01-1. Introduction to the course
2. It's all about power, growth, and decay
3. One graph to rule them all
4. General questions we ask about functions
5. Simple answers domain, range, zeros, y-intercept, monotonicity, invertibility
6. Some extraordinarily complicated questions
02-1. Short and sweet about the number e
2. Summation notation a repetition and some properties
3. Short and sweet about Pascal's Triangle
4. What about powers of a difference
5. Let's practice raising binomials to positive natural powers
6. Factorial and binomial coefficients
7. Short and sweet about the Binomial Theorem
9. A formal proof of the Binomial Theorem by induction
10. Optional A combinatorial proof of the Binomial Theorem
11. Optional, but really delightful
12. Advanced Axiom of Completeness in terms of a supremum
13. Advanced Convergence of a monotone sequence of real numbers
14. Advanced Convergence of geometric sequences and series
15. Advanced Motivation of the definition and irrationality of the number e
2. Powers with positive natural exponents
6. How we expand the definition of powers to other exponents
7. Zero powers and indeterminate forms
8. Powers with negative integer exponents
9. Powers with rational exponents
10. Advanced Existence of roots
11. More about powers with rational exponents
12. Powers with real exponents; graphs of exponential functions
13. Computing various powers, Problem 1
14. Computing various powers, Problem 2
15. Computing various powers, Problem 3
16. Computing various powers, Problem 4
17. Computing various powers, Problem 5
18. Computing various powers, Problem 6
19. Simplifying expressions, Problem 7
20. Simplifying expressions, Problem 8
21. Simplifying expressions, Problem 9
22. Simplifying expressions, Problem 10
23. Simplifying expressions, Problem 11
24. Simplifying expressions, Problem 12
25. Simplifying expressions, Problem 13
26. Careful with signs, Problem 14
27. Careful with signs, Problem 15
28. Careful with signs, Problem 16
29. Comparing numbers, Problem 17
30. Comparing numbers, Problem 18
31. Comparing numbers, Problem 19
32. The charms of squares and conjugates, Problem 20
33. The charms of squares and conjugates, Problem 21
34. The charms of squares and conjugates, Problem 22
35. The charms of squares and conjugates, Problem 23
36. The charms of squares and conjugates, Problem 24
37. The charms of squares and conjugates, Problem 25
38. The charms of squares and conjugates, Problem 26
39. The cubes, Problem 27
40. The cubes, Problem 28
41. Squares and cubes, Problem 29
42. The cubes, Problem 30
43. Squares and cubes, Problem 31
44. An equation, Problem 32
45. The last one, Problem 33
04-1. A general introduction to power functions
2. Power functions with positive natural exponents
3. Power functions with negative integer exponents
4. Power functions with positive fractional exponents
5. Power functions with negative fractional exponents
6. Power functions with real exponents
7. Advanced What is the derivative telling you about monotonicity and cusps
8. Power functions, Exercise 1
9. Power functions, Exercise 2
10. Power functions, Exercise 3
11. Typical graph transformations, Exercise 4
05-1. Properties of exponential functions
2. Comparing powers with the same base, Problem 1
3. Comparing powers with the same base, Problem 2
4. Properties of exponential functions, Problem 3
5. Properties of exponential functions, Problem 4
6. Exponential functions, Problem 5
7. Exponential functions, Problem 6
8. Exponential functions, Problem 7
9. Exponential functions, a trick to remember, Problem 8
10. Graphs of exponential functions, and their transformations, Problem 9
11. Exponential functions, another trick to remember, Problem 10
12. Exponential functions, Problem 11
13. Exponential functions, Problem 12
14. Exponential functions, Problem 13
15. Exponential functions, Problem 14
16. Exponential functions, Problem 15
17. Exponential functions, Problem 16
18. Graphical methods for solving equations, Problem 17
19. How graphs of exponential functions relate to each other
20. Interactions between power functions and exponential functions
