I. Vector algebra

Video lectures

1. Scalars and vectors (5 min 6 sec)
2. Anatomy of a vector (2 min 44 sec)
3. Base vectors and the Cartesian Coordinate System (9 min 37 sec)
4. Vector addition and subtraction (7 min 59 sec)
5. Position and distance vectors (9 min 57 sec)
6. Dot product (26 min 29 sec)
7. Cross product (18 min 32 sec)

II. Coordinate systems

Video lectures

1. Coordinate system intro (4 min 24 sec)
2. Cylindrical coordinate system (35 min 2 sec)
3. Spherical coordinate system (23 min 28 sec)

III. Vector calculus

Video lectures

1. Riemann sum review (13 min 21 sec)
2. Differential elements in three coordinate systems (56 min 54 sec)
3. The gradient (11 min 46 sec)
4. Flux and divergence (19 min 11 sec)
5. Curl and Stokes' Theorem(23 min 20 sec)

Other resources

Tables

• Summary of coordinate transformation relations
• Summary of basic vector relations