Office hours: Tuesdays and Thursdays 10:00 - 11:00 On Zoom, or by appointment.

Email: firstname dot lastname at umanitoba dot ca

In Winter 2022 I will teach Math 1500, Introduction to Calculus, in University of Manitoba.

All lectures will be delivered on Zoom. Please join the class using the Zoom Link.

All office hours will be held on Zoom. Please join the session using the Zoom Link.

Please make sure you log in Zoom with your myumanitoba.ca email address. Otherwise your access might be denied.

• Lecture 1 (Jan. 25, 2022)
  Lecture activities: Course Syllabus, Tentative Schedule, Syllabus Explanation Slides.
  Review on trigonometric functions, Recordings, Supplementary Video
  We went through some of the most essential parts of the syllabus but also left out a lot of important parts due to the limitation of time. Please definitely read the document by yourself.
  During the lecture I covered the first part of the review of trigonometry. The latter part is covered in a 38-minute supplementary video. Plesae go over the materials and internalize the knowledge, so that trigonometric function won't cause you any troubles in 1500.
  Lexique de mathématiques | Mathematics Glossary (Alberta Education) for people went to French schools and are not familiar with mathematics glossaries in English.
  

• Lecture 2 (Jan. 27, 2022)
  Pre-lecture Activities: Watch Video 0 Part 1, Video 0 Part 2 (Review of algebraic techniques), Video 0 Part 3 (Review of functions and related concepts), and attempt all the problems in Exercise 0. Here are the slides for the Video 0-1 and 0-2 and slides for Video 0-3.
  Lecture activities: Recording, Solutions to Exercise 0, Supplementary Video. We went through the solutions to first 13 problems in Exercise 0. I also addressed how to solve inequalties in general. The rest of the solutions are posted in the notes and explained in the supplementary video.

• Lecture 3 (Feb. 1, 2022)
  Pre-lecture Activities: Watch Video 0 Part 4 (Review of linear, polynomial, power and exponential functions), Video 0 Part 5 (New functions out of old functions), Video 1 Part 1, Video 1 Part 2 (Limits of a function), and attempt all the problems in Exercises 1. Here are the slides for Video 0-4, slides for Video 0-5, and slides for Video 1-1 and 1-2.
  Lecture Activities: Solutions to Exercise 1 (updated), Recording.
  We went over the first half of Exercise 1. It was decided by the poll that we will finish the leftovers on Thursday, which should not take more than 30 minutes. After that, we will start Exercise 2.
  Here is the playlist of Eddie Woo's Video on Logarithms. For now, we will only use the fact that the logarithmic function approaches negative infinity as the independent variable approaches zero from the right. But when we discuss logarithmic differentiation, we will have to use everything. I also posted some Logarithm Exercises and their solutions on UM Learn. We will go over these exercises before discussing logarithmic differentiation. They will not be required in Test 1 and Test 2.

• Lecture 4 (Feb. 3, 2022)
  Pre-lecture Activities: Watch Video 2 Part 1, Video 2 Part 2 (Calculating limits using limit laws), Video 2 Part 3 (Important application of squeeze theorem), and attempt as many problems in Exercises 2 as possible. Here are the slides for the video.
  Lecture Activities: Solutions to Exercise 2 (updated), Recording, Supplementary Video (Part 1), Supplementary Video (Part 2).
  We finished everything in Exercise 1 and started Exercise 2. The pace was much slower than I thought. I had to make two supplementary videos explaining everything in Exercise 2. Part 1 explains all the other computational exercises. Part 2 explains the two theoretically important exercises and Problem 6 where you need to provide justification.
  I forgot to explain Problem 12 in Exercise 1. The solution is included in the updated notes. In case you have confusions, I can explain it during my office hours.

• Lecture 5 (Feb. 8, 2022)
  Pre-lecture Activities: Watch Video 3 Part 1, Video 3 Part 2 (Continuity), finish all the problems in Exercises 2 and attempt as many problems in Exercises 3 as possible. Here are the slides for the video.
  Lecture activities: Solutions of Exericse 2, Solutions of Exercise 3 (will update after Thursday), Recording.
  We finished Exercise 2, but only managed to talk about the first two problems in Exercise 3.
  There is a mistake on Page 6 of the solutions to Exercise 0 regarding the inequality problem associated to Problem 6. The notes are corrected.

• Lecture 6 (Feb. 10, 2022)
  Pre-lecture Activities: None. We should finish the discussion of continuity and Exercise 3.
  Lecture Activities: Recording, Solutions to Exercise 3 (will update after next Tuesday), Solutions to Practice Test 2.
  We finished the parts in Exercise 3 that will appear in the upcoming Test 1. We will discuss the leftovers on next Tuesday before going into limits at infinity.

