Math 1110, Jim Belk Cornell University

Calculus I

Course:  Math 1110, Section 08, Fall 2021

Time & Place:  MWF 12:25 – 1:15 pm in Malott 207

Instructor:  Jim Belk (jmb226@cornell.edu)

Office Hours:

Links: Textbook, gradescope

General Math 1110 Information:

Homework Study Group:

Math Support Center: The Math Support Center (MSC) in Malott 256 offers free, drop-in tutoring Monday to Thursday from 10:00 am to 4:30 pm, as well as Wednesday and Thursday evenings. No appointment is required.

Announcements

Final Exam

The final exam is today from 7:00 pm to 9:30 pm in Rockefeller Hall (RCK) 203.

COVID Situation

The university has determined that it is safe to hold in-person finals. The exam room has been assigned with less than 50% occupancy and masking will be rigorously enforced. Please bring a mask that will sit tightly on your face and cover both your mouth and your nose. It is not possible for us to move this final online.

If you are feeling ill, please DO NOT come to the final. Send an email notification with details about your situation to me (jmb226@cornell.edu), Brock Schmutzler (bas386@cornell.edu), and Yun Liu (yl2649@cornell.edu). The appropriate course of action will be determined based on your individual circumstances. Please be patient. We will respond, but we may not be able to get back to you immediately.

Notecards

You are allowed to bring two 4 by 6 square inch notecards or one 6 by 8 square inch piece of paper with your own handwritten notes on both sides. If the combined area of your notecard(s) is larger than 48 square inches, it may be taken from you during the exam. Put your name on your notecards, as they will be collected when you turn in your exam.

Please do not try to cram an unnecessary amount of material on your notecards. If you do that, it will be very hard to use during the exam and you will waste time. The only things you should put on your notecard are basic facts you personally find difficult to remember. For example, the unit circle, definitions, theorems, formulas, rules, laws…anything useful that you have a hard time remembering. YOU ARE NOT ALLOWED TO PUT WORKED OUT SOLUTIONS ON YOUR NOTECARDS.

Two Theorems

It is very likely that either the Sandwich Theorem or the Intermediate Value Theorem will appear on the exam. Here is a study guide and some practice problems on these theorems:

Optimization Practice

Here are some additional optimization word problems for practice: Note: An error in the solution to #1 has now been fixed.

Study Guides

Here are some study guides on new material:

Office Hours

I will be having office hours at the following times this week:

Homework 10

Homework 10 is due this Friday, December 3 at 11:00 pm. Here is the assignment:

Prelim 2 Information

Related Rates Practice

Here are some extra practice problems on related rates that you can use to study for the exam. Solutions are at the end:

Extra Office Hours

I will be having extra office hours at the following times: Please stop by if you have any questions or would like to go over any of the material that we've covered.

General Information

The second prelim is this Tuesday, 7:30 – 9 pm in Malott 228. Please make sure to arrive at least 15 minutes in advance, and bring the following items with you: No calculators will be allowed on the exam.

Conflicts and Extended Time

If you have a conflict or testing accommodations through SDS (or both), please fill out the following survey:

Your Notecard

You are allowed to bring one 4 inch × 6 inch notecard with notes for the exam. Here are the rules for the notecard: Please do not try to cram an unnecessary amount of material on your note card. If you do that, it will be very hard to use during the exam and you will waste time. The only things you should put on your note card are things you personally find difficult to remember. For example, the unit circle, definitions, theorems, formulas, etc. Anything useful that you have a hard time remembering.

Formula Sheet

In addition to your notecard, there will be a formula sheet provided with the prelim. See the following link:

Exam Coverage

The exam covers the following material: No material from later sections (e.g. L'Hospital's Rule, Applied Optimzation, etc.) will appear on the exam.

New Study Guides and Problems

We haven't had a quiz that covered Sections 4.2 (which covers Rolle's Theorem and the Mean Value Theorem) or 4.4 (which covers material related to second derivatives). Here are some study guide on this material: The Mean Value Theorem study guide has its own exercises, while the second derivatives study guide suggests some problems from the textbook.

Prelim Practice and Review

Here are some practice problems for the prelim: Here are the solutions:

Solutions and Old Study Guides

Here are the solutions to all of the homework and quizzes: Here are all of the study guides:

Math Support Center

You can stop by the Math Support Center (MSC) any time this week if you have questions about calculus, and the tutors there will be able to answer your questions. The MSC is in Malott 256 (down the hall from our classroom) and is open Monday to Thursday from 10:00 am to 4:30 pm.

