The manga guide to calculus
Book - 2009
- Subjects
- Published
-
Tokyo : San Francisco :
Ohmsha
[2009]
- Language
- English
Japanese - Corporate Author
- Main Author
- Corporate Author
- Other Authors
- Edition
- English edition
- Item Description
- Originally published as: Manga de wakaru bibun sekibun. Toyko : Ohmsha, 2005.
- Physical Description
- xii, 238 pages : illustrations ; 24 cm
- Bibliography
- Includes index.
- ISBN
- 9781593271947
- Preface
- Prologue: What is a Function?
- Exercise
- 1. Let's Differentiate a Function!
- Approximating with Functions
- Calculating the Relative Error
- The Derivative in Action!
- Step 1.
- Step 2.
- Step 3.
- Calculating the Derivative
- Calculating the Derivative of a Constant, Linear, or Quadratic Function
- Summary
- Exercises
- 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
- Exercises
- 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 $$ Exact Value
- Step 6. p(x) Is the Derivative of q(x)
- Using the Fundamental Theorem of Calculus
- Summary
- A Strict Explanation of Step 5
- 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
- Exercises
- 4. Let's Learn Integration Techniques!
- Using Trigonometric Functions
- Using Integrals with Trigonometric Functions
- Using Exponential and Logarithmic Functions
- Generalizing Exponential and Logarithmic Functions
- Summary of Exponential and Logarithmic Functions
- More Applications of the Fundamental Theorem
- Integration by Parts
- Exercises
- 5. Let's Learn About Taylor Expansions!
- Imitating with Polynomials
- How to Obtain a Taylor Expansion
- Taylor Expansion of Various Functions
- What Does Taylor Expansion Tell Us?
- Exercises
- 6. Let's Learn About Partial Differentiation!
- What Are Multivariable Functions?
- The Basics of Variable Linear Functions
- Partial Differentiation
- Definition of Partial Differentiation
- Total Differentials
- Conditions for Extrema
- Applying Partial Differentiation to Economics
- The Chain Rule
- Derivatives of Implicit Functions
- Exercises
- Epilogue: What Is Mathematics For?
- A. Solutions to Exercises
- Prologue
- Chapter 1.
- Chapter 2.
- Chapter 3.
- Chapter 4.
- Chapter 5.
- Chapter 6.
- B. Main Formulas, Theorems, and Functions Covered in this Book
- Linear Equations (Linear Functions)
- Differentiation
- Derivatives of Popular Functions
- Integrals
- Taylor Expansion
- Partial Derivatives
- Index