In our last class meeting for the semester, we reviewed some theorems from the course. The slides from class are available. The final exam takes place 3:00–5:00 in the afternoon of Thursday, May 2.
April 24
We worked on some review exercises on limits. The slides from class are available.
April 23
We worked on a review exercise about vector calculus. The slides from class are available.
April 18
We worked on some computations of integrals via substitution. The slides from class are available.
We discussed the fundamental theorem of calculus. The slides from class are available.
April 11
Class was canceled because of my medical emergency.
April 10
Our teaching assistant supervised some review.
April 9
The start of class was delayed half an hour by a fire alarm. After that, we discussed the concept of determining area by taking a limit of areas of approximating rectangles. The slides from class are available.
April 4
We discussed antiderivatives and optimization word problems. The slides from class are available.
April 3
We worked in groups on some exercises about l’Hôpital’s rule, antiderivatives, and extreme values.
April 2
We discussed l’Hôpital’s rule and worked some examples. The slides from class are available.
We reviewed for the examination being given in class tomorrow.
March 26
We discussed the first-derivative test and the second-derivative test for local extrema, Rolle’s theorem, and the mean-value theorem. The slides from class are available.
Here are some good review problems to prepare for the exam that takes place in class on Thursday.
From the Chapter 3 Review Exercises on pages 267–269: 9, 13, 15, 29, 49, 51, 57, 61, 69, 75, 97, 99.
From the Chapter 4 Review Exercises on pages 359–360: 1, 5, 15, 17, 19, 21, 45, 49.
March 21
We finished the exercises from yesterday and worked on an exercise about how the first and second derivatives explain the shape of graphs. The slides from class are available.
We discussed related-rates problems and the tangent-line approximation. The slides from class are available.
February 28
We finished the exercises from yesterday and talked about higher-order derivatives. The slides from class are available. There is no assignment to do for next time.
We looked at Exercise 15 in Section 3.5 and discussed an example of determining a unit tangent vector to a parametric curve and worked on Exercises 12 and 14 in Appendix K2. The slides from class are available.
February 21
We discussed the exercises from yesterday, the chain rule, and the technique of implicit differentiation. Because of a network outage, the slides were not viewable during class, but they are available now. The assignment is shown on the last page of the slides.
February 20
We worked in groups on some exercises about tangent lines, derivatives, the power rule, and the product rule.
February 19
We discussed how differentiation interacts with addition, multiplication, division, and function composition. The slides from class are available.
We did some review for the exam taking place tomorrow. The slides from class are available.
February 12
We continued the discussion of derivatives, looking at exponential functions and trigonometric functions. The slides from class are available.
February 7
We discussed how differentiability can fail and looked at some examples of interpreting the derivative both through formulas and through graphs. The slides from class are available. We took a quiz in groups; solutions are available.
February 6
We worked on some exercises from the textbook: Exercise 40 in Section 2.6 (answer: \(-\pi/2\)), Exercise 59 in Section 2.6 (answer: \(5\)), and Exercise 60 in Section 2.7 (answer: yes, \(0\)).
February 5
We discussed tangent lines and the definition of the derivative. The slides from class are available.
We worked in groups on some exercises shown in the slides from class.
January 29
We discussed the precise definition of limit. The slides from class are available.
January 24
We discussed a subtlety about how limits behave under sums and products, and we looked at an example of the sandwich theorem. There was a quiz, for which solutions are available.
The slides from class are available too.
January 23
We worked in groups on some exercises about limits, shown in the slides from class.
January 22
We looked at some examples of limits of functions. The assignment is shown on the last page of the slides from class.
January 17
We discussed the vector projection and parametric equations and took a quiz in groups.
Solutions to the quiz are available, and
the slides from class are available.
January 16
We discussed the dot product and the notion of projection. The slides from class are available.
Our teaching assistant, Angelique, will hold office hours in Blocker 221B on Tuesday and Thursday afternoons 1:00–2:00 and on Wednesday afternoons 3:00–4:00.
Tuesday, January 15
We did a couple of warm-up problems (shown on the slides from class) and then discussed basic notions of vectors. The assignment (not to hand in) is to work the odd-numbered problems 1–15 in Appendix J.1 and check your answers in Appendix L.
Saturday, January 12, 2019
Welcome to Math 171. This site went live today. There will be regular updates to this page throughout the semester.