Lec #  topics  readings 

I. Vectors and Matrices  
1  Vectors in 2 and 3space Dot Product 
Text: Sections 17.3, 18.1, 18.2 
2  Determinants of Orders 2 and 3 Cross Product 
Text: Section 18.3 Notes: Section D 
3  Matrices; Inverse Matrices  
4  Solving Systems of Linear Equations; Lines, Planes  
5  Parametric Curves; Velocity, Acceleration  Text: Sections 18.4, 17.1, 17.4 
6  Kepler's Second Law  Text: 17.7 Notes: Section K 
Exam 1 (Covering Lectures 16)  
II. Partial Derivatives  
7  Level Curves, Partial Derivatives, Tangent Plane  Text: Sections 19.119.3 Notes: Section TA 
8  MaxMin Problems Least Squares Approximation 
Text: Section 19.7 Notes: Section LS 
9  2nd Derivative Test; Boundaries and Infinity  
10  Differentials; Chain Rule  Text: Section 19.6 
11  Gradient, Directional Derivative  Text: Section 19.5 
12  Lagrange Multipliers  Text: Section 19.8 
13  Nonindependent Variables  
14  Partial Differential Equations Review 
Text: Section 19.8 
Exam 2 (Covering Lectures 714)  
III. Double and Triple Integrals  
15  Double and Iterated Integrals  Text: Sections 20.1, 20.2 Notes: Section I.1 
16  Double Integrals in Polar Coordinates Applications 
Text: Sections 20.3, 20.4 Notes: Section I.2 
17  Change of Variables  Text: Section 20.3 
18  Triple Integrals in Rectangular and Cylindrical Coordinates  Text: Sections 20.5, 10.6 
19  Spherical Coordinates Gravitational Attraction 
Text: Section 20.7 
IV. Vector Calculus in 2 and 3space  
20  Line Integrals in the Plane  Text: Section 21.1 Notes: Section V1 
21  Gradient Fields and Path Independence  Text: Section 21.2 Notes: Section V2.1 
22  Conservative Fields and Potential Functions  
23  Green's Theorem 2dimensional Curl (Vorticity) 
Text: Section 21.3 Notes: Section V4.3 
24  Simplyconnected Regions Review 

Exam 3 (Covering Lectures 1524, Except 1819)  
25  Flux Form of Green's Theorem  
26  Vector Fields in 3space; Surface Integrals and Flux  
27  Divergence (= Gauss's) Theorem  Text: Section 21.4 Notes: Section V10 
28  Divergence Theorem (cont.)  
29  Line Integrals in Space, Exactness, and Potentials  
30  Stokes' Theorem  Text: Section 21.5 Notes: Section V4.3, V13 
31  Understanding Curl Review 

Exam 4 (Covering Lectures 1819, 2531)  
32  Topological Issues  
33  Conservation Laws; Heat/Diffusion Equation  
34  Course Review  
35  Course Evaluation Maxwell's Equations 
Text: Section 21.6 Notes: Section V15 