Math 184, Section 922
Differential Calculus with Applications to Commerce and Social Sciences
update August 2, 2012: All of the linked files on this page have now been removed. If you took this course from me and would like access to any of our materials, please send me an email.
Summer 2012, Term 1
Instructor: Kelly Paton
Email: kmpaton at math.ubc.ca
Class location and time: MATX (Math Annex) 1100; Mon 1PM-1:50PM, Tues/Wed/Thurs/Fri 1PM-2:50PM
References: The required text is Calculus: Early Transcendentals, First Edition, by Briggs and Cochran. Supplemental notes and additional resources will be posted on this site.
Office hours: Tuesday, Wednesday, and Thursday 3PM-4PM after class in MATX 1118 (down the hall).
Marker/TA: Jeffrey Yiu. He is available to provide help on Monday and Wednesday, 11AM-noon, in the Math Learning Centre (LSK basement).
Grading scheme: 50% final exam, 28% weekly exams (9% each for your two best exams; 5% each for your two worst exams), 10% participation, 12% assignments.
Schedule: The tentative schedule is as follows. Exact timing of topics may vary slightly, but this should be mostly accurate.
- Final exam: The final exam will take place on June 16; it will be 150 minutes in duration.
- Weekly exams: Instead of a midterm, there are four weekly exams scheduled during the term. These will be in-class exams, tentatively scheduled for May 14, 22, 28, and June 4. If you miss a test for a documented reason, bring me a note (doctor's note, for example) when you return, and the other tests will be weighted more heavily.
- Participation: In the winter semester, Math 184 has a 1.5 hour workshop each week along with 3 lecture hours. In summer, all these hours are combined into lecture hours (and a summer `week' is equivalent to 2 winter `weeks', which is why we have 9 hours of class per week). Participation (and, to some degree, performance) in in-class activities, surveys, and worksheets will make up the workshop portion of the course.
Online assignments will be given twice weekly. Several short online assignments at a time will be given as we cover the topics. Due dates will allow at least 3 days to work on each assignment. The nature of online assignments allows for real-time feedback, which is invaluable during such a fast-paced course.
There will also tentatively be one written assignment each week in which you will be expected to show all your work. This will allow the marker to provide detailed feedback about your thought process and notation.
Assignment due date extensions will not be granted; this course moves quickly, and we won't have time to drag topics out. However, your lowest-scoring online assignment and your lowest-scoring written assignment will be forgiven and will not count towards your grade.
*Note that Monday May 21st is a holiday (Victoria Day), so there will be no class on this day.
- Week 1 [May 7--11]: Review of Exponentials, Logarithms, and Inverse Functions; Introduction to Limits; Continuity; Business Terminology. Sections 1.3, 2.2, 2.6, plus business-related notes.
- Week 2 [May 14-18]: Limit Calculations; Intermediate Value Theorem (IVT); Definition of the derivative; a few Rules of Differentiation. Sections 2.1, 2.3, 2.6 (IVT), 3.1--3.5.
- Week 3 [May 22-25]*: more Rules of Differentiation; Elasticity; Compound Interest. Sections 3.6, 3.8, 6.8, and elasticity notes.
- Week 4 [May 28-June 1]: Implicit Differentiation; Related Rates; Optimization Problems. Sections 3.7, 3.10, 4.1, 4.2, 4.4,
and inventory control notes.
- Week 5 [June 4-8]: Graphing; Linear Approximation. Sections 4.3, 4.5.
- Week 6 [June 11-15]: Quadratic Approximations; Trig Function and their Inverses. Section 9.1 (up to p.591, not including Taylor polynomials), 3.9.
General information: MATH 184 is a course in differential calculus, with applications and examples drawn primarily from business and economics. MATH 184 and 104 are equivalent in technical content to MATH 100/180/102 and serve as a pre-requisite for any of MATH 101/103/105. The text book for MATH 104/184 is Calculus: Early Transcendentals, First Edition, by Briggs and Cochran. Any supplemental notes for specific topics will be posted on the websites for each section. Content taught in this course will be the same across both summer sections 921 and 922, and both sections will be prepared for the common final exam. The grading scheme is the same for both sections.
Academic integrity: Please see the UBC Calendar (Chapter V, Student Conduct and Discipline) for information on academic misconduct.
