Proposed Syllabus

Lecture(s)  

Sections    

Comments/Topics

Optional Homework

1

various

Review of Highschool Math

1

2.1, 2.2

Motivations, Limit of a function and limit laws

2.2: 5, 9, 10, 19, 28, 35, 51, 52, 55, 77

2

2.3

Precise definition of limit

2.3: 7, 13, 21, 23, 37, 38, 39, 41, 46, 49

1

2.4

One-sided limits

2.4: 3, 7, 51, 53

1.5

2.5

Continuity

2.5: 1, 7, 13, 19, 13, 15, 17, 43, 57, 61, 69

1.5

2.6

Limits involving infinity; asymptotes of graphs

2.6: 5, 15, 19, 25, 33, 43, 45, 49, 57, 71

0.5

3.1

Tangents and the derivative at a point

11, 15, 29, 31, 35

1

3.2

The derivative as a function

23, 25, 27, 29, 31, 45, 49, 55

1.5

3.3

Differentiation rules

9, 17, 35, 55, 59, 71, 79

1

3.4

The derivative as a rate of change

3, 7, 13, 15, 21

0.5

3.5

Derivatives of trigonometric functions

9, 21, 31, 49, 53, 59, 63

1.5

3.6

The Chain Rule

11, 25, 29, 45, 77, 89, 97

1

3.7

Implicit differentiation

11, 15, 25, 31, 37, 45, 49, 53

1

3.8

Derivative of inverse functions and logarithms

5, 17, 23, 31, 39, 49, 57, 65, 79, 93

1

3.9

Inverse trigonometric functions

3, 5, 11, 17, 21, 25, 33, 37, 45, 49

1

3.10

Related rates

11, 15, 19, 21, 23, 29, 31, 37, 38, 39, 43

1

4.1

Extreme values of functions

11, 13, 23, 25, 31, 41, 55, 59, 69, 71, 78

1

4.2

The Mean Value Theorem

3, 5, 13, 15, 17, 29, 51, 53, 63, 69

1

4.3

Monotonic functions and the first derivative test

5, 7, 11, 15, 25, 37, 53, 57, 71

1

4.4

Concavity and curve sketching

3, 7, 13, 17, 27, 33, 45, 47, 51, 93, 95, 109

1

4.5

Indeterminate forms and L'Hopital's Rule

5, 11, 17, 27, 35, 41, 45, 49, 55, 57, 63, 69, 71, 77, 79

1

4.6

Applied optimization

3, 5, 9, 13, 19, 23, 27, 31, 35, 39, 43, 47, 51, 65

1

Newton's method

3, 5, 9, 11, 12, 13, 23, 25