The Manga Guide to Calculus

by Kojima, Hiroyuki; Togami, Shin; Ltd., Becom Co.

• ISBN13: 9781593271947
• ISBN10: 1593271948
• Format: Paperback
• Copyright: 2009-08-01
• Publisher: No Starch Press

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.