The above information is from the syllabus. The pdf version is here.
Final Exam Info
Date: Saturday June 16 2012, 1:00PM - 3:30PM.
Location: HEBB 100 (on East Mall)
More details are listed here. This document is based upon the standard protocol for Math 184 final exams.
I've had a few questions about passing the final to pass the class. I asked the course coordinator, and no, you are not required to pass the final to pass the class. (Note, however, that if you do abysmally on the final, you may not have been doing that well in the course anyway... so the final probably isn't your biggest problem.)
A note on content: inverse trig functions (Section 1.4), derivatives of inverse trig functions (Section 3.9), and higher-order (i.e., higher than quadratic) Taylor polynomials (part of Section 9.1) will not be examined on the final. You are expected to know all other topics from the syllabus and learning goals.
Updates to this webpage will be noted here; check frequently for new assignments, notes, schedule changes, and more. Class begins Monday May 7 in MATX 1100 at 1PM.
June 20: (Same message sent out by email:) Final grades have been submitted and should be available either immediately or very soon, depending on whether or not the SSC interface has any buffer time. Again, thank you for a busy and intense 6 weeks. Enjoy the rest of your summer. I wish you the best of luck in your future endeavours (mathematical or otherwise)!
Note: If you'd like to view your final, you must first (1) submit a "Viewing" form to the Math Office (form available in Math Office or on Math Department website here), and then (2) email me to make a viewing appointment with me. Note that this is just to view your final, NOT to have it re-graded -- that is yet another procedure and form, and has a fee attached to it.
June 17: Marking... I will make an announcement via email once all the grades are completed and submitted to the SSC. This should occur within the next few days.
June 15 (evening): That's it, folks! Thank you for an engaging, challenging, and entertaining 6 weeks of class.
I will be posting Solutions to today's selected practice problems are posted momentarily. I have sent out this email to everyone with a reminder about the final exam. See you tomorrow... (also, the link to yesterday's timed practice problems has been fixed). Also, students who attended class today had the option to complete an anonymous survey for participation points, just for my information about how the course went for you and how I can improve it (and myself) in the future; I'll offer this survey (and the points) directly after the exam tomorrow to those who weren't here today.
June 14 (evening): The final assignment for marks, a16Taylor, is due tomorrow (Friday) at 1 PM. The review assignment (for participation points) is due tomorrow at 11:59 PM. As announced a few days ago, I will have an extra office hour tomorrow (Friday) from 12-1 in MATX 1118. Friday is our last class, and it will run as usual from 1-3. We will do review problems in groups (for participation points), and I will go over some of the problems on the board. If you would like to know your grade going into the final, please send me an email or come by during my office hour tomorrow. Please note that I will unfortunately be unavailable after class tomorrow, but I will still continue answering emails on Friday evening. I will do my best to answer emails Saturday morning as well, although my time will become limited as the final approaches, so please get any questions or concerns to me sooner rather than later. Keep practicing problems! Today's timed practice problems
will be posted shortly are now posted; since we discussed solutions in detail in class, I will not be posting solutions.
Please complete the online teaching evaluation tonight if you have not already done so. I will not see the evaluation data until after the final grades have been submitted, and all evaluations will remain anonymous.
June 14 (before class): A pdf with a few full solutions to the graphing/word problem practice has been posted (see Additional Review under Suggested Problems).
June 13 (late): I've added a new section just above this News section titled "Final Exam Info". Please see the document there with details on the final exam rules, format, and grading procedures. I've also posted answers to the graphing and word problem practice problems. Finally, please note that all uncollected assignments, worksheets, and quizzes are available in the box outside our classroom.
June 13 (evening): As of today we are done with new material. Thursday and Friday will be review days, with participation points for activities on each day. We will do a short "exam conditions" quiz on Thursday (not graded) to give you some practice graphing and solving word problems under a time constraint. Today's Taylor polynomial worksheet
will be posted shortly is posted. Solutions to Assignment D will be posted shortly are posted. Assignment C was handed back today; any leftover marked assignments are now in the box outside our classroom. If you would like to know your grade going into the final, please send me an email or come see me during office hours on Thursday 3-4 or Friday 12-1 (MATX 1118).
