Learning Outcomes for Math 113
At the end of the course, Math 113 students should be able to...
1. compute dot products, projections, determinants, cross products, equations of planes and
volumes of parallelopipeds.
2. use the dot product to find the angle between two vectors.
3. use the right hand rule to determine the direction of a cross product.
4. compute the distance between an point and a line, or a point and a plane.
5. match an algebraic description of an object (a curve, quadric surface, the graph of a
function, or a vector field) with a visualization of it.
6. compute and interpret derivatives of functions ~r : R → R3 .
7. compute and interpret arc length, curvature, normal and binormal vectors.
8. determine if limits of multivarible functions exist, and evaluate those that do.
9. compute partial derivatives (either directly or via an application of the chain rule).
10. interpret a visualization of a function or a vector field by providing qualitative information
about derivatives (partial derivatives, divergence, or curl).
11. compute the equations of tangent planes to surfaces (both graphs of functions, and implicitly defined ones).
12. compute and interpret directional derivatives and the gradient.
13. solve problems about motion in space (involving motion of particles as well as reflection
of light).
14. maximize and minimize functions of several variables (both unconstrained and constrained).
15. apply the 2nd derivative test for functions of two variables to analyze the nature of critical
points.
16. compute divergence and curl and describe their physical interpretations.
17. evaluate multiple integrals (either directly, by switching the order of integration, or changing to polar coordinates).
18. decide which of the techniques for computing multiple integrals is most appropriate to
apply in a given situation.
19. compute and interpret scalar line integrals using the definition.
20. compute and interpret vector line integrals (either using the definition, the theory of
conservative vector fields, or Green’s theorem).
21. decide which of the techniques for computing vector line integrals is most appropriate in
a given situation.
22. determine if a vector field is conservative, and if so compute a potential function for it.
23. parse a problem statement involving continuous probability and determine the relevant
density function.
24. compute probabilities and expected valued by evaluating integrals of probability density
functions.
25. use Maple to compute partial derivatives, plot curves, functions and vector fields, solve
systems of equations, and compute multiple integrals.