1. Graphing functions; 2. Introduction to limits of functions; 3. Zooming in; 4. Discovering the derivative; 5. Investigating the intermediate value theorem; 6. Relationship between a function and its derivative; 7. Linking up with the chain rule; 8. Sensitivity analysis; 9. Newton's method; 10. Indeterminate limits and l'Hôpital's Rule; 11. Riemann sums and the definite integral; 12. Area functions; 13. Average value of a function; 14. Arc length; 15. A mystery function; 16. Exploring exponentials; 17. Patterns of integrals; 18. Numerical integration; 19. Becoming secure with sequences; 20. Getting serious about series; 21. Limit comparison test; 22. Approximate functions by polynomials; 23. Radius of convergence for power series; 24. Polar equations; 25. Differential equations and Euler's method; 26. Shapes of surfaces; Syllabi for calculus I and II.
