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 |
Table of Contents provided by Ingram. All Rights Reserved. |