Multivariable Calculus 1: Vectors and Derivatives

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
• Review
• Vectors and derivatives in three dimensions and higher