18.01 | Fall 2006 | Undergraduate
Single Variable Calculus

Calendar

SES # TOPICS KEY DATES
Derivatives
0 Recitation: graphing  
1 Derivatives, slope, velocity, rate of change  
2

Limits, continuity

Trigonometric limits

 
3 Derivatives of products, quotients, sine, cosine  
4

Chain rule

Higher derivatives

 
5 Implicit differentiation, inverses Problem set 1 due
6

Exponential and log

Logarithmic differentiation; hyperbolic functions

 
7 Exam 1 review  
8 Exam 1 covering Ses #1-7  
Applications of Differentiation
9 Linear and quadratic approximations  
10 Curve sketching  
11 Max-min problems Problem set 2 due
12 Related rates  
13 Newton’s method and other applications  
14

Mean value theorem

Inequalities

Problem set 3 due
15 Differentials, antiderivatives  
16 Differential equations, separation of variables  
17 Exam 2 covering Ses #8-16  
Integration
18 Definite integrals  
19 First fundamental theorem of calculus Problem set 4 due
20 Second fundamental theorem  
21 Applications to logarithms and geometry  
22 Volumes by disks, shells Problem set 5 due
23 Work, average value, probability  
24 Numerical integration  
25 Exam 3 review  
Techniques of Integration
26 Trigonometric integrals and substitution  
27 Exam 3 covering Ses #18-24 Problem set 6 due
28 Integration by inverse substitution; completing the square  
29 Partial fractions  
30 Integration by parts, reduction formulae Problem set 7 due
31 Parametric equations, arclength, surface area  
32

Polar coordinates; area in polar coordinates

Exam 4 review

 
33 Exam 4 covering Ses #26-32  
34 Indeterminate forms - L’Hôspital’s rule  
35 Improper integrals  
36 Infinite series and convergence tests  
37 Taylor’s series Problem set 8 due
38 Final review  
  Final exam  
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