Teaching for Winter 2020
Undergraduate - MATH 137 Calculus I
MATH 137 - Calculus I
The course will cover sequences & series, limits and continuity, differentiation and Taylor polynomials. The course syllabus is here. I've posted some study tips here.
There will not be a final exam in this course. Instead, the final course grade will be the largest of 100% midterm OR 35% midterm+65% assignments, where the assignment mark is computed from your highest 3 (out of 4) assignment marks..
The text for this course is 'Math 137 Calculus I for Honours Mathematics' by Barbara A. Forrest and Brian E. Forrest (2019). A black and white hard copy is available in the University of Waterloo bookstore. An electronic version can be found here, along with online lectures covering the basic Math 137 material.
The assignments are posted below. It is expected that you will work on the written assignment material on a continuous basis in the weeks preceding its hand-in date, as they will be too long to complete the day before.
All assignments will be submitted through Crowdmark, which is an online submission portal. For instructions on how to submit an assignment, see here. Several days before the due date, you will receive a personalized link for assignment upload - if you have not received the invitation link 48 hours prior to the due date, please let me know.
| Assignment 1 | Assignment 2 | Assignment 3 | Assignment 4 |
Assignment solutions are posted below. All assignments are marked out of a total of 20. Even if you received full marks on the assignment, please go through the solutions to check your work.
| Solutions 1 | Solutions 2 | Solutions 3 | Solutions 4 |
Tutorial material:
| Absolute value | Sequences | Sequences, too |
| Series | Limits | Differentiation |
| Linear Approx. | MVT | Sketching |
| Taylor | Big O | Applications |
Lecture notes are here, posted by week:
| Week 1 | Week 2 | Week 3 |
| Week 4 | Week 5 | Week 6 |
| Week 7 | Week 8 | Week 9 |
| Week 10 | Week 11 |
For extra practice problems, I will post optional problem sets below, and post solutions a few days later. It might be useful to try these problems first before attempting the assignment problems.
| Sequences (Solutions) | Series (Solutions) | Continuity (Solutions) |
| Derivatives (Solutions) | MVT (Solutions) | Taylor (Solutions) |
I have also put some books on reserve at the Davis library. Please take the call number to the Reserve Desk to acquire the item. You can find many other books in the main stacks around QA303.
| Early Transcendentals | J. Stewart | QA303.2 .S73 2016 |
| Modern Engineering Mathematics | G. James | TA330 .J36 2007 |
| Calculus | M. Spivak | QA303 .S78 1994 |
This guy does an incredible job explaining calculus -
3Blue1Brown - The Essence of Calculus
The Khan Academy is another excellent resource -
Khan Academy - Calculus 1
Other material that may be of interest:
| Mathematical notation | More sequence examples | Dedekind cuts |
| Thomae's function | Thomae, too | Taylor polynomials |
| Complex numbers |