Old Announcements

Homework 9

Homework 9 is due this Thursday, November 11 at 11:00 pm. Here is the assignment:

Quiz 7

Quiz 7 will be this Wednesday, November 10 and will cover Sections 3.11 (linearization), 4.1 (extreme values), and 4.3 (the first derivative test). Here is a study guide for this material: Section 4.4 (second derivatives and concavity) will not be covered on the quiz, but will be on next week's prelim. Practice problems on Section 4.4 will be posted soon.

Homework 8

Homework 8 is due this Wednesday, November 3 at 11:00 pm. Here is the assignment:

Quiz 6

Quiz 6 will be this Friday, October 29 and will cover Sections 3.9 (inverse trig functions) and 3.10 (related rates), but not 3.11. Here is a study guide for this material, including exercises:

Homework 7

Homework 7 is due this Wednesday, October 27 at 11:00 pm. Here is the assignment:

Quiz 5

Quiz 5 will be this Friday, October 22 and will cover Sections 3.5, 3.6, 3.7, and 3.8. Here is a study guide for these topics: There are quite a few recommended problems this week, so make sure to get started early, especially if you haven't taken calculus before.

Homework 6

Homework 6 is due this Wednesday, October 20 at 11:00 pm. Here is the assignment:

Reading

If you haven't done so yet, please read through the rest of Chapter 3. We've covered everything in class except 3.7 (which we will be covering on Friday) and 3.11 (which we will be covering next week).

Homework 5

Homework 5 is due Thursday, October 14 at 11:00 pm. Here is the assignment:

No Quiz

There will be no quiz the week of fall break. The next quiz will be Friday, October 22.

Prelim 1 Information

General Information

The first prelim is this Thursday, 7:30 – 9 pm in Phillips Hall (PHL) room 101. Please make sure to arrive at least 15 minutes in advance, and bring the following items with you: No calculators will be allowed on the exam.

Conflicts and Extended Time

If you have a conflict or testing accommodations through SDS (or both), please fill out the following survey:

Your Notecard

You are allowed to bring one 4 inch × 6 inch notecard with notes for the exam. Here are the rules for the notecard: Please do not try to cram an unnecessary amount of material on your note card. If you do that, it will be very hard to use during the exam and you will waste time. The only things you should put on your note card are things you personally find difficult to remember. For example, the unit circle, definitions, theorems, formulas, etc. Anything useful that you have a hard time remembering.

Exam Coverage

The exam covers the following material: No material from later sections (e.g. the rest of Chapter 3) will appear on the exam.

New Study Guides and Problems

We haven't had a quiz that covered Section 3.2, which is about graphing derivatives and differentiability. (We covered this material in class last Wednesday.) Here is a study guide on this material: In addition, we haven't done much in class with abstract functions, but they have featured heavily on the homework. Here are a few more practice problems that involve such functions:

Prelim Practice and Review

Here are some practice problems for the prelim: Here are the solutions to the practice:

Solutions and Old Study Guides

Here are the solutions to all of the homework as well as quizzes 1 through 3: Here are all of the study guides so far:

More Practice Problems and Resources

Mark Jauquet (who teaches the support class Mathh 1101) has put a large number of materials, including two more sets of practice problems for the prelim, on the Canvas site for Math 1101. Here is a link to the enrollment key for the site: If you have already enrolled in the site, here are direct links to the prelim review problems: The site has much more useful material, including short videos and textbook section summaries.

Review Sessions

Mark Jauquet will be doing four review sessions this week: Review 1A covers chapter 2 material, and review 1B covers chapter 3 material. Each review is held two times, but there is no need to come to the same review twice.

Math Support Center

You can stop by the Math Support Center (MSC) any time this week if you have questions about calculus, and the tutors there will be able to answer your questions. The MSC is in Malott 256 (down the hall from our classroom) and is open this Monday to Thursday from 10:00 am to 4:30 pm, as well as this Wednesday night from 7:30 pm to 9:45 pm.

Old Announcements

Quiz 4

There will be a short quiz this Friday covering the definition of the derivative and derivative rules (3.1 and 3.3). Here are some exercises on this material: Here is a study guide on this material, which includes answers to the exercises: You do not need to hand any of these exercises in.

Prelim 1: Conflicts and Extended Time

Prelim 1 is from 7:30 pm to 9:00 pm on Thursday, October 7. If you have a conflict or testing accommodations through SDS (or both), please fill out the following survey:

Homework 4

Homework 4 is due Wednesday, September 29 at 11:00 pm. Here is the assignment: The assignment covers material in Sections 3.2, 3.3, and 3.4 of the textbook.

