Math 227 -Calculus III- Fall 2022

Weekly schedule

Week 1
Vectors in 2-3 dimensions, dot product
Week 2
Cross product, the equation of a plane
Week 3
Quadratic surfaces, cylindrical and spherical coordinates and vector valued functions
Week 4
Calculus of vector valued functions, arc length and speed
Week 5
Curvature and motion in 3-space

Midterm 1

Week 6
Multi-variable functions and their limits, partial derivatives
Week 7
Differentiability, gradient and directional derivatives
Week 8
The chain rule and optimization

Midterm 2

Week 9
Integration  in 2 variables
Integration on general regions, triple integrals
Week 11
Integration in polar and cylindrical coordinates

Midterm 3

Week 12
Vector fields, line integrals and conservative fields
Week 13
Green and Stoke’s theorems