Math 20 Syllabus

Note: two of these sections run on a MWF schedule
and one of the sections runs on a TuTh schedule.
For this reason, there might not be an exact day-to-day
match between the listed topics and the lectures.
However, the syllabus should be very accurate on a
week by week basis.

Week 1 Chapter 12

• 12.1-12.3 review of vectors: dot and cross product,
  

Week 2 Chapter 12

• 12.4 lines and planes
• 12.5 parametric curves
• 12.6 curvature and acceleration

Week 3 Chapter 13

• 13.1-13.2 intro to functions of several variables.
• 13.3 continuity of functions of several variables.
• 13.4 partial deriatives

Week 4 Chapter 13

• 13.5 first derivative test in several variables.
• 13.6 matrices and linear approximation

Week 5 Chapter 13

• 13.7 chain rule
• 12.8 gradient and directional derivatives

Week 6 Chapter 13

• 13.9 Lagrange multipliers
• 13.10 second derivative test

Week 7 Chapter 14

• 14.1: definition of double integral
• 14.2: doing double integrals in practice
• 14.3: area and volume using double integrals

Week 8 Chapter 14

• 14.4: double integrals in polar coords.
• 14.5: further applications of double integrals
• 14.6: triple integrals

Week 9 Chapter 14

• 14.7: triple integrams in spherical and cylindrical coords.
• 14.8: surface area
• 14.9: change of variables (especially cylindrical & spherical)

Week 10 Chapter 14

• 15.1: vector fields; div, grad, curl
  
• 15.2: line integrals

Week 11 Chapter 15

• 15.3: conservative vector fields; independence of path
  
• 15.4: Green's theorem
  

Week 12 Chapter 15

• 15.4: Green's theorem
• 15.5: Surface integrals

Week 13 Chapter 15

• 15.6: divergence theorem

Week 14 Chapter 15

• 15.6: Stokes' theorem