MultiV
Multivariable Calculus
2021-22
Marlborough School
Dr. Kessner
Class Info
Resources
Topics
Schedule
Assignments
About
1.1-1.3 3D, Vectors, Dot Product
1.4 Matrices and determinants
1.5 Cross product
1.6 Lines and planes
1.7 Cyl/Sphere Coordinates
Bonus: Projection and Regression
Unit 1
2.1 Vector valued functions
2.2 Calculus (vector valued)
2.3 Arc length
2.4 Tangent, normal, binormal
2.5 Motion (and Conics)
2.6 Polar Conics
2.7 Kepler's Laws
Unit 2
3.1 Functions of Several Variables
3.2 Limits and continuity
3.3 Partial derivatives
3.4 Differentiability
3.5 Linear transformations
3.6 Chain rule
3.7 Directional derivatives
3.8 Level surfaces
Unit 3
4.1 Rotation of axes
4.2 Optimization
4.3 Constrained optimization
4.4 Lagrange multipliers
Unit 4
5.1 Double integrals
5.2 More double integrals
5.3 More more double integrals
5.4 Polar coordinates
5.5 Parametric surfaces
5.6 More surfaces
5.7 Triple integrals
5.8 Cyl/Sphere Coordinates
5.9 Change of variables
5.10 Centroids
5.11 Disks and shells
5.12 Pappus' Theorem
Unit 5
6.1 Wedge Product
6.2 Geometric Product
6.3 Wedge Product in 3D
6.4 Geometric Product in 3D
6.5 Cramer's Rule
6.6 Rotations
Unit: Geometric Algebra
5.2 More double integrals
Topics:
double integrals over non-rectangular regions
notes (pdf)