MATH 171 Suggested Weekly Schedule

Week 1:

Introduction to two-dimensional vectors, dot products. Sections 1.1, 1.2. Instructors may want to introduce the definitions of dot product in Rn for n > 2, but this is not necessary, nor should much time be spent on vectors in dimensions higher than two. One nice application of these ideas is proofs of geometric facts (these are not in the text so handouts should be prepared) via vector techniques. Be sure to cover the subject of work in section 1.2

Week 2:

Sections 1.3, 2.1, 2.2, and 2.4. Sections 1.3 and 2.2 should be covered together. The main purpose of 1.3 is the discussion of parametric curves. Section 2.1 should be done quickly as it is there just to explain why the ideas of limits are needed. Note that section 2.3 is not covered before section 2.4.

Week 3:

Sections 2.3, 2.6, 2.5. When proving limit theorems use epsilons and deltas. We suggest doing 2.6 before 2.5. It is a good idea to ask students to prove simple limit statements. For example, prove from the definition of a limit that

lim (2x − 6) x→4

= 2

This is relatively simple, and at the level we want our students to be able to handle.

Week 4:

Sections 2.7, 3.1, 3.2. Sections 2.7 and 3.1 contain intuitive descriptions of the derivative. Be sure to discuss velocity and speed of a particle in R2 . Most of the differentiation formulas should be proved. Note that the text has these proofs in an appendix. Section 3.3 should be assigned as reading material for the student. If you can, cover some of the simple anti differentiation formulas. This is a request from the physics’ department.

Week 5:

Sections 3.4, and 3.5. Somewhere around here exam 1 should be given. This exam should cover through 3.3.

Week 6:

Sections 3.6, 3.7, 3.8, and 3.9. Section 3.8, Higher Derivatives, is a 10 minute discussion.

Week 7:

Sections 3.9, 3.10, and 3.11. Section 3.11 discusses linear and quadratic approximation. The material on quadratic approximation does not have to be covered. Section 3.12, Newton’s method, can be covered if the instructor wishes to do so, but it is not a required part of the syllabus.

Week 8:

Sections 4.1, 4.2, 4.3, and 4.4.

Week 9:

Sections 4.6 and 4.8. In section 4.6, Inverse Trig Functions, there is no need to talk about the inverse functions of secant, co-secant, and co-tangent.

Week 10:

Sections 5.2, 5.3, and have the class read 5.1. Problems from section 5.5 in which the function has a bounded domain can be included in section 5.2. Exam 2 should be given about now, and should cover through Chapter 4.

Week 11:

Sections 5.5 and 5.7. The material in section 5.4 should not be covered, and 5.6 may be given as a reading assignment if the instructor wishes.

Week 12:

Sections 6.1, 6.2, and 6.3. A few of the summation formulas should be proven. Preferably with an induction argument. Don’t feel you have to spend a lot of time on induction, but students should see this type of reasoning, and this is a good place for it.

Week 13:

Sections 6.4 and 6.5. In the Fall semester, Thanksgiving break falls in this week.

Week 14:

Exam 3 and review.