June 13 (extremely early): The learning goals for weeks 5 and 6 have been updated. Also, I have posted some practice problems on graphing and word problems under suggested problems. Answers (and maybe some full solutions) will be posted by the end of the week. These are excellent practice for the final, if you're looking for additional problems to work on. Read the word problems carefully to figure out what they are asking you for. Is it a related rates problem? Optimization? Something else entirely? Understanding the problem and setting it up carefully is crucial to solving it.
June 12 (evening): I just sent out this email regarding two important notes: first, test solutions to previous final exams will not be posted (contrary to what I announced in class today). Second, both Jeffrey and I have extended office hours this week. See the email for details. Note that we will still go over some of the questions from the 2009 final during Friday's review class, and I may draw upon some of the 2010 or 2011 problems for Thursday's review class as well. In other news, the final webwork review assignment (for participation points) is now available, due Friday at 11:59PM. Answers will be released right at midnight for you to check and study from.
June 12 (after class): Suggested problems for quadratic approximations and Taylor polynomials have been posted. Remember, we are covering p 590-595 of Section 9.1, and we are NOT covering the remainder formula. [However, you may notice that putting n=1 into the remainder formula on p. 597 gives the maximum error formula for the linear approximation that we used in class, which is a formula that you are expected to know.]
June 12 (before class): Two pencast examples for linear and quadratic approximation (which we will cover today) have been posted under suggested problems. The final marked WeBWorK assignment, a16Taylor, is opening today, due Friday at 1PM, NOT 11:59PM as usual. We will cover Taylor polynomials today and tomorrow.
June 11 (5PM):
Solutions to the final exams from the 2010 and 2011 winter sessions will be posted by the end of the week to help you study for the final. It would be a good idea to work through the problems first (maybe even time yourself so that you have an idea of what the final will feel like), and then use the solutions to check your work. Friday's review session will be used as an opportunity for you to work through the 2009 final exam in groups (for participation points), so I'd suggest you save working on the 2009 final until then.
June 11: The solutions for quiz 4 are posted, with grading comments
to be posted momentarily now posted. Please see me if you have any questions about your grade after reading the comments and viewing the solutions. Average was 58%. Keep working on the final written assignment D (due Wed, start of class) and WeBWorK a15LinApprox (due Tues 11:59PM). The last webwork assignment will become available tomorrow, and a review webwork assignment (for participation points) will appear within the next day or two. More examples of the linear approximation with error estimation (like sin(1.6) today) can be found under suggested problems as pencasts. I've posted two more suggested problems about approximating the change in y at a point using linear approximation. If you'd like to read ahead for tomorrow, please look at the quadratic approximation and taylor polynomials in Section 9.1 (but not the error formulas).
June 9: The final written assignment (D) has been posted and is due Wednesday June 13 at the start of class. If you had already completed and handed in #5 (graphing a surge function) on the previous written assignment (C), then you may skip #1 on D. I've also posted three examples (pencasts created by a colleague, Warren Code) of linear approximations, including error estimation based on the second derivative. Recall that we finished class on Friday by deriving the formula for the maximum error of a linear approximation based on the maximum value of the second derivative within the interval of interest. Although I will go over at least one example of how to calculate this maximum error on Monday, please look at Warren's pencasts (under Suggested Problems) for further examples. They are quite instructive (and you can replay them until the concepts and calculations make sense).
June 8 (after class): Today's in-class worksheet has been posted (although not filled in). Another webwork assignment has appeared, on linear approximation: a15LinApprox, due Tuesday at 11:59PM. You may expect one more webwork assignment after that one (a16-something), plus perhaps a review assignment to help you prepare for the final. The last written assignment will be posted either tonight or tomorrow. Suggested problems for linear approximation (4.5) are posted; check back later tonight or tomorrow for some links to online examples of computing linear approximations (and errors; notice that the error based on the second derivative, as we introduced today, isn't covered in your text). Quiz 4 will be returned in class on Monday.
June 7 (evening): The solutions to today's graphing worksheet have been posted. Note that the graphs are computer generated, which means that (a) yours may not be as accurate, although all the major features should be the same, and (b) many of the points and details are not labelled, but yours should be. For example, all critical points, inflection points, and intercepts should be clearly labeled.
