Softcover ISBN:  9781470469962 
Product Code:  AMSTEXT/60 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470472436 
Product Code:  AMSTEXT/60.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Softcover ISBN:  9781470469962 
eBook: ISBN:  9781470472436 
Product Code:  AMSTEXT/60.B 
List Price:  $198.00 $148.50 
MAA Member Price:  $178.20 $133.65 
AMS Member Price:  $158.40 $118.80 
Softcover ISBN:  9781470469962 
Product Code:  AMSTEXT/60 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470472436 
Product Code:  AMSTEXT/60.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Softcover ISBN:  9781470469962 
eBook ISBN:  9781470472436 
Product Code:  AMSTEXT/60.B 
List Price:  $198.00 $148.50 
MAA Member Price:  $178.20 $133.65 
AMS Member Price:  $158.40 $118.80 

Book DetailsPure and Applied Undergraduate TextsVolume: 60; 2023; 364 ppMSC: Primary 00; 26; 92
The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one or twosemester course. By boiling calculus down to six commonsense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning — to focus on when and why to use the tools of calculus, not just on how to apply formulas.
Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm.
The Biology Edition of the Six Pillars series has been extensively fieldtested at the University of Texas. It features hundreds of examples and problems specifically designed for students in the life sciences. The core ideas are introduced by modeling the spread of disease, tracking changes in the amount of \(\mathrm{CO}_{2}\) in the atmosphere, and optimizing blood flow in the body. Along the way, students learn about optimal drug delivery, population dynamics, chemical equilibria, and probability.
Additional material available:
 MATLAB files
 Online learning modules
 Worksheets
 WebAssign
ReadershipUndergraduate students interested in calculus with applications.

Table of Contents

Cover

Title page

Copyright

Contents

Instructors’ Guide and Background

Chapter 1. What is Calculus? The Six Pillars

Chapter 2. Predicting the Future: The SIR Model

2.1. Worried Sick

2.2. Building the SIR Model

2.3. Analyzing the Model Numerically

2.4. Theoretical Analysis: What Goes Up Has to Stop Before It Comes Down

2.5. Covid19 and Modified SIR Models

2.6. Same Song, Different Singer: SIR and Product Marketing

2.7. Chapter Summary

2.8. Exercises

Chapter 3. Close is Good Enough

3.1. The Idea of Approximation

3.2. Functions

3.3. Linear Functions and Their Graphs

3.4. Linear Approximations and Microscopes

3.5. Euler’s Method and Compound Interest

3.6. The SIR Model by Computer

3.7. Solving Algebraic Equations

3.8. Chapter Summary

3.9. Exercises

Chapter 4. Track the Changes

4.1. Atmospheric Carbon

4.2. Other Derivatives and Marginal Quantities

4.3. Local Linearity and Microscopes

4.4. The Derivative

4.5. A Global View

4.6. Chapter Summary

4.7. Exercises

Chapter 5. Computing and Using Derivatives (What Goes Up Has to Stop Before It Comes Down)

5.1. Building Blocks

5.2. Adding, Subtracting, Multiplying, and Dividing Functions

5.3. The Chain Rule

5.4. Optimization

5.5. The Shape of a Graph

5.6. Newton’s Method

5.7. Chapter Summary

5.8. Supplemental Material: Small Angle Approximations

5.9. Exercises

Chapter 6. Models of Growth and Oscillation

6.1. Modeling with Differential Equations

6.2. Exponential Functions and Logarithms

6.3. Simple Models of Growth and Decay

6.4. Two Models of Oscillation

6.5. More Sophisticated Population Models

6.6. Chemistry

6.7. Chapter Summary

6.8. Supplemental Material: A Crash Course in Trigonometry

6.9. Exercises

Chapter 7. The Whole Is the Sum of the Parts

7.1. Slicing and Dicing

7.2. Riemann Sums

7.3. The Definite Integral

7.4. The Accumulation Function

7.5. Chapter Summary

7.6. Exercises

Chapter 8. The Fundamental Theorem of Calculus (One Step at a Time)

