Information about Exam III for Math 2433-001H

Mathematics 2433-001H - Honors Calculus III - Fall 2005

Information about Exam III

Exam III will be in the usual classroom on Friday, November 18, 2005. It will cover sections 12.9 and 12.10 (these make up about half the exam), and 13.1-13.5.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with. As usual, give brief, clear answers without unnecessary explanation. Of course it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The main topics are Taylor and Maclaurin series, dot product, cross product, and equations of lines and planes. The following will definitely be covered, although the exam not necessarily limited to these topics:

  1. The Taylor series of a function. Know the general form well.
  2. Maclaurin series. You need to know the standard Maclaurin series for 1/(1-x), sine, cosine, exponential, and ln(1+x) from memory (and you might as well know that hyperbolic sine and cosine are just the same series as sine and cosine except with all plus signs).
  3. Applying the standard Maclaurin series to problems such as taking limits and finding integrals.
  4. The error term R_n(x). You do not need to know the Taylor and Lagrange expressions for R_n(x) from memory, but you should understand what they express and how they can be used to estimate the error of approximation by Taylor polynomials.
  5. Dot product and especially cross product; their geometric meaning, how to calculate with them, their algebraic properties.
  6. Equations of lines and planes. You should be able to use the three forms for the equation of a line, and the equation of a plane, without difficulty in routine problems.

You do not need to know the proof of Taylor's Theorem, and your understanding of the basic matters such as 3-dimensional coordinates, how components of vectors work, and so on will be taken for granted. The following do not appear on the exam: multiplication and division of power series, power series for arctan(x), radius of convergence, Euler's Formula and power series involving complex numbers.

1.	The Taylor series of a function. Know the general form well.
2.	Maclaurin series. You need to know the standard Maclaurin series for 1/(1-x), sine, cosine, exponential, and ln(1+x) from memory (and you might as well know that hyperbolic sine and cosine are just the same series as sine and cosine except with all plus signs).
3.	Applying the standard Maclaurin series to problems such as taking limits and finding integrals.
4.	The error term R_n(x). You do not need to know the Taylor and Lagrange expressions for R_n(x) from memory, but you should understand what they express and how they can be used to estimate the error of approximation by Taylor polynomials.
5.	Dot product and especially cross product; their geometric meaning, how to calculate with them, their algebraic properties.
6.	Equations of lines and planes. You should be able to use the three forms for the equation of a line, and the equation of a plane, without difficulty in routine problems.