Change and Motion - Calculus Made Clear
This course is crafted to make the key concepts and triumphs of calculus accessible to nonmathematicians. It requires only a basic acquaintance with beginning high-school level algebra and geometry. This series is not designed as a college calculus course; rather, it will help you see calculus around you in the everyday world
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 ? 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
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 ? 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