• Lecture 7 (Feb. 15, 2022)
  Pre-lecture Activities: Watch Video 4 (Limit at infinity; horizontal asymptotes) and attempt all the problems in Exercises 4. Here are the slides for the video.
  Lecture activities: Recording. Solutions to Exercise 3, Solutions to Exercise 4.
  Supplementary Videos (Part 1) two tricky IVT problems, (Part 2) Problem 14 and 30 in Exercise 4, (Part 3) all other problems Exercise 4.
  In class we discussed the most important problems that are most relevant to the tests from Exercise 3 and 4. To keep up with the schedule, we will have to start the derivatives on Thursday. Thus I uploaded the solutions to all other problems in Exercise 3 and 4 and explained all of them in the supplementary videos.

• Lecture 8 (Feb. 17, 2022)
  Pre-lecture Activities: Watch and Video 5 Part 1 (Derivatives and rates of change), Video 5 Part 2 (Derivative as a function), and attempt all the problems in Exercises 5. Here are slides for the video 5-1, and the slides for the video 5-2.
  Lecture Activities: Recordings, Solutions of Exercise 5.
  Supplementary Videos: (Part 1) Two velocity problems, (Part 2) Problem 3, 42, 44 and 61 with some very important conceptual points, (Part 3) More on piecewise functions.
  We discussed the velocities, the equation of tangents, and the computation of derivatives using the definition. I will make supplementary videos explaning the rest. They will be available next Thursday. At the beginning of the following lecture on Mar. 1, I will briefly discuss some of the most important ones in class.

• Lecture 9 (Mar. 1, 2022)
  Pre-lecture Activities: Watch Video 6 Part 1 (Derivatives of exponential and polynomial functions), Video 6 Part 2 (Product and quotient rules), and attempt all the problems in Exercises 6. Here are the slides for the video 6-1, and the slides for the video 6-2.
  Lecture Activities: Recording. Solutions to Exercise 6 (will update after Thursday), Supplementary Video.
  We finished the first half of Exercise 6 but did not start the product rule or quotient rule. Problem 70 and 76 are explained in the supplementary video. To catch up with the schedule, we must start Exercise 7 on Thursday. I will have to leave some problems in Exercise 6 in supplementary videos.

• Lecture 10 (Mar. 3, 2022)
  Pre-lecture Activities: Watch Video 7 (Derivative of trigonometric functions) and attempt all the problems in Exercises 7. Here are the slides for the video 7.
  Lecture Activities: Recording, Solutions to Exercise 7, Supplementary Video.
  We finished most Exercise 6 and the computation exercises in Exercise 7. The leftovers in Exercise 6 and the geometric problems in Exercise 7 are explained in the supplementary video. Next Tuesday we will finish the limit problems at the end of Exercise 7. Then we shall discuss Exercise 8.

• Lecture 11 (Mar. 8, 2022)
  Pre-lecture Activities: Watch Video 8 (Chain rule) and attempt all the problems in Exercises 8. Here are the slides for the video 8.
  Lecture Activities: Recording, Solutions to Exercise 7, Solutions to Exercise 8 (will update after Thursday).
  We finished in Exercise 7 and went over every problem in Exercise 8 except for the last one. Due to the importance of that problem, I will go over it in class instead of making supplemenatary videos.

• Lecture 12 (Mar. 10, 2022)
  Pre-lecture Activities: Watch Video 9 (Implicit Differentiation) and attempt all the problems in Exercises 9. Here are the slides for the video 9.
  Lecture Activities: Recording, Supplementary Video, Solution to Exercise 9.
  We finished everything in Exercise 8 and almost everything in Exercise 9, except for last three. The solutions are explained in the supplementary video.

• Lecture 13 (Mar. 15, 2022)
  Pre-Lecture Activities: I wasn't able to make any pre-lecture videos for the review of inverse functions. So I will go over the knowledge in class.
  Lecture Activities: Recording, Slides, Office Hour Notes.
  We finished going over the slides, but did not go very far in solving the exercises. Next lecture I will only solve some of them. Please definitely try to practice by yourself.

• Lecture 14 (Mar. 17, 2022)
  Pre-lecture Activities: Watch Video 10 Part 1 (Eddie Woo's video on Logarithms) Video 10-2 (Logarithmic Differentiation) and attempt all the problems in Exercises 10. Here are the slides for the video 10.
  Lecture Activities: Recordings, Solutions to Exercise 10.
  We finished those problems regarding derivatives of logarithmic functions, but only barely started logarithmic differentiation. I will discuss the solutions to all the rest of the problems next Tuesday.

• Lecture 15 (Mar. 22, 2022)
  Pre-lecture Activities: Watch Video 11 (Related Rates) and attempt all the problems in Exercises 11. Here are the slides for the video 11.
  Lecture Activities: Recording, Supplementary Video, Solutions to Exercise 11.
  We finished everything in Exercise 10 and almost everything in Exercise 11 except for Problems 20, 22 and 25 in class. These three problems are explained in the supplementary video.
  Prof. Borgerson also uploaded a Related Rates Worksheet. If you are not comfortable with word problems, please attempt as many as you can. Please do not hesitate to ask questions should you have any confusions.
  In case you have never seen similar triangles before, here is a video from Organic Chemistry Tutor explaining the related computations. This video is sufficient for our class (while many others are not).