Quiz 3 Friday (No Calculators)

There will be a short quiz this Friday covering some material on trigonometric functions (Sections 1.3) as well as Sections 2.5 and 2.6. No calculators will be allowed on Friday's quiz. The trigonometry will be confined to finding values of trigonometric functions using the unit circle, as described in the following study guide: And here is a study guide for Sections 2.5 and 2.6: As always, all of the exercises are odd-numbered, so you can find their answers in the back of the book. You do not need to hand any of these exercises in.

Homework 3

Homework 3 is due Wednesday, September 22 at 11:00 pm. Here is the assignment: The assignment covers material in Sections 2.5, 2.6, and 3.1 of the textbook.

Reading

Please read Sections 2.6, 3.1 and 3.2 in the textbook as soon as possible.

Zoom Office Hours

I will be holding Zoom office hours this Thursday from 11 am to 12 pm. I will be sending out a Zoom link by e-mail if you'd like to join.

Quiz 2 Friday

There will be a short quiz this Friday covering exponents and logarithms (Sections 1.5 and 1.6) as well as Sections 2.2 and 2.4. Here is a study guide for exponentials and logarithms: And here is a study guide for Sections 2.2 and 2.4: Again, all of the exercises are odd-numbered, so you can find their answers in the back of the book. You do not need to hand any of these exercises in.

Homework 2

Homework 2 is due Wednesday, September 15 at 11:00 pm. Here is the assignment: The assignment covers material in Sections 2.2 and 2.4 of the textbook.

Writing Mathematics Well

Part of your grade for homework will be your overall presentation and the clarity of your explanations. Take a look at the following guidelines as you write your solutions:

Reading

Please read Sections 2.4 and 2.5 in the textbook as soon as possible. (We are skipping Section 2.3.)

Quiz 1 Friday

There will be a quiz this Friday covering the material on functions from Chapter 1 as well as Section 2.1. (Trigonometry, exponential functions, and logarithms are also covered in Chapter 1, but will be not be tested explicitly on the quiz.) Here is a study guide on the Chapter 1 material that will be covered: The study guide gives a list of covered topics as well as suggested exercises on each topic. All of the exercises are odd-numbered, so you can find their answers in the back of the book. Do as few or as many as you need to feel comfortable with the material. You do not need to hand any of these exercises in.

In addition, here are some suggested exercises from Section 2.1:

Again, all of the exercises are odd-numbered, so you can find their answers in the back of the book. You do not need to hand any of these exercises in.

Homework 1

Homework 1 is due Wednesday, September 8 at 11:00 pm. Here is the assignment: The assignment covers material in Chapter 1 as well as Section 2.1.

Chapter 1 Videos

As you continue to review chapter 1 of the textbook, here are some videos by Mark Jauquet that you might want to look at:

No Quiz

There is no quiz on Friday, September 3. The first quiz will be on September 10.

In Class (September 1)

Here are the in-class problems from Wednesday's class:

In Class (August 30)

Here are the in-class problems from Monday's class:

Homework 0

Homework 0 is due Wednesday, September 1 at 11:00 pm. Here are some links to the assignment: The assignment involves reading a few articles about mathematics education and answering questions about them. All of the questions will be graded for completion (not correctness). Here are some links to the articles: You should turn in your assignment as a PDF using gradescope. If you haven't used gradescope before, here's a short introductory video, as well as some instructions from the Canvas site:

Reading

Please read Sections 2.1 and 2.2 in the textbook as soon as possible.

Review

Please look over Sections 1.1–1.3, 1.5, and 1.6 in the textbook and review any material that you don't remember well.

MATH 1011: Academic Support for MATH 1110

This 1-credit course (S/U only) reviews material presented in MATH 1110 lectures, providing problem-solving techniques and tips as well as prelim review. There are two sections this semester, both being taught by Mark Jauquet: Please contact Mark Jauquet (maj29@cornell.edu) for more information.

Welcome!

Welcome to Math 1110. I will be using this course webpage to post all announcements and documents.

Textbook Information

The textbook is Thomas' Calculus: Early Transcendentals (14th ed.), originally by George B. Thomas, Jr., and revised by Joel Hass, Christopher Heil, and Maurice D. Weir. We will cover Chapters 2–5, after a quick review of functions.

You can access the online textbook by clicking on the Instant Access – VitalSource tab in Canvas. Please note that all students are automatically opted-in to the instant access program by default. If you do not intend to use the online textbook, you must click on Instant Access – VitalSource and choose to opt-out. If you do not opt-out before September 16, 2021, your bursar account will be charged. You have free trial access to the online textbook until Sept. 16. You do not need to use the online textbook, a physical copy would work fine.

