The manga guide to calculus
Edition
English edition.
Languages
Translated from the Japanese.
Publication Information
San Francisco, CA : No Starch Press ; [Tokyo, Japan] : Ohmsha, Ltd., [2009]
Physical Description
xii, 238 pages : chiefly illustrations ; 24 cm.
Uniform Title
Series
Summary
"In The Manga Guide to Calculus, you'll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You'll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor)."--Page 4 of cover.
Notes
Includes index.
"The manga guide to calculus is a translation of the Japanese original, Manga de wakaru bibun sekibun, published by Ohmsha, Ltd. of Tokyo Japan, ©2005 by Hiroyuki Kojima and Becom Co., Ltd." -- Title page verso.
Contents
- Prologue. What is a function?
- 1. Let's differentiate a function. Approximating with functions ; Calculating the relative error ; The derivative in action ; Calculating the derivative ; Calculating the derivative of a constant, linear, or quadratic function
- 2. Let's learn differentiation techniques. The sum rule of differentiation ; The product rule of differentiation ; Differentiating polynomials ; Finding maxima and minima ; Using the mean value theorem ; Using the quotient rule of differentiation Calculating derivatives of composite functions ; Calculating derivatives of inverse functions
- 3. Let's integrate a function. Illustrating the fundamental theorem of calculus. Step 1. When the density is constant. Step 2. When the density changes stepwise ; Step 3. When the density changes continuously ; Step 4. Review of the imitating linear function ; Step 5. Approximation vs. exact value
- Using the fundamental theorem of calculus ; Using integral formulas ; Applying the fundamental theorem. Supply curve ; Demand curve
- Review of the fundamental theorem of calculus ; Formula of the substitution rule of integration ; The power rule of integration
- 4. Let's learn integration techniques ; Using trigonometric functions ; Using integrals with trigonometric functions ; Using exponential and logarithmic functions ; Integration by parts
- 5. Let's learn about Taylor Expansions. Imitating with polynomials ; How to obtain a Taylor expansion ; Taylor expansion of various functions
- 6. Let's learn about partial differentiation. What are multivariable functions? ; Basics of variable linear functions ; Partial differentiation ; Total differentials ; Conditions for extrema ; Applying partial differentiation to economics ; The chain rule ; Derivatives of implicit functions
- Epilogue: what is mathematics for?
- A. Solutions to exercises
- B. Main formulas, theorems, and functions covered in this book. Linear equations (Linear functions) ; Differentiation ; Derivatives of popular functions ; Integrals ; Taylor expansion ; Partial derivatives.