Math 251: Calc I - Fall 2010

Instructor: Jodi Fasteen

This is a tentative schedule, the schedule and the assignments in gray are subject to change. Links will be made active when they are ready. Answers to odd numbered problems are in the back of the book. You are encouraged to attempt corresponding odd numbered problems and check your solutions. Check this website for changes and beware of announcements and worksheets handed out in class.

Tentative Class Schedule

Homework Assignments

Due Date
Placement In week one there will be an online placement test to determine if you are prepared for Calculus I. This should allow for time for you to switch to a different class, such as 111 or 112 if necessary. To link to the online placement test, go to PSU Learner Web. You may not use a calculator or outside reference tools. The goal of this placement test is to help you find the correct class so that you will have a successful mathematical experience.

The placement test must be completed online by 11:59pm on Thursday of Week 1.

Thurs, Sept 3th

11:59pm.

Week 1: Review Algebra, Graphing, & Slope

Relevant Sections: Chapter 1 of Rogawski book and your math books from previous math classes (such as Math 70, 95, 111, and 112 at PSU).

Slopes of Lines WKST .(not hw)

Introducing Limits (Sect 2.2)

Build Your Own Discontinuities Worksheet (From Friday).

Homework 1:

  1. Ch 1 Review: (p59) 2, 3, 7, 8, 13, 14, 17, 18, 19, 22, 47, 48, 49 (If you have not yet acquired a copy of the textbook, you may pick up a copy of these problems outside my office door, NH 328.)
  2. Create a study sheet about the trig functions sin(x), cos(x), tan(x). It should be one full sheet, one side, in excellent handwriting. Make sure it answers the following questions:
    • What do these functions mean in terms of the unit circle (or in terms of triangles)?
    • What are the graphs of these functions?
    • What is interesting about the patterns of these functions? (How long are the cycles, how big and small do their graphs get?)
    • How do you find the exact values for x=0, pi/2, pi/4, pi, 4pi/3?

Friday, Oct 1st
Monday, Week 1 If you missed class on Monday On Monday (Oct 4th), the class did a Derive lab in the math computer lab NH 465. The Derive Tutorial is available here . The lab assignment, which is due at the start of class on Wednesday, is available here. You are encouraged to complete this with a partner. Wed, Oct 6th
Week 2: Introduction to Limits

Estimating Limits & Continuity

Relevant Sections: 2.2-2.4 in Rogawski book

Limits 2 Worksheet

Limits 3 Worksheet
Make sure you understand: (section 2.2) p76: Preliminary Questions: 1-8
and (section 2.4) p90: Preliminary Questions: 1-5

Homework 2:

  • (section 2.2) p76: 3, 6, 8, 23, 24, 27, 28, 38-40, 44-46, 49, 50
  • (section 2.4) p91: 2-5, 9, 10, 15, 16, 20-36 (even), 61, 65, 68, 81, 82
Fri, Oct 8th
Week 2 MAA Calculus Survey Information Instructions for Students:

Students in fall term Calculus I: Your calculus class has been selected to participate in a nationwide survey of Calculus I instruction, funded by the National Science Foundation and run by the Mathematical Association of America. The goal of this study is to improve college-level calculus by enhancing our understanding of who takes calculus and what factors contribute to a successful course. We need your help to do this.

Please go to https://www.surveymonkey.com/s/GPKSDH2?c=756 and complete the survey. It should take about 10–15 minutes of your time. No individually-identifiable information about any student will be released to anyone.

Thank you for your assistance in this important study. Toward the end of the term, you will be asked to go back online to comment on your experience of the course.

If you have any questions, please contact the MAA: programs@maa.org.

