18.01 | Fall 2006 | Undergraduate
Single Variable Calculus

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
Instructor
Departments
As Taught In
Fall 2006
Learning Resource Types
assignment Problem Sets
grading Exams with Solutions
notes Lecture Notes
theaters Lecture Videos