June 7 (after class): Suggested problems for 4.3 [graphing] and some more graphing problems from 4.2 have been posted. The solutions to the even-numbered (#36) matching problem from 2.4 have been posted. Please note that Assignment C is due tomorrow (except for #5 - graphing a 'surge function' - which will be moved to the next assignment. Note that this is #5 in the current, rearranged set of problems!).
June 7 (before class): A tentative set of learning goals for weeks 5 and 6 has been posted. Some details may change depending on what we cover over the next week, but the foundation will remain the same. I will announce if/when any changes are made.
June 6 (late): Next week Jeffrey will be available in the MLC from 11-12 on Monday as usual, but he has volunteered to extend his Wednesday hours to 11-1 to help you out with your studying.
June 6 (early evening): A new WebWorK assignment has appeared on graphing: a14graphs. It will open tomorrow (Thurs) after class, and will be due Sunday at 11:59PM. I expect to have two more WeBWorK assignments after that one, and potentially a review assignment as well (to help you review for the final). As mentioned in class today, there will be one more written assignment (D) posted by or on the weekend that will be due next Wednesday.
June 6 (after after class...): I just sent out this email to the class with this information about the final exam: as previously mentioned, the date/time is June 16, 1-3:30PM; the location is now set as HEBB100. Make sure you know where this is well in advance of the final.
June 6 (after class): Suggested problems for 2.4 and 2.5 [vertical asymptotes: infinite limits; and horizontal asymptotes: limits at infinity] are now posted, in preparation for graphing. The problems for 2.4 are fair game after our discussion of vertical asymptotes today, and the problems for 2.5 will be accessible to you by the end of tomorrow's class (although you can certainly try them out today if you feel adventurous). Suggested problems for 4.2 [first and second derivative tests] and 4.4 [optimization problems] were posted yesterday. If you want to read ahead for tomorrow, please look at section 2.5 [evaluating limits at infinity, in the context of 'end' behaviour or horizontal asymptotes] and 4.3 [graphing].
June 5 (late evening): Solutions to today's optimization worksheet have been posted. Note that the main goal for the in-class problem was to set it up and get to the point where you had the area as a function of 1 variable. Actually solving for the critical point is a difficult task, and not one that I would expect you to do. I've included the full solution in case you're curious. Do attempt the second problem on your own though; it is quite reasonable, and takes some thinking to understand and set up properly (but then is quite simple to solve).
I've also posted a link to the previous final exams that the department has made available. The link is at the very bottom of this page, under Additional Resources.
June 5 (evening): Question #1 on written assignment C hasn't been covered yet, but you can work on #2 and #3 already. To make the assignment a bit shorter, let's take out question #5; I'll put it on the last assignment instead.
June 4 (10PM): Two short new webwork assignments (one on minima and maxima, one with a few optimization word problems) are appearing tonight, due Thursday at 11:59PM. We have already covered most of the material for a12optIntro. We should get through most of the material for a13optimization on Tuesday, possibly extending to Wednesday.
June 4 (9PM): Rearranged assignment C slightly. The questions are unchanged, but their order has been altered to closer match the order in which we'll cover the topics.
June 4 (evening): Quiz 3 has been returned. Grading comments are posted below. Written assignment C has been posted and is due Friday at the start of class; it is based on the material we are covering now: 4.1 through 4.4 (graphing and optimization), and
2.7 2.5 (limits at infinity, in the context of asymptotes). Remember that Jeffrey is available on Wednesday from 11-12 in the Math Learning Centre in the basement of LSK, and I have office hours 3-4 on Tues/Wed/Thurs either in our classroom or down the hall in MATX 1118. Please note that although "inventory control" was included in the syllabus, it is actually no longer covered in Math 184. We will not be covering inventory control.
June 1 (late): All worksheets and solutions are now updated up to Week 4. It was brought to my attention that there is no question #4 on the webwork assignment a10impDiff; this was just a numbering error that I missed, so please ignore it and complete the 7 questions: #1-3, 5-8.
June 1 (evening): Quiz 4 will take place on Monday June 4 (40 minutes), and will cover all the material from week 4. To prepare, look at the suggested problems, weekly learning goals for week 4, assignments, and all the notes/worksheets from this week. All suggested problems for this week have been posted/updated (including some new business-oriented related rates problems). Learning goals for Week 4 are posted. The remaining solutions (diagrams for yesterday's worksheet, solutions for today's worksheet, and solutions to Goldstein's elasticity problems) will be posted by the end of tonight.
