The Manga Guide to Calculus

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  • Format: Trade Paper
  • Copyright: 2009-08-01
  • Publisher: No Starch Press
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Supplemental Materials

What is included with this book?


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

Prefacep. xi
Prologue: What is a Function?p. 1
Exercisep. 14
Let's Differentiate a Function!p. 15
Approximating with Functionsp. 16
Calculating the Relative Errorp. 27
The Derivative in Action!p. 32
p. 34
p. 34
p. 35
Calculating the Derivativep. 39
Calculating the Derivative of a Constant, Linear, or Quadratic Functionp. 40
Summaryp. 40
Exercisesp. 41
Let's Learn Differentiation Techniques!p. 43
The Sum Rule of Differentiationp. 48
The Product Rule of Differentiationp. 53
Differentiating Polynomialsp. 62
Finding Maxima and Minimap. 64
Using the Mean Value Theoremp. 72
Using the Quotient Rule of Differentiationp. 74
Calculating Derivatives of Composite Functionsp. 75
Calculating Derivatives of Inverse Functionsp. 75
Exercisesp. 76
Let's Integrate a Function!p. 77
Illustrating the Fundamental Theorem of Calculusp. 82
When the Density Is Constantp. 83
When the Density Changes Stepwisep. 84
When the Density Changes Continuouslyp. 85
Review of the Imitating Linear Functionp. 88
Approximation $$ Exact Valuep. 89
p(x) Is the Derivative of q(x)p. 90
Using the Fundamental Theorem of Calculusp. 91
Summaryp. 93
A Strict Explanation of Step 5p. 94
Using Integral Formulasp. 95
Applying the Fundamental Theoremp. 101
Supply Curvep. 102
Demand Curvep. 103
Review of the Fundamental Theorem of Calculusp. 110
Formula of the Substitution Rule of Integrationp. 111
The Power Rule of Integrationp. 112
Exercisesp. 113
Let's Learn Integration Techniques!p. 115
Using Trigonometric Functionsp. 116
Using Integrals with Trigonometric Functionsp. 125
Using Exponential and Logarithmic Functionsp. 131
Generalizing Exponential and Logarithmic Functionsp. 135
Summary of Exponential and Logarithmic Functionsp. 140
More Applications of the Fundamental Theoremp. 142
Integration by Partsp. 143
Exercisesp. 144
Let's Learn About Taylor Expansions!p. 145
Imitating with Polynomialsp. 147
How to Obtain a Taylor Expansionp. 155
Taylor Expansion of Various Functionsp. 160
What Does Taylor Expansion Tell Us?p. 161
Exercisesp. 178
Let's Learn About Partial Differentiation!p. 179
What Are Multivariable Functions?p. 180
The Basics of Variable Linear Functionsp. 184
Partial Differentiationp. 191
Definition of Partial Differentiationp. 196
Total Differentialsp. 197
Conditions for Extremap. 199
Applying Partial Differentiation to Economicsp. 202
The Chain Rulep. 206
Derivatives of Implicit Functionsp. 218
Exercisesp. 218
Epilogue: What Is Mathematics For?p. 219
Solutions to Exercisesp. 225
Prologuep. 225
p. 225
p. 225
p. 226
p. 227
p. 228
p. 229
Main Formulas, Theorems, and Functions Covered in this Bookp. 231
Linear Equations (Linear Functions)p. 231
Differentiationp. 231
Derivatives of Popular Functionsp. 232
Integralsp. 233
Taylor Expansionp. 234
Partial Derivativesp. 234
Indexp. 235
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