Hardcover ISBN:  9780883857878 
Product Code:  CLRM/50 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781614441182 
Product Code:  CLRM/50.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857878 
eBook: ISBN:  9781614441182 
Product Code:  CLRM/50.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 
Hardcover ISBN:  9780883857878 
Product Code:  CLRM/50 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781614441182 
Product Code:  CLRM/50.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Hardcover ISBN:  9780883857878 
eBook ISBN:  9781614441182 
Product Code:  CLRM/50.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 

Book DetailsClassroom Resource MaterialsVolume: 50; 2015; 228 pp
This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs.
The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth.
A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.

Table of Contents

Chapters

The Foundation On Which Calculus Stands

1. Critical Points and Graphing

2. Inverse Functions

3. Exponential and Logarithmic Functions

4. Linear Approximation and Newton’s Method

5. Taylor Polynomial Approximation

6. Global Extreme Values

7. Angular Velocity and Curvature

8. $\pi $ and $e$ are Irrational

9. Hanging Cables

10. The Buffon Needle Problem

11. Optimal Location

12. Energy

13. Springs and Pendulums

14. Kepler’s Laws of Planetary Motion

15. Newton’s Law of Universal Gravitation

16. From Newton To Kepler and Beyond


Additional Material

Reviews

“The Heart of Calculus” guides readers through a variety of focused and indepth investigations to demonstrate the beauty and completeness of the calculus. ...
Mathematics Teacher


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This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs.
The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth.
A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.

Chapters

The Foundation On Which Calculus Stands

1. Critical Points and Graphing

2. Inverse Functions

3. Exponential and Logarithmic Functions

4. Linear Approximation and Newton’s Method

5. Taylor Polynomial Approximation

6. Global Extreme Values

7. Angular Velocity and Curvature

8. $\pi $ and $e$ are Irrational

9. Hanging Cables

10. The Buffon Needle Problem

11. Optimal Location

12. Energy

13. Springs and Pendulums

14. Kepler’s Laws of Planetary Motion

15. Newton’s Law of Universal Gravitation

16. From Newton To Kepler and Beyond

“The Heart of Calculus” guides readers through a variety of focused and indepth investigations to demonstrate the beauty and completeness of the calculus. ...
Mathematics Teacher