May 31 (late): Solutions to today's worksheet have been posted. Diagrams to accompany the solutions for the extra problems will be posted tomorrow.
May 31 (after class): Suggested problems for today's class (related rates, 3.10) have been posted below. Solutions to today's worksheet will be up by the end of the day. Two new assignments have appeared on WeBWorK: one on implicit differentiation (a10impDiff) and one on related rates (a11RelatedRates). Both are due Sunday at 11:59PM. As announced in class today, the 12% of your grade for assignments will be split into 8% for webwork and 4% for written assignments.
May 30: Solutions/answers to today's worksheet have been posted. Grading comments for quiz 2 are now up, and you can pick up your graded quiz 2 tomorrow in class if you haven't already. Suggested problems for implicit differentiation (3.7) are posted; we'll finish one more bit of implicit differentiation tomorrow and then move on to related rates (3.10). Remember to get your assignments (Written B, webwork a9) done for tomorrow (at the start of class, and at 11:59PM, respectively)! Some of the WeBWorK expressions are long (which I recognize is frustrating; it's difficult find good problems that simplify to a simple expression, which makes some questions very tedious to enter), so make sure you allow yourself enough time to do the calculations and check your math to ensure your expressions are okay. You can email me up til 6 PM tomorrow with problems.
May 29: The filled-in notes/worksheets for today's class have been posted under Class Notes. The solutions to quiz 3 are also up. We'll cover implicit differentiation tomorrow (3.7), and possibly delve into related rates (3.10); I have high hopes that I'll be able to speak by tomorrow. All unclaimed marked worksheets, assignments, and quiz 1s are in a box outside the classroom, ready to be picked up. Suggested problems on elasticity (see your notes today, and the additional notes under suggested problems) and exponential growth/decay (6.8) have been posted.
May 27 (late): Written assignment B has been posted below. It is due this Thursday in class. A webwork assignment, a9, on log differentiation (covered last Friday, Section 3.8) and elasticity (to be covered Tuesday, additional notes to be posted here) is due Thursday at 11:59PM.
May 27 (afternoon): Answers to the additional relative rates problems have been posted under Suggested Problems.
May 26: A few additional relative rates problems have been posted under Suggested Problems. Solutions or answers will appear by the end of Sunday, hopefully sooner. Solutions to the extra business problems, plus corrections to the solution for question 5, have been posted.
May 25 (late enough to be May 26): The following items are now posted below: Week 3 Learning Goals, Week 3 suggested problems, Week 3 worksheets and solutions, solutions for Written Assignment A. I will try to dig up and post a few practice problems for relative rates of change, since this is lacking in our textbook. Solutions to the Extra Business Problems will be posted by the end of the weekend. I will answer emails regarding WeBWorK when I can; please do not leave your questions until Sunday afternoon/evening as I may not get to them before the deadline.
May 25 (after class): As mentioned in class, by the end of tonight this site will be updated with all the suggested problems for week 3 and the learning goals for week 3. These should give you an idea of what will be tested in Quiz 3 on Monday May 28. Sometime on the weekend I will post solutions to the recent worksheets, solutions to the written assignment A, and I will also post your next written assignment (likely due Thursday). Another WeBWorK assignment will be appearing soon with logarithmic differentiation on it; I'll announce it here when it's available.
May 24 (after class): The solutions to quiz 2 are now posted. Suggested problems for 3.5 (derivatives as rates of change) are posted; we will finish the "marginal" concept (also in 3.5) tomorrow, and move on to Section 3.8. Solutions for written assignment A will be posted tomorrow, and the next written assignment will appear sometime on the weekend. Quiz 3 is scheduled for Monday May 28 and it will cover the material up to and including this Friday.
May 23 (late): Regarding written assignment A, question 3b: If the chain rule is new and unfamiliar territory, it may be easier to do question 3b on the written assignment using the quotient rule. If you expand the
denominator, then you can simply use the quotient rule with the numerator as 1 and the denominator as x^2-4x+4. (If the function was
something like 1/(2-x)^50 then this method obviously wouldn't work, but 1/(2-x)^2 is reasonable to expand.)