8.1. Three Different Quantities

8.2. FTC2: The Integral of the Derivative

8.3. FTC1: The Derivative of the Accumulation

8.4. AntiDerivatives and Ballistics

8.5. Computing AntiDerivatives

8.6. Chapter Summary

8.7. Exercises

Chapter 9. Methods of Integration

9.1. Integration by Substitution

9.2. Integration by Parts

9.3. Numerical Integration

9.4. Chapter Summary

9.5. Exercises

Chapter 10. One Variable at a Time

10.1. Partial Derivatives

10.2. Linear Approximations

10.3. Double Integrals and Iterated Integrals

10.4. Chapter Summary

10.5. Exercises

Chapter 11. Taylor Series

11.1. What Does 𝜋=3.14159265⋯ Mean?

11.2. Power Series

11.3. Taylor Polynomials and Taylor Series

11.4. Sines, Cosines, Exponentials, and Logs

11.5. Tests for Convergence

11.6. Intervals of Convergence

11.7. Chapter Summary

11.8. Exercises

Index

Back Cover


Additional Material

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 Book Details
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 Additional Material
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The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one or twosemester course. By boiling calculus down to six commonsense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning — to focus on when and why to use the tools of calculus, not just on how to apply formulas.
Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm.
The Biology Edition of the Six Pillars series has been extensively fieldtested at the University of Texas. It features hundreds of examples and problems specifically designed for students in the life sciences. The core ideas are introduced by modeling the spread of disease, tracking changes in the amount of \(\mathrm{CO}_{2}\) in the atmosphere, and optimizing blood flow in the body. Along the way, students learn about optimal drug delivery, population dynamics, chemical equilibria, and probability.
Additional material available:
 MATLAB files
 Online learning modules
 Worksheets
 WebAssign
Undergraduate students interested in calculus with applications.

Cover

Title page

Copyright

Contents

Instructors’ Guide and Background

Chapter 1. What is Calculus? The Six Pillars

Chapter 2. Predicting the Future: The SIR Model

2.1. Worried Sick

2.2. Building the SIR Model

2.3. Analyzing the Model Numerically

2.4. Theoretical Analysis: What Goes Up Has to Stop Before It Comes Down

2.5. Covid19 and Modified SIR Models

2.6. Same Song, Different Singer: SIR and Product Marketing

2.7. Chapter Summary

2.8. Exercises

Chapter 3. Close is Good Enough

3.1. The Idea of Approximation

3.2. Functions

3.3. Linear Functions and Their Graphs

3.4. Linear Approximations and Microscopes

3.5. Euler’s Method and Compound Interest

3.6. The SIR Model by Computer

3.7. Solving Algebraic Equations

3.8. Chapter Summary

3.9. Exercises

Chapter 4. Track the Changes

4.1. Atmospheric Carbon

4.2. Other Derivatives and Marginal Quantities

4.3. Local Linearity and Microscopes

4.4. The Derivative

4.5. A Global View

4.6. Chapter Summary

4.7. Exercises

Chapter 5. Computing and Using Derivatives (What Goes Up Has to Stop Before It Comes Down)

5.1. Building Blocks

5.2. Adding, Subtracting, Multiplying, and Dividing Functions

5.3. The Chain Rule

5.4. Optimization

5.5. The Shape of a Graph

5.6. Newton’s Method

5.7. Chapter Summary

5.8. Supplemental Material: Small Angle Approximations

5.9. Exercises

Chapter 6. Models of Growth and Oscillation

6.1. Modeling with Differential Equations

6.2. Exponential Functions and Logarithms

6.3. Simple Models of Growth and Decay

6.4. Two Models of Oscillation

6.5. More Sophisticated Population Models

6.6. Chemistry

6.7. Chapter Summary

6.8. Supplemental Material: A Crash Course in Trigonometry

6.9. Exercises

Chapter 7. The Whole Is the Sum of the Parts

7.1. Slicing and Dicing

7.2. Riemann Sums

7.3. The Definite Integral

7.4. The Accumulation Function

7.5. Chapter Summary

7.6. Exercises

Chapter 8. The Fundamental Theorem of Calculus (One Step at a Time)

8.1. Three Different Quantities

8.2. FTC2: The Integral of the Derivative

8.3. FTC1: The Derivative of the Accumulation

8.4. AntiDerivatives and Ballistics

8.5. Computing AntiDerivatives

8.6. Chapter Summary

8.7. Exercises

Chapter 9. Methods of Integration

9.1. Integration by Substitution

9.2. Integration by Parts

9.3. Numerical Integration

9.4. Chapter Summary

9.5. Exercises

Chapter 10. One Variable at a Time

10.1. Partial Derivatives

10.2. Linear Approximations

10.3. Double Integrals and Iterated Integrals

10.4. Chapter Summary

10.5. Exercises

Chapter 11. Taylor Series

11.1. What Does 𝜋=3.14159265⋯ Mean?

11.2. Power Series

11.3. Taylor Polynomials and Taylor Series

11.4. Sines, Cosines, Exponentials, and Logs

11.5. Tests for Convergence

11.6. Intervals of Convergence

11.7. Chapter Summary

11.8. Exercises

Index

Back Cover