This is a tentative syllabus. This page
will be updated irregularly.





The geometry of Euclidean space 


The geometry of realvalued functions
Limits and continuity 


Differentiation, Introduction to paths,
Properties of the derivative 


Gradients and directional derivatives.
Iterated partial derivatives. 


Taylor's theorem.
Extrema of realvalued functions 


Constrained extrema and Lagrange multipliers.
The implicit function theorem 


Some applications 


Acceleration and Newton's Second Law
Arc Length 

Martin Luther
King Jr. Day 
Classes moved to the Xhour 


Vector fields
Divergence and curl 


The double integral 


The double integral over more general regions
Changing the order of integration 


The triple integral 


The geometry of maps from R^2 to R^2
The change of variables theorem 


The change of variables theorem
Applications of double and triple integrals 
Xperiod Tuesday Feb 5, 2002  6.3, 6.4  Applications of double and triple integrals
Improper integrals 


The path integral
The line integral 
Friday  Feb 8, 2002  Carnival Holiday  Classes moved to the Xperiod 


Parametrized surfaces 


Area of a surface 


Integrals of scalar functions over surfaces 


Surface integrals of vector functions 


Green's theorem 


Stoke's theorem 


Conservative fields 


Gauss' theorem 


Applications to physics, engineering, and differential equations 


Differential forms 

Review 
Last updated: January 1, 2002