now an associate professor in the Faculty of Economics at Teikyo University in Tokyo, Japan. While well-regarded as an economist, he is also active as an essayist and has published a wide range of books on mathematics and economics at the fundamental, practical, and academic levels.
Preface | p. xi |
Prologue: What is a Function? | p. 1 |
Exercise | p. 14 |
Let's Differentiate a Function! | p. 15 |
Approximating with Functions | p. 16 |
Calculating the Relative Error | p. 27 |
The Derivative in Action! | p. 32 |
p. 34 | |
p. 34 | |
p. 35 | |
Calculating the Derivative | p. 39 |
Calculating the Derivative of a Constant, Linear, or Quadratic Function | p. 40 |
Summary | p. 40 |
Exercises | p. 41 |
Let's Learn Differentiation Techniques! | p. 43 |
The Sum Rule of Differentiation | p. 48 |
The Product Rule of Differentiation | p. 53 |
Differentiating Polynomials | p. 62 |
Finding Maxima and Minima | p. 64 |
Using the Mean Value Theorem | p. 72 |
Using the Quotient Rule of Differentiation | p. 74 |
Calculating Derivatives of Composite Functions | p. 75 |
Calculating Derivatives of Inverse Functions | p. 75 |
Exercises | p. 76 |
Let's Integrate a Function! | p. 77 |
Illustrating the Fundamental Theorem of Calculus | p. 82 |
When the Density Is Constant | p. 83 |
When the Density Changes Stepwise | p. 84 |
When the Density Changes Continuously | p. 85 |
Review of the Imitating Linear Function | p. 88 |
Approximation $$ Exact Value | p. 89 |
p(x) Is the Derivative of q(x) | p. 90 |
Using the Fundamental Theorem of Calculus | p. 91 |
Summary | p. 93 |
A Strict Explanation of Step 5 | p. 94 |
Using Integral Formulas | p. 95 |
Applying the Fundamental Theorem | p. 101 |
Supply Curve | p. 102 |
Demand Curve | p. 103 |
Review of the Fundamental Theorem of Calculus | p. 110 |
Formula of the Substitution Rule of Integration | p. 111 |
The Power Rule of Integration | p. 112 |
Exercises | p. 113 |
Let's Learn Integration Techniques! | p. 115 |
Using Trigonometric Functions | p. 116 |
Using Integrals with Trigonometric Functions | p. 125 |
Using Exponential and Logarithmic Functions | p. 131 |
Generalizing Exponential and Logarithmic Functions | p. 135 |
Summary of Exponential and Logarithmic Functions | p. 140 |
More Applications of the Fundamental Theorem | p. 142 |
Integration by Parts | p. 143 |
Exercises | p. 144 |
Let's Learn About Taylor Expansions! | p. 145 |
Imitating with Polynomials | p. 147 |
How to Obtain a Taylor Expansion | p. 155 |
Taylor Expansion of Various Functions | p. 160 |
What Does Taylor Expansion Tell Us? | p. 161 |
Exercises | p. 178 |
Let's Learn About Partial Differentiation! | p. 179 |
What Are Multivariable Functions? | p. 180 |
The Basics of Variable Linear Functions | p. 184 |
Partial Differentiation | p. 191 |
Definition of Partial Differentiation | p. 196 |
Total Differentials | p. 197 |
Conditions for Extrema | p. 199 |
Applying Partial Differentiation to Economics | p. 202 |
The Chain Rule | p. 206 |
Derivatives of Implicit Functions | p. 218 |
Exercises | p. 218 |
Epilogue: What Is Mathematics For? | p. 219 |
Solutions to Exercises | p. 225 |
Prologue | p. 225 |
p. 225 | |
p. 225 | |
p. 226 | |
p. 227 | |
p. 228 | |
p. 229 | |
Main Formulas, Theorems, and Functions Covered in this Book | p. 231 |
Linear Equations (Linear Functions) | p. 231 |
Differentiation | p. 231 |
Derivatives of Popular Functions | p. 232 |
Integrals | p. 233 |
Taylor Expansion | p. 234 |
Partial Derivatives | p. 234 |
Index | p. 235 |
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