• Lecture 16 (Mar. 24, 2022)
  Pre-lecture Activities: Watch Video 12 (Maximum and Minimum Values) and attempt all problems in Exercise 12. Here are the slides for the video 10.
  Lecture Activities: Recording, Solutions to Exercise 12, Supplementary Video.
  We went over most of the problems from Exercise 12 that may appear in the tests. I will discuss Problem A2 and 67 next Tuesday in class. Problem 58, 59, 60, 66 are about transcendental functions and are explained in the supplementary video.

• Lecture 17 (Mar. 29, 2022)
  Pre-lecture Activities: Watch Video 13 (The Mean Value Theorem) and attempt all problems in Exercise 13. Here are the slides for the video 13.
  Lecture Activities: Recording, Solutions to Exercise 13, Some questions about Worksheet 5
  Supplementary Videos: Supplementary Video (Part 1): Uniqueness of roots by Rolle's theorem, Supplementary Video (Part 2): Left over MVT Problems in Exercise 13, Supplementary Video (Part 3): Proof of the important fact on differentiability of piecewise functions
  We went over the solutions of Exercise 13 in class except for 20, 21, 22 (See Part 1), 6, 8, A1 (See Part 2), 28, 29, A2 (will discuss on Thursday).

• Lecture 18 (Mar. 31, 2022)
  Video 14 Part 1 (First derivatives and Increasing / Decreasing Test), Video 14 Part 2 (Second Derivative and Concavity), Video 14 Part 3 (Full Solution to Example 4.3.7), Video 14 Part 4 (Full Solution to Example 4.3.8), and attempt all the problems in Exercises 14. Here are the slides for the all the videos 14-1 to 14-4.
  Lecture Activities: Recordings, Solutions to Exercise 14 (will update next week).
  We finished everything in Exericse 13 and started Exercise 14. The progress was slower than I anticipated because of the mistakes I made in class, for which I should apologize.

• Lecture 19 (Apr. 5, 2022)
  No pre-lecture activities. We will continue the discussion of Exercise 14.
  Lecture Activities: Recordings, Solutions to Exercise 14, Supplementary Video.
  We finished everything in Exericse 14 except for Problem 46, 48 (see supplementary video) and the last part of Problem 44 (will explain in class on Thursday).

• Lecture 20 (Apr. 7, 2022)
  Pre-lecture Activities: Watch Video 15 Part 1 (Graph Sketching: Guidelines and Example 1), Video 15 Part 2 (Graph Sketching: Example 2), Video 15 Part 3 (Graph Sketching: Example 3), Video 15 Part 4 (Graph Sketching: Example 4), Video 15 Part 5 (Graph Sketching: Example 5), and attempt all the problems in Exercises 15. Here are the slides for the video.
  Lecture Activities: Recordings, Notes, Supplement 1 (Problem 20 - 22), Supplement 2 (Problem 44, 46, 48).
  We finished the Exercise 14 and the first two problems of Exercise 15. I will explain the third problem next Tuesday. All other problems are explained in the supplementary videos.

• Lecture 21 (Apr. 12, 2022)
  Pre-lecture Activities: Watch Video 16 Part 1 and Video 16 Part 2 (Optimization Problems), and attempt all the problems in Exercises 16. Here are the slides for the video.
  Lecture Activities: Recording,Supplementary Video (Part 1), Supplementary Video (Part 2), Solutions to Exercise 16.
  We finished Exercise 15 and discussed Problem 14, 15 and 50 of Exercise 16 in class. Since we are now behind the schedule, all the other problems are covered in the supplementary video (Problem 22, 23 and 41 in Part 1, Problem 54, 42 in Part 2).

• Lecture 22 (Apr. 14, 2022)
  Pre-lecture Activities: Watch Video 17 Part 1 (Particular antiderivatives) and Video 17 Part 2 (The most general antiderivatives, aka, indefinite integrals), and attempt all the problems in Exercises 17. Here are the slides for the video.
  Lecture Activities: Recording, Solutions to Exercise 17.
  We started and finished everything in Exercise 17, except for the last three problems. I will explain them next Tuesday.

• Lecture 23 (Apr. 19, 2022)
  Pre-lecture Activities: Watch Video 18 Part 1 (Areas - motivating Example) and Video 18 Part 2 (Areas and definite integrals), Video 18 Part 3 (Properties of definite integrals), and attempt all the problems in Exercises 18. Here are the slides for the video.
  Here is the complementary note on how to obtain sums of squares. It is not required in the final exam. There is no pressure to study them.
  Lecture Activities: Recording. Solution to Exercise 18.
  We finished the discussion of all relevant problems in Exercise 18. No leftovers for Thursday.

• Lecture 24 (Apr. 21, 2022)
  Pre-lecture Activities: Watch Video 19 Part 1 and Video 19 Part 2 (Fundamental Theorem of Calculus), and attempt all the problems in Exercises 19. Here are the slides for the video.
  Lecture Activities: Recording. Solutions to Exercise 19.