Sincerely, David Bressoud, President of Mathematical Association of America, www.maa.org

Week 3: Computing Limits

Relevant Sections: Sections 2.4-2.7

Fancy Theorem Day In class worksheet

Limits 4 Worksheet -- Good review for midterm.
Make sure you understand: (section 2.3) p82: Preliminary Questions: 1-8
and (section 2.6) p102: Preliminary Questions 1-4
(section 2.7) p106: Preliminary Questions: 1-4

Homework 3:

  • (section 2.3) p82: 2, 12, 13, 18, 24, 26, 27
  • (section 2.5) p97: 9, 10, 13, 14, 16, 17, 19, 20, 22, 23, 29, 37-39
  • (section 2.6) p103: 5, 6, 8, 10, 15, 16 ,23, 24, 26, 29
  • Study for the midterm
Fri, Oct 15th (Changed, see below)
Week 3-4 Homework 3 revised: To help you prepare for the midterm, I am extending the homework deadline until Monday (the day of the midterm) so that you can keep your homework to study from. I am also adding the Section 2.7 homework to HW 3, because the midterm includes all of Ch 2. Here is the new homework and deadline:

  • (section 2.3) p82: 2, 12, 13, 18, 24, 26, 27
  • (section 2.5) p97: 9, 10, 13, 14, 16, 17, 19, 20, 22, 23, 29, 37-39
  • (section 2.6) p103: 5, 6, 8, 10, 15, 16 ,23, 24, 26, 29
  • (section 2.7) p106: 2, 3, 17, 19, 21-24
  • Study for the midterm
Monday, Oct 18th
Midterm Relevant Sections:

Chapter 1 and Sections 2.2-2.7 in Rogawski book

Midterm on Monday, Oct 18th

Challenge questions (for Bonus points), due at the time of the exam, Monday. This will be turned in separately from the homework.

Instead of a practice test, the worksheets we've done in class would be a better study tool. They are also posted online. Be prepared to answer concept questions and numerical questions. Be sure you understand the Preliminary Questions at the start of each section.

ex) What is the limit of f(x) as x approaches 7? (with equations/algebra or with graphs)

ex) Why is it that graphing a function is sometimes not enough to find limits? What does it mean if a function approaches two different values from two different sides? What does it mean when a limit goes to infinity? How can you tell if a function is continuous?

ex) Explain formally and informally what a limit is. Explain formally and informally what it means for a function to be continuous.

Week 4: Midterm on Monday

Introduction to Derivatives

Relevant Sections: Sections 3.1

Wednesday's Worksheet: Slope

Building the Power Rule.

Deriv: What do they mean and True/False. Attempt before Monday, Oct 25th. Bring any questions.

 Homework 4:

Wednesday's Worksheet: Slope is Due on Friday

Due to the midterm, the next textbook homework will be delayed until next week. You should be able to start on Section 3.1 after Wednesday's class, so don't put it off too long!

Fri, Oct 22th
Week 5: Applications, Product and Quotient Rules, Higher Order Derivatives

Ch 3

Graphing/Trig worksheet From Friday.

Before beginning each section, you should be reading the section and making sure you understand the Preliminary Questions given just prior to the exercises. Although homework is generally only due once a week, it would appropriate to try the problems of each new section as we cover them in class. We will have covered 3.1 and 3.2 by Friday, Oct 22nd.

HW 5

  • (section 3.1) p124: 4, 6, 10-14, 23-36, 53-58 (Note that the last 6 problems do not ask you to compute any limits.)
  • (section 3.2) p139: 5, 6, 8, 10, 12, 13, 19, 20, 22, 27, 28, 32, 33, 43, 44, 47, 48, 83, 84, 87
  • (section 3.3) (p148): 4-6, 8, 10, 15, 20-23, 28, 33, 34, 44, 45
  • (section 3.4) (p158): 9-10, 12, 14, 15, 19, 22
  • (section 3.5)(p165): 10, 11, 14, 20, 23, 28, 30, 39-40, (#52 for Bonus)
Fri, Oct 29th
Week 6: Higher Order Derivatives, Trig and Chain Rules

Ch 3

Implicit Differentiation Wkst from Wed

Derivatives of Inverses Wkst from Fri

Do the Preliminary Questions for each section before beginning the problems for that section.

HW 6

  • (section 3.6) p170: 4, 6, 8, 12, 16, 20, 21, 28, 33, 36, 43, 44
  • (section 3.7) p178: 2-4, 16-18, 22-24, 27-30, 33-34, 36, 40, 44, 48, 52, 56, 92, 93
  • (section 3.8) p184: 10, 12-14, 20, 23-24, 30, 32, 35, 36, 50, 51
  • Homework hint: Only even numbered problems are graded. Odd numbered problems are for practice. If you choose to write up only a subset of the homework, choose wisely.
We covered sections 3.6 and 3.7 on Friday, Oct 29th. You should be able to do many of these problems now. Don't wait until Wednesday night to start your HW.

