Proposed Syllabus

Sections

Comments/Topics

Lecture 1        

4.8

Antiderivatives

Lecture 2

5.1

Area and estimating with finite sums

Lecture 3

5.2

Sigma notation and limits of finite sums

Lecture 4

5.3

The definite integral

Lecture 5

5.4

The Fundamental Theorem of Calculus

Lecture 6

5.5

Indefinite integrals and the substitution method

Lecture 7

5.6

Substitution and area between curves

Lecture 8

6.1

Volumes using cross sections

Lecture 9

6.2

Volumes using cylindrical shells

Lecture 10

6.3

Arc length

Lecture 11

6.4

Areas of surfaces of revolution

Lecture 12

6.5

Work and fluid forces

Lecture 13

6.6

Moments and centers of mass

Lecture 14

7.1

The logarithm defined as an integral

Lecture 15

7.2

Exponential change and separable differential equations

Lecture 16

8.1, 8.2

Review, Integration by parts

Lecture 17

8.3

Trigonometric integrals

Lecture 18

8.4

Trigonometric substitutions

Lecture 19

8.5

Integrations of rational functions by partial fractions

Lecture 20

8.7

Numerical integration

Lecture 21

8.8

Improper integrals

Lecture 22

11.1

Parametrization of plane curves

Lecture 23

11.2

Calculus with parametric curves

Lecture 24

11.3 & 11.4 & 11.5  

Polar coordinates