106L Materials (OLD: Spring 2022)
Note: Most links have been removed below, as they are semester-specific.
Class Information
- Info Sheet
- Grading
- Textbook: Calculus by Hughes-Hallett et. al., 7th Ed
- Gradescope
- Math Help Room
- Office Hours
- Rann Bar-On: Sunday 8-9pm, Monday 2:30-3:30pm, Thursday 2:30-3:30pm
- Kyrie Johnson: Sunday 4-6pm.
Class Times, Zooms, Emails
| Day and Time | Class/Lab | Location | Zoom Link | Instuctor | TAs | TA Help Room Hours |
|---|---|---|---|---|---|---|
| MWF 10:15-11:05am | Class Section 1 | East Duke 204B | Zoom | Rann Bar-On | Brian Kang Isabella Swigart |
Brian: Tu 4-5pm Isabella: Tu 5-7pm |
| MWF noon-12:50 | Class Section 2 | West Duke 108B | Zoom | Rann Bar-On | Ashley Jones Andre Hall |
Ashley: W 6-7pm Andre: Tu 8-10pm |
| TTh 10:15-11:05am | Lab Section 2 | West Duke 108B | Zoom | Rann Bar-On | Gabriela Pereda | Gabriela: M 5-7pm, Th 4-6pm |
| TTh noon-12:50pm | Lab Section 1 | West Duke 108B | Zoom | Rann Bar-On | Morgan Chen | Morgan: Tu 3-4pm |
| TTh 3:30-4:20pm | Lab Section 3 | West Duke 108B | Zoom | Kyrie Johnson | Elliott Kauffman | Elliott: T 5-7pm |
| Graders | Help Room Hours |
|---|---|
| Zineb Jadi | |
| Leila Nelson | M 4-7pm |
| Ella Smyth | |
| Catherine Yao | Sat 4-5pm |
Gradescope Submissions, Returns, and Resubmissions
All work for 106L will be submitted on Gradescope. Here are some guidelines, links, and instructions for submission:
-
Once you have completed your work, you need to scan it to a PDF. You should use a document scanner app on your phone: Evernote Scannable on iOS (iPhone/iPad), or Genius scan on Android. Instructions for creating a PDF using these can be found here.
-
When logging into Gradescope, be sure to use the ‘School Credentials’ button:
(You can instead log into Gradescope via Sakai if you wish! That will log you in automatically.)
-
After you’ve logged in, find the correct assignment in the Assignments area, and follow the instructions here. Most of the assignments in 106L will require you to assign questions to pages. If you do not do this, your work will not be graded until you fix it.
-
For initial submissions, graders will assign ‘correct’, ’needs work’, or ‘missing’ to each question. They will also comment on your work. No points will be assigned. You will then use their comments to correct your work and resubmit.
-
Each assignment will have a separate resubmit Gradescope assignment:
-
After you resubmit, graders will grade each question out of one point. Once those are returned, you will get a ‘pass’ or ’no-pass’ on each assignment. You will get an email from me if you did not pass an assignment. Pass/no-passes will also be recorded in the Gradebook on Sakai.
Getting Help
You will need help with this class! Everyone will. Math at Duke is challenging, and this class will ask a lot of you, regardless of your math background. There are many resources available for help. Here’s an outline with links:
- Help Room: Located in the Classroom building, the help room is open around 40 hours a week from 1-10pm M-Th and 4-10pm Su. It is staffed by TAs, graders, and others. You can go at any time to get help with your work. You can go do homework there and get help when you need it. It’s a great space to have quiet work time, but have help readily available.
- Office Hours: I will have online office hours three hours per week (see hours above). Here’s a Zoom link for them.
- Individual meetings: I’m available to meet one on one by Zoom if you feel that’s needed. Drop me an email! I’m also available for quicker questions before/after class.
- The Academic Resource Center: Duke’s ARC provides multiple layers of support for classes. From peer tutoring to study groups, this is one of the most useful resources Duke provides. Make an appointment with an advisor there, or sign up for a study group!
Syllabus
The table below lists all topics, assignments, and extra resources for 106L this semester.
The Assignment column links to the PDF of the day’s worksheet or lab, or to an online assignment. Resources, such as lab spreadsheets, needed external websites, or extra videos are linked in the Extra Resources column. Lab PDFs are linked in the relevant lab’s entry in the Topic column.
Worksheets are to be handed in on Gradescope the Monday of the week after they are assigned in class, by 8am. Worksheet regrades are due the Tuesday after worksheet assignments are returned, also by 8am.