May 23 (after class): A new WebWorK assignment a8derivatives3 has shown up, but you don't need to start it until tomorrow; it is based on the material we covered today (3.4, 3.6), as well as the material we'll cover tomorrow (3.6, 3.5, business applications). I'll bring it up in class. Suggested problems for sections 3.4 and 3.6 are now posted. We'll cover more of the chain rule (3.6) tomorrow, as well as derivatives as rates of change (3.5) and some business applications. Remember the first written assignment is due tomorrow in class!
May 22: My apologies for my unexpected absence from class today. I just sent out this email regarding what has been changed as a result.
May 21: I am currently unable to post solutions to the derivative worksheet. For the first half of the worksheet, you may check your answers using Wolfram Alpha. Here is an example of how to input question #15 into Wolfram Alpha. The second half of the worksheet should also be solvable by wolfram alpha (see here for an example of how to input question #2, and here is an example of how you could input question #3), except for question #5. The solution to question #5 is here.
May 18 (after class): The derivative worksheet handed out after class today has been posted, altered to ignore the sin and cos derivative questions as we did not get to those today. Solutions will be posted later this weekend. Quiz 2 will be on Tuesday May 22 for the first 40 minutes of class. After a short break, we will have the second half of class as usual. Section 3.4 (trig derivatives) will *not* be on Quiz 2, but all the material covered this week (see suggested problems for week 2, webwork assignments up to a7, week 2 learning goals, and worksheets for this week) will be on Quiz 2. Monday is a holiday so there is no class or Math Learning Centre hours on Monday. Quiz 1 was handed back today; see below for solutions and the grading scheme.
May 17 (very late): Two new webwork assignments (a6derivatives1, a7derivatives2) have appeared. Both are, as you would guess, on derivatives. a6 covers the material from 3.1 and a7 is based on the material we'll be covering on Friday (power, product, and quotient rule). Both are due Monday at 11:59PM. Suggested problems for 3.2 and 3.3 are now up; I will post problems for 3.4 if we make it that far. Grading comments and solutions for quiz 1 are posted.
May 17 (afternoon): Solutions to today's function vs derivative graph worksheet are posted below. We finished 3.1 today; see suggested problems below. Tomorrow we'll cover 3.2, 3.3, and hopefully 3.4 (how to calculate derivatives using rules instead of the limit definition). One or two new WW assignments will be up within the next 24 hrs, due Monday at 11:59PM.
May 16 (late): Written assignment A is now posted, due Wed May 23 at the start of class.
May 16 (evening): Suggested problems for 1.2 (slopes), 2.1 (secant/tangent lines), and 3.1 (derivatives - we'll cover this material tomorrow) are now posted. Make sure you practice limit calculations by doing the suggested problems for 2.3.
May 15 (afternoon): The IVT worksheet from today is posted under Worksheets and activities along with its solutions. We'll cover evaluating limits (Section 2.3) tomorrow, which will bring you up to speed for assignment a5limits (due Friday). After that will come Section 2.1 and then we'll begin chapter 3. We may cover up to 3.4 by the end of the week. Learning goals for week 2 are posted, but they may be adjusted depending on how the week progresses.
May 15 (morning): A new assignment on limits (a5limits) is now available, due Friday at 11:59PM. We will cover this material today, and possibly spill over to tomorrow if needed. Some suggested problems for today's material (continuity on intervals, IVT, and limit calculations) are listed below.
May 14 (evening): Quiz 1 solutions are posted under a new heading near the bottom of this page, 'Quizzes'.
May 14 (afternoon): Solutions to Quiz 1 will be posted shortly. I will return the quizzes in class when I have them all graded; I expect this to take a few days, but I aim to have them back as soon as possible and before the end of the week. If you missed this quiz for a documented reason, bring me a note (doctor's note, for example) when you return, and the other tests will be weighted more heavily. This is the policy for all four quizzes in this course, and I've added it to the syllabus info above. A new assignment on continuity is now available, due Friday at 11:59PM.
May 14 (morning): Two new assignments will be showing up today and tomorrow on WeBWorK: a4continuity, on continuity, and a5limits, on evaluating limits. These will be due on Friday.
