18.02 | Fall 2007 | Undergraduate

Multivariable Calculus


I. Vectors and matrices
0 Vectors  
1 Dot product  
2 Determinants; cross product  
3 Matrices; inverse matrices  
4 Square systems; equations of planes Problem set 1 due
5 Parametric equations for lines and curves  

Velocity, acceleration

Kepler’s second law

7 Review Problem set 2 due
  Exam 1 (covering lectures 1-7)  
II. Partial derivatives
8 Level curves; partial derivatives; tangent plane approximation  
9 Max-min problems; least squares Problem set 3 due
10 Second derivative test; boundaries and infinity  
11 Differentials; chain rule  
12 Gradient; directional derivative; tangent plane Problem set 4 due
13 Lagrange multipliers  
14 Non-independent variables  
15 Partial differential equations; review Problem set 5 due
  Exam 2 (covering lectures 8-15)  
III. Double integrals and line integrals in the plane
16 Double integrals Problem set 6 due
17 Double integrals in polar coordinates; applications  
18 Change of variables  
19 Vector fields and line integrals in the plane Problem set 7 due
20 Path independence and conservative fields  
21 Gradient fields and potential functions  
22 Green’s theorem Problem set 8 due
23 Flux; normal form of Green’s theorem  
24 Simply connected regions; review  
  Exam 3 (covering lectures 16-24) Problem set 9 due
IV. Triple integrals and surface integrals in 3-space
25 Triple integrals in rectangular and cylindrical coordinates  
26 Spherical coordinates; surface area  
27 Vector fields in 3D; surface integrals and flux Problem set 10 due
28 Divergence theorem  
29 Divergence theorem (cont.): applications and proof  
30 Line integrals in space, curl, exactness and potentials  
31 Stokes’ theorem Problem set 11 due
32 Stokes’ theorem (cont.); review  
  Exam 4 (covering lectures 25-32)  

Topological considerations

Maxwell’s equations

Problem set 12 due
34 Final review  
35 Final review (cont.)  
36 Final exam  

Course Info

As Taught In
Fall 2007
Learning Resource Types
Lecture Videos
Problem Sets
Exams with Solutions
Lecture Notes