Change and Motion: Calculus Made Clear, 2nd Edition

1
Two Ideas, Vast Implications
2
Stop Sign Crime—The First Idea of Calculus—The Derivative
3
Another Car, Another Crime—The Second Idea of Calculus—The Integral
4
The Fundamental Theorem of Calculus
5
Visualizing the Derivative—Slopes
6
Derivatives the Easy Way—Symbol Pushing
7
Abstracting the Derivative—Circles and Belts
8
Circles, Pyramids, Cones, and Spheres
9
Archimedes and the Tractrix
10
The Integral and the Fundamental Theorem
11
Abstracting the Integral—Pyramids and Dams
12
Buffon’s Needle or π from Breadsticks

13
Achilles, Tortoises, Limits, and Continuity
14
Calculators and Approximations
15
The Best of All Possible Worlds—Optimization
16
Economics and Architecture
17
Galileo, Newton, and Baseball
18
Getting off the Line—Motion in Space
19
Mountain Slopes and Tangent Planes
20
Several Variables—Volumes Galore
21
The Fundamental Theorem Extended
22
Fields of Arrows—Differential Equations
23
Owls, Rats, Waves, and Guitars
24
Calculus Everywhere