Lecture Notes

SES # TOPICS LECTURE NOTES
Derivatives
1 Derivatives, slope, velocity, rate of change ( PDF - 1.1 MB) Ses #1-7 complete ( PDF - 5.2 MB)
2

Limits, continuity

Trigonometric limits

( PDF - 2.6 MB)
3 Derivatives of products, quotients, sine, cosine ( PDF)
4

Chain rule

Higher derivatives

( PDF)
5 Implicit differentiation, inverses ( PDF)
6

Exponential and log

Logarithmic differentiation; hyperbolic functions

( PDF)
7 Exam 1 review ( PDF)
8 Exam 1 covering Ses #1-7 (No Lecture Notes)
Applications of Differentiation
9 Linear and quadratic approximations ( PDF) Ses #9-16 complete ( PDF - 6.9 MB)
10 Curve sketching ( PDF - 1.8 MB)
11 Max-min problems ( PDF - 1.1 MB)
12 Related rates ( PDF - 1.0 MB)
13 Newton’s method and other applications ( PDF - 1.2 MB)
14

Mean value theorem

Inequalities

( PDF)
15 Differentials, antiderivatives ( PDF)
16 Differential equations, separation of variables ( PDF)
17 Exam 2 covering Ses #8-16 (No Lecture Notes)
Integration
18 Definite integrals ( PDF) Ses #18-25 complete ( PDF - 8.6 MB)
19 First fundamental theorem of calculus ( PDF)
20 Second fundamental theorem ( PDF)
21 Applications to logarithms and geometry ( PDF - 1.4 MB)
22 Volumes by disks and shells ( PDF - 1.7 MB)
23 Work, average value, probability ( PDF - 2.2 MB)
24 Numerical integration ( PDF - 1.1 MB)
25 Exam 3 review ( PDF)
Techniques of Integration
26 Trigonometric integrals and substitution ( PDF) Ses #26-38 complete ( PDF - 8.6 MB)
27 Exam 3 covering Ses #18-24 (No Lecture Notes)
28 Integration by inverse substitution; completing the square ( PDF)
29 Partial fractions ( PDF)
30 Integration by parts, reduction formulae ( PDF - 1.4 MB)
31 Parametric equations, arclength, surface area ( PDF)
32

Polar coordinates; area in polar coordinates

Exam 4 review

( PDF - 2.0 MB)

( PDF)

33 Exam 4 covering Ses #26-32 (No Lecture Notes)
34 Indeterminate forms - L’Hôspital’s rule ( PDF)
35 Improper integrals ( PDF)
36 Infinite series and convergence tests ( PDF - 1.4 MB)
37 Taylor’s series ( PDF)
38 Final review ( PDF)

Course Info

Learning Resource Types

assignment Problem Sets
grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos