106L Materials

Class Information

Class Times, Zooms, Emails

Day and Time Class/Lab Location Instuctor TAs TA Help Room Hours
MWF 10:20-11:10am Class Section 1 East Duke 204B Rann Bar-On Alaina McBride, Lawson President
MWF noon-12:50 Class Section 2 M: Classroom 103WF: East Duke 204B Rann Bar-On Leo Yang
TTh 8:45-9:35am Lab Section 1 East Duke 204B Rann Bar-On Muskaan Iyer
TTh 10:20-11:10am Lab Section 2 East Duke 204D Pauline Jonglertham Davis Murrell
TTh 3:20-4:10pm Lab Section 3 East Duke 204B Brooklyne Noel Danira Mukhamedyarova

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Graders Help Room Hours
Sonali Patel

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. Adobe Scan works great too! Instructions for creating a PDF using these can be found here.
  • When logging into Gradescope, be sure to use the ‘School Credentials’ button: 
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  • (You can instead log into Gradescope via Canvas 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. You must scan and submit all parts of every worksheet, as Gradescope will automatically assign questions to the right place. If you do not do this, your work may not be graded.
  • Each question will be scored 1 (perfect), 0.9 (minor error), 0.5 (partly correct), or 0. Each question will get commented upon. You will then use comments to correct your work and resubmit.
  • Each assignment will have a separate resubmit Gradescope assignment: 
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  • After you resubmit, graders will regrade each question you ask them to regrade by using the ‘Regrade’ checkbox below each question number. Once resubmissions 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 Canvas.

