18.022 | Fall 2010 | Undergraduate

Calculus of Several Variables


Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session


18.01 Single Variable Calculus


This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. Topics include:

  • Vector algebra, dot product, matrices, determinant.
  • Functions of several variables, continuity, differentiability, derivative.
  • Parametrized curves, arc length, curvature, torsion.
  • Vector fields, gradient, curl, divergence.
  • Multiple integrals, change of variables, line integrals, surface integrals.
  • Stokes’ theorem in one, two, and three dimensions.


Colley, Susan Jane. Vector Calculus. 3rd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2006. ISBN: 9780131858749.


Homework assignments are due on the second day of class every week. Late problem sets are not accepted, however the lowest problem set score will be dropped.


Assignments 25%
Hour exams 45%
Final exam 30%


1 Vectors in R2 and R3
2 Dot product
3 Cross product
4 Planes and distances
5 n-dimensional space
6 Cylindrical and spherical coordinates
7 Functions
8 Limits
9 The Derivative
10 More about derivatives
11 Higher derivatives
12 Chain rule
13 Implicit functions
14 Parametrised curves
15 Arclength
16 Moving frames
17 Vector fields
18 Div grad curl and all that
19 Taylor polynomials
20 Maxima and minima: I
21 Maxima and minima: II
22 Double integrals
23 Inclusion-exclusion
24 Triple integrals
25 Change of coordinates: I
26 Change of coordinates: II
27 Line integrals
28 Manifolds with boundary
29 Conservative vector fields revisited
30 Surface integrals
31 Flux
32 Stokes theorem
33 Gauss theorem
34 Forms on Rn

Course Info

As Taught In
Fall 2010
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes
Instructor Insights