Course Exams
Note: More information will be added as the exam dates near
First Midterm Exam: Wed Feb 29
The first exam will cover Sections 11.1 - 11.4 and 12.1 - 12.2.
In particular you should be able to do the following:
- State basic definitions and theorems
- Write down a parametric or polar expression for a curve
- Given a curve in parametric or polar form, draw a graph
- Go between parametric, polar and Cartesian forms for a curve
- Given a curve in parametric or polar form, find tangent lines,
the area enclosed by a curve, and the arclength of a curve
- Given a sequence or series, determine if it converges or diverges
- Find the limit of a convergent sequence or series
Here are Practice Problems (Set 1) and
My Solutions (warning: I did not check
these).
Here are Practice Problems (Set 2) and
My Solutions (warning: I did not check
these).
Second Midterm Exam: Fri Apr 20
The second exam will cover all of Chapter 12 (primarily from 12.3 onward).
Here are Practice Problems. I will not post
solutions, but ask me if you have any questions.
Final Exam: Thursday May 10, 1:30-3:30pm
The final exam will cover the material from the two midterms above, in addition
to the material covered in lecture since the second midterm, i.e.,
Chapters 11-14 excluding 13.6 and 14.4. Here is a list
of the main topics (but not all topics) covered since the second midterm.
- Vector arithmetic (sums, scaling, dot product, cross product)
- Write down equations for a given line or plane, say determined by two
or three points (or equivalently by two lines)
- Determine the angle between two vectors, lines or planes; or
the angle between a line and a plane
- Find the normal (or unit normal) vector to a plane through a given point,
or find a plane normal to a given vector which contains a given point
- Find the distance between two points, two lines, two planes, or some
combination thereof
- Parametric equations/vector equations for curves in 3 dimensions
- Find a (unit) tangent vector (or tangent line) to a curve at a given point
- Find the length of a curve
Here are some suggested practice problems for Chapter 14, since there was
no homework assignment on this material.
- Section 14.1: 7, 9, 11, 19, 21
- Section 14.2: 9, 17, 19
- Section 14.3: 1, 5
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