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 (Room 137), the help room is open around 25 hours a week: from 5-10pm Su-Th. 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 two hours of in person office hours, and one hour of virtual office hours per week (see hours above). Here’s a Zoom link for the the virtual ones.
  • 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 Canvas 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/Video Date Textbook Section Topic Assignment Due Date Class/Lab Resources Textbook Practice Problems External Resources
1-2 01/07/26 Review of 105L Concepts Worksheet 01/12/26 Use your worksheets from 105L
Lab 01/08/26 1.5 Crash Course in Trigonometry Part I Worksheet 01/12/26 Section 1.5 Exercises 38, 39 Basic Trig
1-3 01/09/26 1.5 Crash Course in Trigonometry Part II Worksheet 01/12/26 Section 1.5 Exercises 24-29 Unit Circle Radians
2-1 01/12/26 Trigonometric Identities and Important Limits Worksheet 01/20/26 Trig identities Angle Addition
Lab: 01/13/26 1.5 Modeling with Trig Functions Spreadsheet Geogebra Applet Sinusoidal Models
2-2 01/14/26 3.5 Differentiating Trigonometric Functions Worksheet 01/20/26 Section 3.5 Exercises 3, 4, 12-14, 18, 19, 22, 32, 34, 42 Problems 57, 64 Diff. Trig Functions More!
Lab 01/15/26 Modeling with Trig Functions Spreadsheet Geogebra Applet
2-3 01/16/26 1.5 Inverse Trigonometric Functions Worksheet 01/20/26 Section 1.5 1-9, 30-34
3-1 01/19/26 MLK Day
Lab: 01/20/26 Modeling with Trig Functions Report: Global Warming (Group) 01/28/26
3-2 01/21/26 3.6 Differentiating Inverse Trigonometric Functions Worksheet 01/26/26 Section 3.6 Exercises 22, 24, 25, 28, 30, 31, 35, 39, 41, 44 Problems 51 Differentiating Inverse Trig Functions
Lab: 01/22/26 Newton’s Laws of Motion 01/30/26
3-3 01/23/26 Trig Related Rates Worksheet 01/26/26 Test 1 Practice Solutions Section 4.6 Exercises 8 Problems 52, 55 SYU 63 Trig Related Rates
4-1 01/26/26 Position from Acceleration 02/02/26
Lab: 01/27/26 Newton’s Laws of Motion Report: Understanding Gravity (Group) 02/04/26
4-2 01/28/26 5.1 Areas Under Curves: Distance from Velocity Worksheet 02/02/26 Section 5.1 Exercises 5, 10-12, 14-20; Problems 37, 38, 39
Lab: 01/29/26 Sums and Sigma Notation Sigma Notation
4-3 01/30/26 Areas Under Curves: Distance from Velocity (ctd.) See 4-2!
5-1 02/02/26 SNOW DAY!
Lab: 02/03/26 Sums and Sigma Notation Sums and Sigma Notation Quiz (Individual) 02/05/26 Riemann Sums with Sigma
5-2 02/04/26 Big Assignment 1 In-Class part Material: Day 1-2 - Day 3-3
Lab: 02/05/26 NO LAB
5-3 02/06/26 5.1 Left- and Right-Hand Sums Worksheet 02/09/26 Sec 5.1: 23, 24; SYU 45, 47; Sec 5.2: 1-5, 54 Riemann Sums
6-1 02/09/26 5.2 From (Riemann Sums) to Definite Integrals Worksheet 02/06/26
Lab: 02/10/26 Riemann Sums Spreadsheet
6-2 02/11/26 5.3 LHS/RHS Precision and Geometric Integrals Worksheet 02/16/26 Sec 5.1: 25, 34; SYU 48, 49; Sec 5.2: 27-33, 42; Sec 6.2: 56-65, 84
Lab: 02/12/26 Riemann Sums Spreadsheet
6-3 02/13/26 7.5 Midpoint and Trapezoid Sums Worksheet 02/16/26 Supplemental Video for Page 4 Sec 7.5: 10, 12, 24, 28-31; SYU 53-54 Midpoint; Trapezoid
7-1 02/16/26 5.3 Fundamental Theorem of Calculus (No Quiz) Worksheet 02/23/26 Sec 5.3: 1-8, 17, 24-30 FTC I Proof
Lab: 02/17/26 Riemann Sums Report: Riemann Sums (Group) 02/25/26 Spreadsheet
7-2 02/18/26 6.2 Constructing Antiderivatives Worksheet 02/23/26 Sec 6.2: 6-13, 16-21, 31, 32, 72-75; SYU 101, 102 Reverse Power Rule
Lab: 02/19/26 Average Value of a Function
7-3 02/20/26 7.1 Integration by Substitution Worksheet 02/23/26 Sec 7.1: 1-15, 26-42, 53-80, 90-92 Substitution
8-1 02/23/26 7.2 Integration by Parts Worksheet 03/02/26 Sec 7.2: 2-13, 24, 32, 41, 46, 74, 76 Parts
Lab: 02/24/26 Average Value of a Function Report: Short Report (Group) 03/04/26
8-2 02/25/26 Integration Practice Worksheet 03/02/26 Any of the integrals in 7.1 or 7.2
Lab: 02/26/26 Quantities of Varying Density Big Assignment Take Home 1 03/06/26 Spreadsheet
8-3 02/27/26 Integration Practice (cont) See 8-1 03/02/26
9-1 03/02/26 7.6 Integrating to Infinity Worksheet 03/02/26 Sec 7.6: 1a-13, 21, 26-35, 42 Improper Integrals
Lab: 03/03/26 Quantities of Varying Density Spreadsheet
9-2 03/04/26 7.6, 7.7 Integrals with Discontinuities Worksheet 03/16/26 No Quiz! Sec 7.6: 1b, 7, 17-39; Sec 7.7: 10-13, 31, 35
Lab: 03/05/26 Quantities of Varying Density Short Report Spreadsheet Midterm 2 Practice Problems

Midterm 2 Practice Problems Solutions
9-3 03/06/26 Integrals with Discontinuities (cont.) See 9-1!
10-1 03/09/26 Spring Break
10-2 03/11/26 Spring Break
10-3 03/13/26 Spring Break
11-1 03/16/26 11.1 Intro to Differential Equations Part I Worksheet 03/23/26 Section 11.1 Exercises 8, 13, 14 Problems 24, 25, 29, 31, 35-38 Section 11.7 1 Intro to Differential Equations
Lab: 03/17/26 Big Assignment 2 In-class part Material: day 4-1 to day 8-3
11-2 03/18/26 11.1 Intro to Differential Equations Part II Worksheet See 11-1!
Lab: 03/19/26 Growth and Decay Individual submission of lab 03/24/26
11-3 03/20/26 11.2, 11.5 Slope Fields Worksheet 03/23/26 Section 11.2 Exercises 4, 6, 11, 12 Problems 19, 20-23, 30 Slope Fields
12-1 03/23/26 11.2, 11.5 Equilibria Worksheet 03/30/26 Section 11.5 Exercises 3, 4, 8a,c,d, 20-22 SYU 45, 46, 49, 50
Lab: 03/24/26 Playing with Differential Equations Geogebra Applet
12-2 03/25/26 11.4 Separation of Variables Worksheet 03/30/26 Section 11.4 Exercises 1, 7, 9, 10, 17, 22, 24-30 Problems 42 Separation of Variables
Lab: 03/26/26 Playing with Differential Equations Report: Short Report (Group) 04/03/26 Geogebra Applet
12-3 03/27/26 11.4 Separation of Variables (cont.) See 12-2! Section 11.4 Exercises 11, 12, 18-20 Problems 38-41, 43, 45
13-1 03/30/26 11.5 Newton’s Law of Cooling Worksheet 04/06/26 Section 11.5 Exercises 1, 2, 4 Problems 34, 37, 41, 44 Exponential Models
Lab: 03/31/26 11.3 Euler’s Method Spreadsheet Euler’s Method
13-2 04/01/26 11.5, 11.6 Mixing Problems Worksheet 04/06/26 Section 11.5 Exercises 7, 8, 10-12 Problems 39, 40 SYU 47 Section 11.6 28-30 Newton’s Law of Cooling
Lab: 04/02/26 11.3 Euler’s Method Report: Short Report (Group) 04/10/26 Spreadsheet Section 11.3 Exercises 8, 9 Problems 14, 17
13-3 04/03/26 11.5, 11.6 Workday for worksheets 13-1 and 13-2 See 13-1 and 13-2!
14-1 04/06/26 11.5, 11.6 Heating and Mixing: Advanced Applications Worksheet 04/13/26 No Quiz today!
Lab: 04/07/26 Chemical Rates Big Assignment Take Home 2 04/17/26
14-2 04/08/26 11.7 The Logistic Model for Population Worksheet 04/13/26 Section 11.7 Exercises 9-16 Problems 31, 33a,b, 34 SYU 43, 44, 49, 51 The Logistic Model
Lab: 04/09/26 Chemical Rates (On Take Home 2)
14-3 04/10/26 11.7 The Logistic Model for Population (cont.) See 14-2!
15-1 04/13/26 11.6, 11.7 Populations Models with Migration Worksheet 04/20/26 Section 11.6 6, 10-13, 35 Section 11.7 33c
Lab: 04/14/26 Logistic Model with Harvesting Geogebra Applet
15-2 04/15/26 Populations Models with Migration (cont.) See 15-1
Lab: 04/16/26 Logistic Model with Harvesting Report: Short Report (Group) 04/24/26 Geogebra Applet
15-3 04/17/26 11.7 The Logistic Model – Applications Worksheet 04/22/26 Section 11.7 38-42
16-1 04/20/26 Big Assignment 3 In-class part Material: Day 9-1 to Day 14-3 No Quiz today!
Lab: 04/21/26 Logistic Model with Harvesting Geogebra Applet
16-2 04/22/26 Course Evaluations
Rann Bar-On
Rann Bar-On
Senior Lecturer in Mathematics

I am primarily a teacher and curriculum designer in calculus and linear algebra.