Section(s)  
1.  Multivariable Functions  
a.  Definitions and notation  14.1, 15.1  
b.  Representations: graphs and images  
c.  Slicing and projections  
2.  Vectors  
a.  Definitions  13.1, 13.2  
b.  Vector operations  13.3, 13.4  
c.  Vector decomposition  13.3  
d.  Angles between vectors  13.3  
3.  Lines and Planes in Space  
a.  Equations: graph, parametric, implicit  13.5, 13.6  
b.  Normal vectors  13.6  
4.  Introduction to Linear Algebra  (In supplement)  
a.  Systems of linear equations  1.1, 1.2, 1.3  
b.  Matrices and matrix arithmetic  1.4, 1.5  
c.  Inverse matrices  1.6  
d.  Determinants  2.1, 2.2  
^{ }5.  Functions of
the form (Surfaces in Space as Graphs of a Funcion)  
a.  Directional derivatives  15.6  
b.  Partial derivatives  15.3  
c.  The gradient vector  15.6  
d.  The normal vector  15.3  
e.  The tangent plane  15.3  
f.  Critical points and optimization problems  15.8, 15.9  
g.  Limits and continuity  15.2  
^{ }6.  Functions of
the form (Parametric Curves in Space)  
a.  Velocity and acceleration  14.2  
b.  Tangent and normal vectors  14.4  
^{ }7.  Functions
of the form (Parametric Surfaces in Space)  
a.  Partial derivatives  15.7  
b.  The normal vector and tangent plane  
c.  The Jacobian matrix  
d.  The multivariable chain rule  15.5  
^{ }8.  Functions of
the form (Implicit Surfaces in Space)  
a.  Gradients and partial derivatives  15.1, 15.7  
b.  Tangent planes and normal vectors  15.7 
See the course calendar for details concerning exams and quizzes.

