Unless noted otherwise, all textbook readings are from:
Apostol, Tom M. Calculus, Vol. 2: MultiVariable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley, 1969. ISBN: 9780471000075.
Additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus, are also provided.
SES #  TOPICS  TEXTBOOK READINGS  COURSE NOTES READINGS 

1  Linear spaces and subspaces  1.11.6  Course Notes A (A1A6) 
2  Dependence, basis, dimension  1.71.8, 1.111.12  Course Notes A (A7A15) 
3  Linear transformations and invertibility  2.12.7  
4  GaussJordan elimination, matrices 
Course Notes A (A17A23) Course Notes B (B1B5) 

5  Matrix of a transformation, Linear systems  2.102.11  Course Notes B (B6B16) 
6  Matrix inverses, determinant  Course Notes B (B25B51)  
7  Cross product, Lines and planes 
Course Notes B (B53B56) Course Notes A (A25A33) Course Notes B (B18B23) 

8  Vector valued functions, tangency  (14.114.5) (Apostol Vol. I)  
9  Velocity/Acceleration, arclength  (14.614.12) (Apostol Vol. I)  
10  Curvature, Polar coordinates  (14.11414.16) (Apostol Vol. I)  Course Notes B (B57B63) 
11  Planetary motion, scalar and vector ﬁelds  (14.17, 14.20), 8.18.5 (Apostol Vol. I)  
12  Total derivative, gradient  8.68.8, 8.108.13  
13  Level sets, tangent planes, derivative of vector ﬁelds  8.158.17  
14  Exam 1  
15  Chain rule  8.188.21  
16  Implicit diﬀerentiation, inverse functions  9.69.7  Course Notes C (C10C21) 
17  Hessian matrix, maxima, minima, saddle points  9.9  
18  Second derivative test, Taylor’s Formula  9.99.12  Course Notes C (C22C27) 
19  Implicit function theorem  
20  Extreme Values, Lagrange Multipliers  9.14  Course Notes C (C28C33) 
21  Line integrals  10.110.7  
22  Fundamental theorem of line integrals  10.1010.14  
23  Gradient ﬁelds  10.1510.16  
24  Potential functions, conservation  10.17, 10.21  
25  Double integrals over rectangles  11.111.8  
26  Existence and Fubini’s Theorem  11.1011.11  Course Notes D (D1D17) 
27  Double integrals over more general regions  11.1211.14  Course Notes D (D17D25) 
28  Applications of multiple integrals  11.16, 11.17, 11.31  
29  Exam 2  
30  Green’s Theorem  11.1911.23  
31  Applications  Course Notes E (E1E22)  
32  Change of variables  11.2611.31  Course Notes E (E23E33) 
33  Cylindrical and spherical coordinates  11.32, 11.33  
34  Parameterized surfaces  12.112.5  
35  Area, surface integrals  12.712.9  
36  Stokes’s Theorem  12.1112.12, 12.18  
37  Stokes’s Theorem (cont.)  Course Notes F (F1F5)  
38  Divergence Theorem  12.19  
39  Minimal Surfaces  Course Notes F (F7F16)  
40  Final Exam 