18.022 | Fall 2010 | Undergraduate
Calculus of Several Variables

Lecture Notes

 1 Vectors in R2 and R3 (PDF)
 2 Dot product (PDF)
 3 Cross product (PDF)
 4 Planes and distances (PDF)
 5 n-dimensional space (PDF)
 6 Cylindrical and spherical coordinates (PDF)
 7 Functions (PDF)
 8 Limits (PDF)
 9 The Derivative (PDF)
 10 More about derivatives (PDF)
 11 Higher derivatives (PDF)
 12 Chain rule (PDF)
 13 Implicit functions (PDF)
 14 Parametrised curves (PDF)
 15 Arclength (PDF)
 16 Moving frames (PDF)
 17 Vector fields (PDF)
 18 Div grad curl and all that (PDF)
 19 Taylor polynomials (PDF)
 20 Maxima and minima: I (PDF)
 21 Maxima and minima: II (PDF)
 22 Double integrals (PDF)
 23 Inclusion-exclusion (PDF)
 24 Triple integrals (PDF)
 25 Change of coordinates: I (PDF)
 26 Change of coordinates: II (PDF)
 27 Line integrals (PDF)
 28 Manifolds with boundary (PDF)
 29 Conservative vector fields revisited (PDF)
 30 Surface integrals (PDF)
 31 Flux (PDF)
 32 Stokes theorem (PDF)
 33 Gauss theorem (PDF)
 34 Forms on Rn (PDF)
Course Info
As Taught In
Fall 2010
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
grading Exams with Solutions
notes Lecture Notes
co_present Instructor Insights