Course Information

Introduction

Broadly speaking, calculus is the mathematics of change. Since change is all around us, the concepts from calculus are widely used to better understand our world in many different contexts. Whether we want to talk about instantaneous change (derivatives) or net change (integrals), calculus gives us the ability to talk about these types of changes with mathematical precision. The two main ideas in calculus—differentiation and integration—are based on the notion of a limit. As such, our journey in calculus begins with an introduction to limits of functions, which serves as the basis for later discussion of continuous, differentiable, and integrable functions. These concepts form a fundamental part of the mathematical language of science, and can be applied in many areas including physics, chemistry, biology, engineering, business, economics, computer science, anthropology, and philosophy (just to name a few).

Workload

This is a 4 credit course, so you should expect to spend around 8-12 hours working on calculus outside of class each week. Please distribute your workload throughout the week instead of trying to do it all in a few days.

Attendance

All classes will be held in-person. Success in this course is directly correlated to attendance and participation, so you will be expected to attend all class meetings unless you have a good reason (e.g., illness). We will do everything we can to help you succeed, but it is your responsibility to show up and do the work. If you miss class, it is your responsibility to keep up with class materials and assignments. You do not need to contact us if you miss class for one week or less. But if you miss class for more than one week at a time, please contact the Czar and your instructor immediately. Missing class for more than a week is likely to have a negative impact on your ability to learn the material in this course.

Grading

The grade will be based on the weekly homework, your section grade, and exams (including two prelims and one final):

Homework 30%
Section 10%
Exams 60%

Precise letter grade cut-offs will only be determined at the end of the semester after all scores have been recorded. However, students with an overall weighted average of 90% or higher will get at least an A−, students with an overall weighted average of 80% or higher will get at least a B−, and students with an overall weighted average of 70% or higher will get at least a C−.

Homework

Homework sets will be available on Gradescope, on Canvas in the weekly modules, and on the course web page. You will submit homework assignments via Gradescope according to the weekly schedule at the end of this syllabus. The homework sets will be due on Wednesdays by 11:00 pm ET. You will have 24 hours (Thursdays, 11:00 pm ET) to submit an assignment for a 10% late penalty. Extensions or make-up assignments will not be offered.

Working Together: You are encouraged work together on homework sets, provided such collaboration does not involve possessing a copy of (all or part of) the work done by someone else, in any form (e.g., paper copy, email, text, tweet, Word doc, Box file, Google sheet). If you work in a group, you should give credit to your collaborators by putting their names on your assignment, in addition to your own name. Students involved with a copying violation (those who gave as well as received) will be given a zero for the assignment.

Homework Grading: Some homework problems will be graded for completion, and the others will be graded for correctness. Each completion problem will be graded on a 0-1-2 point scale, while the other homework problems will be graded for correctness on a 0-1-2-3-4 point scale. Also, each homework set will be graded on a 0-1-2 point scale for the overall clarity and presentation of your solutions. Please read this short document by Francis Su for some tips for good mathematical writing.

Homework Average: Your lowest homework score will be dropped to compensate for unexpected circumstances that prevent you from completing an assignment (e.g., illness, bad luck). After your lowest homework score is dropped, the average of your percentage scores on each assignment will contribute 30% to your final grade.

Section Grade

Your section grade will be based on weekly quizzes and class participation, as well as perhaps some short in-class or pre-class assignments. I am planning to have a quick (10–15 minute) quiz almost every Friday covering material related to the most recent homework assignment.

Exams

We will be having two preliminary exams during the semester and a final exam at the end: During exams, you must do all your own work. Talking or discussion is not permitted, nor may you compare papers, copy from others, or collaborate in any way. Violations could result in failure of the exam, failure of the course, or University disciplinary action.

Exam Weighting: The exams will count for 60% of your final grade, which will be distributed as follows:

Your Highest Exam Grade 30%
Your Lowest Prelim Grade 10%
Your Remaining Exam Grade 20%

Note that your final exam grade will always count for at least 20%. It's only the lower of your two prelim grades that will count 10%.

Calculators

You do not need a calculator for this course. The quiz and exam questions will be designed so that you do not need a calculator, and calculators will not be allowed for these. You should feel to use a calculator or computer for the homework, and you might find software such as Desmos or Wolfram Alpha to be helpful for computations and graphing.

Course Policies

Forbidden Overlap

Due to an overlap in content, students will not receive credit for both MATH 1110 and MATH 1106.

