Information about Exam I for Math 2443-006H

Mathematics 2443-006H - Honors Calculus IV - Spring 2006

Information about Exam I

Exam I will be in the usual classroom on Tuesday, February 14, 2006. It will cover the material up through the gradient, that is, sections 14.3-14.4 15.1, and 15.3-15.6.

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.

The exam will be challenging (but doable), exam grades in this class usually run from 40% to 85%. Just relax and do your best. As on any exam, it is wise to start with the problems that you feel confident that you know how to do, before moving on to others.

The first main topic is the geometry of curves in space, that is, the unit tangent, normal, and binormal vectors, curvature, and torsion. You do not need to memorize the formulas, as all necessary formulas for calculation will be given. On the other hand, you need to be familiar with them if you expect to be able to use them with any facility, and you should know the definition and meaning of curvature and torsion.

Most of the exam covers partial derivatives, the Chain Rule, and the gradient. The gradient is heavily emphasized, and one needs to know both the geometric content and the details of using the gradient in calculations. The following will definitely be covered, although the exam not necessarily limited to these topics:

  1. Functions of more than one variable, their graphs, and their level lines/surfaces.
  2. Calculation and geometric interpretation of partial derivatives.
  3. Implicit differentiation.
  4. The differential of a function of more than one variable, and its use in linear approximation. Problem 15.4 #38 is a very good example.
  5. Everything about the gradient. Know the core material, and be able to use the gradient to calculate directional derivatives, normal lines to level curves, and normal lines and tangent planes to level surfaces. For the latter, it is necessary to know the equations for lines (at least, the parametric and vector-valued function versions) and the equation for a plane in terms of a normal vector.

The following topics do not appear, at least not explicitly: the tangential and normal components of acceleration, equation of the tangent plane, error of linear approximation, limits.

Exams from previous Honors Calculus classes can be found on their course pages (links to them appear on the course pages page). Some were 50-minute classes, but most were 75-minute classes. Of course, these were different classes, so the exams may be quite a bit different.

1.	Functions of more than one variable, their graphs, and their level lines/surfaces.
2.	Calculation and geometric interpretation of partial derivatives.
3.	Implicit differentiation.
4.	The differential of a function of more than one variable, and its use in linear approximation. Problem 15.4 #38 is a very good example.
5.	Everything about the gradient. Know the core material, and be able to use the gradient to calculate directional derivatives, normal lines to level curves, and normal lines and tangent planes to level surfaces. For the latter, it is necessary to know the equations for lines (at least, the parametric and vector-valued function versions) and the equation for a plane in terms of a normal vector.