Textbook sections containing material relevant to a given day’s class or lab are listed in the table below. It is recommended that students read the relevant textbook sections. Questions at the end of textbook sections may be done as background and supplementary material. Some suggested exercises are listed under ‘Textbook Practice Problems’ in the table below. Solutions to all textbook questions can be found on Sakai under ‘Resources’ -> ‘Textbook Solutions’. No questions from the textbook will be collected or graded.
All assignments have due dates listed in the table below. Note that all assignments are due by 8am on the day listed.
Following each class day, the numbers in the ‘Day’ column below will become video links to a recording of the lecture within 24 hours.
| Day | Date | Textbook Section | Topic | Assignment | Due Date | Class/Lab Resources | Textbook Practice Problems | External Resources |
|---|---|---|---|---|---|---|---|---|
| 1-2 | 01/05/22 | Review of 105L Concepts | Worksheet | 01/10/22 | Use your worksheets from 105L (Gradescope) | |||
| Lab: | 01/06/22 | 1.5 | Crash Course in Trigonometry Part I | Worksheet (Individual) | 01/12/22 | Video Segment 1 Video Segment 2 Video Segment 3 |
Section 1.5 Exercises 38, 39 |
Basic Trig |
| 1-3 | 01/07/22 | 1.5 | Crash Course in Trigonometry Part II | Worksheet | 01/12/22 | Video Segment 1 Video Segment 2 |
Section 1.5 Exercises 24-29 |
|
| 2-1 | 01/10/22 | Trigonometric Identities and Important Limits | Worksheet | 01/17/22 | ||||
| Lab: | 01/11/22 | 1.5 | Modeling with Trig Functions | Spreadsheet Geogebra Applet |
Sinusoidal Models | |||
| 2-2 | 01/12/22 | 3.5 | Differentiating Trigonometric Functions | Worksheet | 01/17/22 | Section 3.5 Exercises 3, 4, 12-14, 18, 19, 22, 32, 34, 42 Problems 57, 64 |
||
| Lab | 01/13/22 | Modeling with Trig Functions | Report: Global Warming (Group) | 01/21/22 | Spreadsheet | |||
| 2-3 | 01/14/22 | 1.5 | Inverse Trigonometric Functions | Worksheet | 01/17/22 | Section 1.5 1-9, 30-34 |
Inverse Trig Functions | |
| 3-1 | 01/17/22 | MLK Day | ||||||
| Lab: | 01/18/22 | Newton’s Laws of Motion | ||||||
| 3-2 | 01/19/22 | 3.6 | Differentiating Inverse Trigonometric Functions | Worksheet | 01/24/22 | Section 3.6 Exercises 22, 24, 25, 28, 30, 31, 35, 39, 41, 44 Problems 51 |
Differentiating Inverse Trig Functions | |
| Lab: | 01/20/22 | Newton’s Laws of Motion | Report: Understanding Gravity (Group) | 01/28/22 | ||||
| 3-3 | 01/21/22 | Trig Related Rates | Worksheet | 01/24/22 | Section 4.6 Exercises 8 Problems 52, 55 SYU 63 |
Trig Related Rates | ||
| 4-1 | 01/24/22 | 6.3 | Position, Velocity and Acceleration | Worksheet | 01/31/22 | Section 6.3 14, 21 (excl (f)), 29-33 |
||
| Lab: | 01/25/22 | NO LAB | Big Assignment 1 | 02/04/22 | ||||
| 4-2 | 01/26/22 | 5.1 | Distance from Velocity | Worksheet | 01/31/22 | Section 5.1 Exercises 5, 10-12, 14-20 Problems 37, 38, 39 |
||
| Lab: | 01/27/22 | Sums and Sigma Notation | Sigma Notation | |||||
| 4-3 | 01/28/22 | 5.1 | Left- and Right-Hand Sums | Worksheet | 01/31/22 | Section 5.1 Exercises 23, 24 SYU 45, 47 Section 5.2 Exercises 1-5 Problems 54 |
Riemann Sums | |
