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

3.8 Level surfaces

Topics:

level surfaces
- $F(x,y,z) = \text{const}$
tangent plane
- $\nabla F \cdot (\vec{r} - \vec{r_0}) = 0$

homework
homework (pdf)