May 11 (middle evening..): As announced in class today, the quiz on Monday will be 5 questions on the topics from Week 1. The first four problems will be on:
(1) Logarithmic and exponential functions, Section 1.3,
(2) Business problems, like the worksheet, the example in class, and the problems listed under suggested problems,
(3) Limit concepts and finding limits from graphs, Section 2.2,
(4) Determining continuity, Section 2.6.
The fifth question is to be determined, and will be a lovely surprise!
To prepare for the quiz, you should be comfortable with all the Suggested problems below, the assignment problems (for assignments a1 through a3), the Worksheets and activities from class (solutions posted below), the material covered in Class notes below, as well as the actual notes you have taken during class this week. The Learning Goals for Week 1 (posted below) are a good guide to what you are responsible for knowing.
Send me your questions by email (kmpaton at math.ubc.ca) before 6PM Sunday and I'll get back to you, but I can't guarantee that emails after 6PM Sunday will be answered in time for the exam.
May 11 (early evening): The Paint Store worksheet and its solutions are posted under 'Worksheets and activities'; we will likely go over Task 2 on Monday after the quiz, if there is interest in that. Solutions to the compound interest worksheet are also posted under 'Worksheets and activities'. Two new documents have been added to class notes: a basic summary of the business terms of revenue, cost, and profit, as well as notes on continuous compounding of interest.
May 11 (after class): Suggested problems for section 2.6 (Continuity, but NOT the Intermediate Value theorem or questions with complicated limits) are listed below. For those wanting more practice with logs and exponents, I've added a link to a website with some more log/exponent problems and listed the problems that you could look at. This is all under 'Suggested problems,' Week 1. You'll now find solutions for the additional business problems here as well.
May 10 (late): Suggested problems for section 2.2 (introduction to limits, mostly from graphs) are now listed below. The loan shark worksheet solutions should be up sometime tomorrow morning. I've sent out this email regarding office hours and email help for the next few days.
May 10 (after class): The clarifying notes for finding the linear demand equation in yesterday's UBC farm example have been posted under 'Class notes'. WeBWorK assignment a3 (introduction to limits) is now open and is due Sunday at midnight.
May 9 (late): More business problems similar to the worksheet we did in class today have been posted under Suggested Problems. Solutions will be posted in a few days, after you've had a chance to work on them.
May 9 (early evening): I've just opened a short new WeBWorK assignment on logarithmic and exponential functions, a2. I also sent out this email explaining what's happening with the next few WW assignments.
May 9: Solutions to today's business worksheet are now posted. My email is now linked to WeBWorK; please email me if you encounter a problem. See below under 'Assignments' for a note on #15, assignment a1.
May 8 (evening): Since our discussion on logarithms was cut a bit short today, I've posted additional notes below under 'Class notes'. Please add these to your notes from today. I've also posted solutions to the worksheet we did today, and the solutions to the skills test from Monday (see 'Worksheets and Activities' below). Suggested problems for Section 1.3 are now listed under 'Suggested problems'. Finally, since we're just getting started this week, "office hours" will take place right after class in the classroom. Official office hours will begin next week.
May 8: Webwork and Vista should be up and running today! The 'first' webwork assignment, a0, will be available at noon, due May 11 at 11:59PM. This is simply an introduction to using WeBWorK (it does not count toward your assignment grade). The first real assignment, a1, will be available later today, also due at 11:59PM on May 11. It will be introductory questions, much like the test we did on the first day of class. See the 'Assignments' section below for links to Vista and WeBWork.
Also, if the test on the first day made you feel a little unsure of your basic skills, that's okay -- now you know, and you can do something about it. The better your basic skills are, the easier calculus will be, so it's definitely worth taking the time to practice. See the new link in 'Additional Resources' below for some algebra review and practice problems.
Documents and resources
These goals describe the types of things you should be able to do after our time in class and your work at home, with textbook problems provided as examples. The idea is not just to be able to solve the exact problems listed (which is an important start), but ideally to write and solve a similar problem or variation that also addresses the same learning goal, or to explain how different example problems are similar and how they relate to the learning goal. These will be posted each week.
Week 1 Learning Goals <--- posted May 8
Week 2 Learning Goals <--- posted May 15. Accurate EXCEPT for 2(t): we did not cover trig derivatives.
