# 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 Hyperbolic functions and 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)

33 Exam 4 covering Ses #26-32 (No Lecture Notes)
34 Indeterminate forms - L'HÃ´spital'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)