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The Manga Guide to Calculus

Book Description

Noriko is just getting started as a junior reporter for the Asagake Times. She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye.

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).

Mr. Seki teaches Noriko how to:

  • Use differentiation to understand a function's rate of change
  • Apply the fundamental theorem of calculus, and grasp the relationship between a function's derivative and its integral
  • Integrate and differentiate trigonometric and other complicated functions
  • Use multivariate calculus and partial differentiation to deal with tricky functions
  • Use Taylor Expansions to accurately imitate difficult functions with polynomials

Whether you're struggling through a calculus course for the first time or you just need a painless refresher, you'll find what you're looking for in The Manga Guide to Calculus.

This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.

Table of Contents

  1. Table of Contents
  2. Preface
  3. Prologue:What Is A Function? (1/3)
  4. Prologue:What Is A Function? (2/3)
  5. Prologue:What Is A Function? (3/3)
  6. Chapter 1: Let’s Differentiate a Function!
    1. Approximating with Functions (1/2)
    2. Approximating with Functions (2/2)
    3. Calculating the Relative Error (1/2)
    4. Calculating the Relative Error (2/2)
    5. The Derivative in Action! (1/2)
    6. The Derivative in Action! (2/2)
    7. Calculating the Derivative
    8. Summary
    9. Exercises
  7. Chapter 2: Let’s Learn Differentiation Techniques!
    1. The Sum Rule of Differentiation (1/2)
    2. The Sum Rule of Differentiation (2/2)
    3. The Product Rule of Differentiation (1/2)
    4. The Product Rule of Differentiation (2/2)
    5. Differentiating Polynomials
    6. Finding Maxima and Minima (1/2)
    7. Finding Maxima and Minima (2/2)
    8. Using the Mean Value Theorem
    9. Using the Quotient Rule of Differentiation
    10. Calculating Derivatives of Composite Functions
    11. Calculating Derivatives of Inverse Functions
    12. Exercises
  8. Chapter 3: Let’s Integrate a Function!
    1. Illustrating the Fundamental Theorem of Calculus (1/2)
    2. Illustrating the Fundamental Theorem of Calculus (2/2)
    3. Using the Fundamental Theorem of Calculus (1/2)
    4. Using the Fundamental Theorem of Calculus (2/2)
    5. Applying the Fundamental Theorem (1/2)
    6. Applying the Fundamental Theorem (2/2)
    7. Review of the Fundamental Theorem of Calculus
    8. Formula of the Substitution Rule of Integration
    9. The Power Rule of Integration
    10. Exercises
  9. Chapter 4: Let's Learn Integration Techniques!
    1. Using Trigonometric Functions (1/2)
    2. Using Trigonometric Functions (2/2)
    3. Using Integrals with Trigonometric Functions (1/2)
    4. Using Integrals with Trigonometric Functions (2/2)
    5. Using Exponential and Logarithmic Functions (1/2)
    6. Using Exponential and Logarithmic Functions (2/2)
    7. Summary of Exponential and Logarithmic Functions
    8. More Applications of the Fundamental Theorem
    9. Exercises
  10. Chapter 5: Let’s Learn About Taylor Expansions!
    1. Imitating with Polynomials (1/2)
    2. Imitating with Polynomials (2/2)
    3. How to Obtain a Taylor Expansion (1/2)
    4. How to Obtain a Taylor Expansion (2/2)
    5. Taylor Expansion of Various Functions
    6. What Does Taylor Expansion Tell Us?
    7. Exercises
  11. Chapter 6: Let’s Learn About Partial Differentiation!
    1. What Are Multivariable Functions?
    2. The Basics of Variable Linear Functions (1/2)
    3. The Basics of Variable Linear Functions (2/2)
    4. Tanaka School Sunday
    5. Partial Differentiation (1/2)
    6. Partial Differentiation (2/2)
    7. Total Differentials
    8. Conditions for Extrema
    9. Applying Partial Differentiation to Economics
    10. The Chain Rule (1/3)
    11. The Chain Rule (2/3)
    12. The Chain Rule (3/3)
    13. Derivatives of Implicit Functions
    14. Exercises
  12. Epilogue:What Is Mathematics for?
  13. Appendix A: Solutions to Exercises
    1. Prologue
    2. Chapter 1
    3. Chapter 2
    4. Chapter 3
    5. Chapter 4
    6. Chapter 5
    7. Chapter 6
  14. Appendix B: Main Formulas, Theorems, and Functions Covered in this Book
    1. Linear Equations (Linear Functions)
    2. Differentiation
    3. Derivatives of Popular Functions
    4. Integrals
    5. Taylor Expansion
    6. Partial Derivatives
  15. Index