If you missed class on Monday Nov 1st, you missed a quiz. You can make this up during office hours, provided you contact me via email prior. You should arrange to make this up before Wednesday's class, as the Make-up version is likely to be much harder.

* There was no quiz on Friday, though there is a quiz planned for Monday, Nov 8th. It will be open book/open notes. It would be wise to complete Friday's worksheet before Monday.

Friday, Nov 5th
Week 7: Implicit functions

Derivatives of Inverses

Related Rates Wednesday's Worksheet

Midterm on Friday.

Midterm 2, Scheduled Friday of Week 7. Emphasis will be on Ch 3. (Ch 2 limits will appear as they do in section 3.1 and 3.2. Refresh Section 2.5 if you are still struggling with solving limit equations.)

HW 7:

  • (section 3.9) p191: 5-6, 9-12, 16, 26-29
  • (section 3.10) p197: 3-18, 51-55
  • (section 3.11) p204: 9-12, 14, 17-21
  • There are Review Exercises at the end of Ch 3 (p207-210). This is a good study resource.
MIDTERM IS ON FRIDAY NOV 12th. You may bring one page of notes (front and back) with formulas, examples, etc. You may use the pink formula handout as your base, or another page of your choosing. No calculators for the exam. 		Friday, Nov 12th
Week 8 In class worksheet - due Extreme Concepts Worksheet from Monday is due at the start of class on Wednesday.

Wed, Nov 17th
Week 8: Ch 4: What does the derivative tell us about the function?

Shapes of graphs, asymptotes

4.2-4.5

HW 8:
  • (section 4.2) p227: 1, 2, 6-10, 12-13, 15-16, 25-26, 31-32, 37-38, 52-54, 61-62
  • (section 4.3) p236: 12-13, 16-17, 26, 28, 30, 36, 40-42
Friday, Nov 19th
Survey MAA Calculus Survey Information Students in fall term Calculus I:

Please go to https://www.surveymonkey.com/s/CTNJQRF?c=756 and complete the survey. It should take about 15–20 minutes of your time.

This is a follow-up to the nationwide calculus survey that was given to your class at the start of this term. Even if you did not complete the survey at the start of the term, it is important to answer this survey so that we can gather a picture of student impressions of their calculus instruction across many different types of institutions and instruction.

If you have any questions, please contact Olga Dixon at the MAA: programs@maa.org or telephone at (202) 319-8498.

Sincerely, David Bressoud, President

Mathematical Association of America, www.maa.org

Week 9: Continue Ch 4

Graphing functions based on 1st and 2nd derivative

Horizontal Asymptotes Worksheet (Monday)

Optimization

Newton's Method (see Bonus opportunity)

No School on Friday: Happy Turkey Day!
  • (section 4.4) p243: 2, 4, 10-12, 16-18, 25-26, 34, 36, 40, 50, 53, 56-57
  • (section 4.5) p257: 16-18, 26-28, 32-34, 52-54, 59-60, 62-64
  • (section 4.6) p265: 2, 4, 8, 9, 19-20, 27-28, 36
Bonus Opportunity on Newton's Method and Optimization 		No School Friday, so HW will be due on Monday, Nov 29th
Week 10: Finish Material and Review Worksheet on L'Hopital's Rule is due on Wednesday. The second side is the HW. The first side was done in class on Monday. Wed, Dec 1st
Review Review Problems from the last day of class

You may have a non-graphing calculator for the final exam and one page of notes (both sides). Bring your photo ID. You may not use your cell phone during the exam.

Finals Week: The final exam will be cumulative. You must have a strong grasp of Calc I before continuing on toe Calc II. Therefore, you must pass the final to pass the course. The 11:30-12:35 Section will have their final Thurs Dec 9th, 12:30-2:20pm. in NH 375

The 12:45-1:50 Section will have their final Monday, Dec 6th, 12:30-2:20pm in NH 364