| 5-1 | 01/31/22 | 5.2 | Definite Integral | Worksheet | 02/07/22 | Section 5.2 Exercises 6-9 Problems 24, 34-36, 44, 55, 57 |
Definite Integral | |
| Lab: | 02/01/22 | Sums and Sigma Notation | Sums and Sigma Notation Quiz (Individual) | 02/04/22 | Riemann Sums with Sigma | |||
| 5-2 | 02/02/22 | Catch Up Day/Big Assignment Help | ||||||
| Lab: | 02/03/22 | Riemann Sums | Spreadsheet | |||||
| 5-3 | 02/04/22 | 7.5 | Midpoint and Trapezoid Sums | Worksheet | 02/07/22 | Section 7.5 Exercises 10, 12, 24, 28-31 SYU 53-54 |
||
| 6-1 | 02/07/22 | 5.3 | FTC I | Worksheet | 02/14/22 | Section 5.1 Problems 25, 34 SYU 48, 49 Section 5.2 27, 28, 30, 32, 33, 42 Section 6.2 Exercises 56-65 Problems 84 |
||
| Lab: | 02/08/22 | Riemann Sums | Spreadsheet | |||||
| 6-2 | 02/09/22 | 5.3 | FTC I/Interpreting the Definite Integral | Worksheet | See 6-1 | Section 5.3 Exercises 1-8 Problems 17, 24-30 |
FTC I Proof | |
| Lab: | 02/10/22 | Riemann Sums | Report: Riemann Sums (Group) | 02/18/22 | Spreadsheet | |||
| 6-3 | 02/11/22 | 5.4 | Theorems about Definite Integrals | Worksheet | 02/14/22 | Section 5.4 Exercises 1-5, 13, 15-19 Problems 35, 36, 38, 43a, 44, 48 |
Properties of Definite Integrals | |
| 7-1 | 02/14/22 | 6.2 | Constructing Antiderivatives | Worksheet | 02/21/22 | Section 6.2 Exercises 6-8, 10-13, 16-18, 21, 31, 32, 72-75 SYU 101, 102 |
||
| Lab: | 02/15/22 | Average Value of a Function | ||||||
| 7-2 | 02/16/22 | 7.1 | Integration by Substitution | Worksheet | 02/21/22 | Section 7.1 Exercises 1, 4, 5, 9, 14, 15, 26, 28, 41, 42, 53, 65, 68, 79, 80 Problems 90-92 |
Integration by Substitution | |
| Lab: | 02/17/22 | Average Value of a Function | Report: Short Report (Group) | 02/25/22 | ||||
| 7-3 | 02/18/22 | 7.2 | Integration by Parts | Worksheet | 02/21/22 | Section 7.2 Exercises 2-7, 11, 13, 24, 32, 41, 46 Problems 74, 76 |
Integration By Parts | |
| 8-1 | 02/21/22 | Antidifferentiation Practice | Worksheet | 02/28/22 | Any of the integrals in 7.1 or 7.2 | |||
| Lab: | 02/22/22 | Quantities of Varying Density | Big Assignment 2 | 03/04/22 | Spreadsheet | |||
| 8-2 | 02/23/22 | Antidifferentiation Practice | See 8-1! | Any of the integrals in 7.1 or 7.2 | ||||
| Lab: | 02/24/22 | Quantities of Varying Density | Spreadsheet | |||||
| 8-3 | 02/25/22 | 7.6 | Integrating to Infinity | Worksheet | 02/28/22 | Section 7.6 Exercises 1a, 2, 5, 6, 9-13, 21, 26, 27, 31, 33, 35 Problems 42 |
Improper Integrals | |
| 9-1 | 02/28/22 | 7.6, 7.7 | Other Improper Integrals | Worksheet | 03/14/22 | Section 7.6 1b, 7, 17-20, 28, 30, 36, 39 Section 7.7 Exercises 10-13 Problems 31, 35 |
||
| Lab: | 03/01/22 | Quantities of Varying Density | On Big Assignment | Spreadsheet | ||||
| 9-2 | 03/02/22 | Big Assignment Help | ||||||
| Lab: | 03/03/22 | NO LAB | ||||||
| 9-3 | 03/04/22 | 6.4 | FTC II | Worksheet (optional) | 03/14/22 | Section 6.4 Exercises 4, 7-15, 22, 24 Problems 26, 34-36 |
||
| 10-1 | Spring Break | |||||||
| Spring Break | ||||||||
| 10-2 | Spring Break | |||||||
| Spring Break | ||||||||
| 10-3 | Spring Break | |||||||
| 11-1 | 03/14/22 | 11.1 | Differential Equations and Initial Value Problems | Worksheet | 03/21/22 | Section 11.1 Exercises 8, 13, 14 Problems 24, 25, 29, 31, 35-38 Section 11.7 1 |