Missing an Exam

All exams will be in-person. The university centrally schedules the exams for MATH 1110, along with many other courses. Given these constraints, students are required to take each exam at the scheduled time. Make-up exams will not be offered. If you miss an exam for a legitimate reason (e.g., illness), please contact the Czar immediately. If you have a university-sanctioned event that conflicts with one of these exam times, please contact the Czar at least two weeks before the exam date.

Regrade Requests

We will correct grading errors on a homework set or exam. Regrade requests are handled exclusively through Gradescope, and must be made within one week of being published on Gradescope. Before you request a regrade, please compare your answers to the solutions we post on Canvas. You should request a regrade only if you think there has been a grading mistake or oversight (e.g., grader did not see part of your solution). If you request a regrade, the entire problem (and perhaps the entire assignment) will be regraded to make sure that all rubric items were applied correctly. This means your grade could go up or down (or stay the same), so please do not request a regrade unless you are confident that a grading mistake or oversight occurred.

Inclusive Classrom

We understand that the members of our academic community represent a rich variety of backgrounds and perspectives. Everyone in the Mathematics Department and across departments at Cornell University is committed to providing an atmosphere for learning that respects diversity. While working together to build this community, we ask all of our members to practice the following guiding principles.

Student Accommodations

In compliance with the Cornell University policy and equal access laws, we are available to discuss appropriate academic accommodations for students with disabilities. If you would like to discuss your accommodations, please reach out to your instructor, the Czar, or the Assistant Czar. Students should register with Student Disability Services to verify their eligibility for appropriate accommodations. Please try to make requests for academic accommodations during the first three weeks of the semester (except in unusual circumstances) so that proper arrangements can be made as soon as possible.

Academic Integrity

Each student in this course is expected to abide by the Cornell University Code of Academic Integrity. Any work submitted by a student in this course for academic credit must be the student's own work. You may not submit work for this course that has been previously submitted for another course. The penalty for violation of this Code could potentially extend to include failure of the course or university disciplinary action.

Weekly Schedule

This schedule might change slightly as the semester unfolds.

Week        Topics Assignments
Aug. 27 Introduction
Ch 1 Review of Functions		 Read syllabus
Aug. 30 – Sept. 3 2.1 Rates of Change and Tangent Lines to Curves
2.2 Limits of Functions and Limit Laws		 HW 0 due Sept. 1
No class Sept. 6 (Labor Day)
Sept. 8 – Sept. 10 2.4 One-Sided Limits
2.5 Continuity		 HW 1 due Sept. 8
Quiz 1 Sept. 10
Sept. 13 – Sept. 17 2.6 Limits Involving Infinity; Asymptotes of Graphs
3.1 Tangent Lines and the Derivative at a Point		 HW 2 due Sept. 15
Quiz 2 Sept. 17
Sept. 20 – Sept. 24 3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 The Derivative as a Rate of Change		 HW 3 due Sept. 22
Quiz 3 Sept. 24
Sept. 27 – Oct. 1 3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation		 HW 4 due Sept. 29
Quiz 4 Oct. 1
Oct. 4 – Oct. 8 3.8 Derivatives of Inverse Functions and Logarithms
3.9 Inverse Trigonometric Functions		 Prelim 1 Oct. 7
No class Oct. 11 (Fall Break)
Oct. 13 – Oct. 15 3.10 Related Rates
Catch Up		 HW 5 due Oct. 14 (Thursday)
Oct. 18 – Oct. 22 3.11 Linearization
4.1 Extreme Values of Functions on Closed Intervals		 HW 6 due Oct. 20
Quiz 5 Oct. 22
Oct. 25 – Oct. 29 4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test		 HW 7 due Oct. 27
Quiz 6 Oct. 29
Nov. 1 – Nov. 5 4.4 Concavity and Curve Sketching
4.5 Indeterminate Forms and L'Hopital's Rule		 HW 8 due Nov. 3
Nov. 8 – Nov. 12 4.6 Applied Optimization
4.8 Antiderivatives		 Quiz 7 Nov. 8
HW 9 due Nov. 10
Nov. 15 – Nov. 19 5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums		 Prelim 2 Nov. 16
Nov. 22 5.3 The Definite Integral —
No class Nov. 24 – Nov. 26 (Thanksgiving)
Nov. 29 – Dec. 3 5.4 The Fundamental Theorem of Calculus
5.5 The Substitution Rule (Optional)		 HW 10 due Dec. 1
Quiz 8 Dec. 3
Dec. 6 Catch Up and Review Final Exam T.B.A.