| Softcover ISBN: | 978-1-4704-6996-2 |
| Product Code: | AMSTEXT/60 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-7243-6 |
| Product Code: | AMSTEXT/60.E |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| Softcover ISBN: | 978-1-4704-6996-2 |
| eBook: ISBN: | 978-1-4704-7243-6 |
| 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: | 978-1-4704-6996-2 |
| Product Code: | AMSTEXT/60 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-7243-6 |
| Product Code: | AMSTEXT/60.E |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| Softcover ISBN: | 978-1-4704-6996-2 |
| eBook ISBN: | 978-1-4704-7243-6 |
| 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 |
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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 two-semester course. By boiling calculus down to six common-sense 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 field-tested 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. Covid-19 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. Anti-Derivatives and Ballistics
-
8.5. Computing Anti-Derivatives
-
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
-
RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseInstructor's Solutions Manual – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense 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 field-tested 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. Covid-19 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. Anti-Derivatives and Ballistics
-
8.5. Computing Anti-Derivatives
-
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
