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Math 234 — Final Exam Review
Syllabus |
Homework assignments |
About the exams |
Using your computer |
Lecture schedule
TOPICS
-
The linear approximation formula.
-
The second order Taylor approximation.
-
The chain rule applied to first and second partial derivatives.
-
Maxima and Minima: find critical points, and apply the second derivative
test to determine if they are local maximum, local minimum, saddle points.
In the case of saddle points use the second order Taylor expansion to find
the two tangent lines to the level set.
-
Maxima and Minima with constraints: the method of Lagrange multipliers.
-
Multiple integrals:
- Straightforward: integral over a rectangle, or a region of the form
\[
\cR = \bigl\{(x,y) \mid a\leq x\leq b, c(x)\leq y\leq d(x)\bigr\}
\]
- Switch the order of integration: i.e. given an integral of the
form
\[
I =\iint_\cR f(x, y)\, dA = \int_a^b \int_{c(x)}^{d(x)} f(x, y)\, dy\,dx,
\]
where $a$, $b$, $c(x)$, and $d(x)$ are given,
know how to find the region $\cR$ over which the integral is taken, and be
able to rewrite the integral as
\[
I = \int_{\text{?}}^{\text{?}} \int_{\text{?}}^{\text{?}} f(x, y) \, dx\,dy.
\]
- Special Coordinates: Know how to do integrals in Polar,
Cylindrical, and Spherical coordinates.
-
Line integrals and Green's theorem.
See the line integral summary for a
list of all the formulas on one page.