Unit 1: Functions of two variables
Graphing functions and slicing
Level curves
Partial derivatives
Tangent planes
Linear approximation
Unit 2: Geometry of derivatives
Vectors
Dot products
Gradients
Vector fields
Directional derivatives
Unit 3: Optimization
Critical points
Second derivative test
Constrained optimization
Lagrange multipliers
Least squares approximation
Unit 4: Matrices
Systems of equations
Matrix algebra
Undetermined and overdetermined systems
Linear functions as matrix maps
Unit 5: Curves
Parametric curves in 2 and 3 dimensions
Chain rule
Vectors and derivatives in three dimensions and higher
Syllabus