The Manga Guide to Calculus
by Kojima, Hiroyuki; Togami, Shin; Ltd., Becom Co.Format: Paperback
Pub. Date: 2009-08-01
Publisher(s): No Starch Press
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Summary
The Manga Guide to Calculus teaches calculus in an original and refreshing way, by combining Japanese-style Manga cartoons with serious content. This is real calculus combined with real Manga. The book's story revolves around heroine, Noriko. Noriko takes a job with a local newspaper and quickly befriends the geeky Kakeru, a math whiz who wants to help her understand the practical uses of calculus in journalism. Kakeru begins by teaching Noriko (and the book's readers) the basics of calculus, such as approximating with functions, derivatives, techniques of differentiation, and polynomials. As the book progresses, Noriko and readers learn calculus, including complex concepts like the Fundamental Theorem of Calculus, exponential and logarithmic functions, the Taylor Expansion, and partial differentiation. This charming, easy-to-read guide uses real-world examples like celebrity weight gain, TV commercials, and economics, and includes examples and exercises (with answer keys) to help readers learn.
Author Biography
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.
Table of Contents
| 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. |
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