Intro to Differential Equations | |
| Lab: | 03/15/22 | Force and Work | ||||||
| 11-2 | 03/16/22 | 11.1 | Differential Equation and Initial Value Problems | Worksheet | See 11-1! | |||
| Lab: | 03/17/22 | Force and Work | Report: Force and Work (Group) | |||||
| 11-3 | 03/18/22 | 11.2,11.5 | Slope Fields and Equilibria | Worksheet | See 12-1! | Section 11.2 Exercises 4, 6, 11, 12 Problems 19, 20-23, 30 |
Slope Fields | |
| 12-1 | 03/21/22 | 11.2,11.5 | Slope Fields and Equilibria (continued) | 03/28/22 | Section 11.5 Exercises 3, 4, 8a,c,d, 20-22 SYU 45, 46, 49, 50 |
|||
| Lab: | 03/22/22 | Playing with Differential Equations | Geogebra Applet | |||||
| 12-2 | 03/23/22 | 11.4 | Separation of Variables | Worksheet | 03/28/22 | Section 11.4 Exercises 1, 7, 9, 10, 17, 22, 24-30 Problems 42 |
Separation of Variables | |
| Lab: | 03/24/22 | Playing with Differential Equations | Report: Short Report (Group) | 04/01/22 | Geogebra Applet | |||
| 12-3 | 03/25/22 | 11.4 | Separation of Variables (continued) | See 12-2! | Section 11.4 Exercises 11, 12, 18-20 Problems 38-41, 43, 45 |
|||
| 13-1 | 03/28/22 | 11.5 | Growth and Decay | Worksheet | 04/04/22 | Section 11.5 Exercises 1, 2, 4 Problems 34, 37, 41, 44 |
Exponential Models | |
| Lab: | 03/29/22 | 11.3 | Euler’s Method | 04/08/22 | Spreadsheet | Euler’s Method | ||
| 13-2 | 03/30/22 | 11.5, 11.6 | Applications: Heating and Mixing I | Worksheet | 04/04/22 | Section 11.5 Exercises 7, 8, 10-12 Problems 39, 40 SYU 47 Section 11.6 28-30 |
Newton’s Law of Cooling | |
| Lab: | 03/31/22 | 11.3 | Euler’s Method | Report: Short Report (Group) | 04/08/22 | Spreadsheet | Section 11.3 Exercises 8, 9 Problems 14, 17 |
|
| 13-3 | 04/01/22 | 11.5, 11.6 | Applications: Heating and Mixing I (continued) | See 13-2! | ||||
| 14-1 | 04/04/22 | 11.5, 11.6 | Applications: Heating and Mixing II | Worksheet | 04/11/22 | |||
| Lab: | 04/05/22 | Chemical Rates | Big Assignment 3 | 04/15/22 | ||||
| 14-2 | 04/06/22 | 11.7 | The Logistic Model for Population | Worksheet | 04/11/22 | Section 11.7 Exercises 9-16 Problems 31, 33a,b, 34 SYU 43, 44, 49, 51 |
The Logistic Model | |
| Lab: | 04/07/22 | Chemical Rates | (On Big Assignment 3) | 04/15/22 | ||||
| 14-3 | 04/08/22 | 11.7 | The Logistic Model for Population (continued) | See 14-2! | ||||
| 15-1 | 04/11/22 | 11.6, 11.7 | Populations Models with Migration | Worksheet | 04/18/22 | Section 11.6 6, 10-13, 35 Section 11.7 33c |
||
| Lab: | 04/12/22 | Logistic Model with Harvesting: Fishery Management | Geogebra Applet | |||||
| 15-2 | 04/13/22 | Big Assignment Help | ||||||
| Lab: | 04/14/22 | Logistic Model with Harvesting: Fishery Management | Report: Short Report (Group) | 04/20/22 NOTE: No resubmit! |
Geogebra Applet | |||
| 15-3 | 04/15/22 | 11.7 | The Logistic Model – Applications | Worksheet | 04/20/22 (Note: Wednesday submission!) |
Section 11.7 38-42 |
||
| 16-1 | 04/18/22 | 11.7 | The Logistic Model – Applications (continued) | See 15-3! | ||||
| Lab: | 04/19/22 | Logistic Model with Harvesting: Fishery Management | ||||||
| 16-2 | 04/20/22 | Course Evaluations |
Rann Bar-On
Senior Lecturer in Mathematics
I am primarily a teacher and curriculum designer in calculus and linear algebra.