Week 3 Learning Goals <--- posted May 25
Week 4 Learning Goals <--- posted June 1
Week 5 and 6 Learning Goals <--- edited June 12 to reflect our error analysis for linear approximations, and our lack of error analysis for the higher-order Taylor polynomials. New items are blue, removed items are crossed out.
Assignments will be posted here as they are assigned, and crossed off as they are past due. The online homework will be through WeBWorK; you can access WeBWorK assignments by logging into WeBWorK directly or via Vista. Written assignments will be posted here as pdf files, and they are to be handed in during class.
Current or upcoming assignments:
- Introductory WeBWorK Assignment, a0: available May 8 at noon, due May 11 at 11:59PM.
- First real WeBWorK Assignment, a1: available May 8 at 10PM, due May 11 at 11:59PM.
For some reason, #15 requires you to input the answers separated by the word 'or': 'x=__ or x=__'. Sorry for this inconsistency. Most questions with multiple answers will accept two values separated by a comma.
- SHORT Logarithmic and exponential functions WeBWorK Assignment, a2: available May 9 at 7PM, due May 13 at 11:59PM.
- SHORT intro to limits WeBWorK Assignment, a3: available May 10 at 3PM, due May 13 at 11:59PM.
- Continuity WeBWorK Assignment a4continuity: available May 14 at 4PM, due May 18 at 11:59PM.
- Evaluating limits WeBWorK Assignment, a5limits: available May 15 at 10:30AM, due May 18 at 11:59PM.
- Derivative intro (3.1) WeBWorK Assignment a6derivatives1: available May 18, due May 21 at 11:59PM.
- Evaluating derivatives (3.2, 3.3) WeBWorK Assignment, a7derivatives2: available May 18, due May 21 at 11:59PM.
- Written Assignment A:
due Wed May 23 in class. extended to Thurs May 24, in class. Solutions.
- Final derivatives (3.4, 3.5, 3.6, business applications) WeBWorK assignment, a8derivatives3: available May 23, due May 27 at 11:59PM.
- Written Assignment B: due Thurs May 31, in class. Solutions.
- Log differentiation and elasticity (3.8, class notes Tues May 29) WeBWorK assignment, a9: available May 28 2PM, due Thurs May 31 11:59PM.
- Implicit differentiation (3.7, class May 30) WeBWorK assignment, a10impDiff: available May 31, due Sun June 3 11:59PM.
- Related rates (3.10, class May 31) WeBWorK assignment, a11RelatedRates: available May 31, due Sun June 3 11:59PM.
- Maxima and minima (4.1, 4.2) WeBWorK assignment, a12optIntro: available June 4, due Thurs June 7 11:59PM.
- Optimization (4.4) WeBWorK assignment, a13optimization: available June 4, due Thurs June 7 11:59PM.
- Written Assignment C: due Friday June 8 at the start of class. Solutions. DO NOT DO QUESTION 5 (graphing a surge function). It will be moved to the last assignment instead. Edited at 9PM Monday June 4. The questions are unchanged, but their order has been altered to closer match the order in which we'll cover the topics.
- Graphing (4.3) WeBWorK assignment, a14graphing: available June 7, due Sunday June 10 11:59PM.
- Linear approximation WeBWorK assignment, a15LinApprox: available June 8, due Tues June 12 11:59PM.
- Final Written Assignment D: due Wednesday June 13 at the start of class. Solutions.
- Taylor approximation WeBWorK assignment, a16taylor: available June 12, due Friday June 15 1 PM.
- For participation points: Review WeBWorK assignment, aReview, is available now, due Friday June 15 11:59PM (answers available at midnight).
Suggested problems will be posted here as we cover the topics. Along with the in-class activities and out-of-class assignments, the suggested problems are intended to give you a sense of what problems on the weekly tests will look like.
Week 1: (for quiz 1 on Monday May 14)
Note: expressions involving logs can be written in multiple ways, so don't be alarmed if your answers don't match those in the back of the text. In particular, the answers for #45 and 47 can also be written as ratios of logarithms.
-Section 1.3: #33, 35, 41, 43, 45, 47, 58, 59, 71, 72. Additional problems: see problems 6, 7, 9, 10, 11, 12, 13, 17, 18 on this website.
-Business problems: Not in the text. Instead, here are some more business problems and their solutions (in addition to the 'A Business Problem' worksheet we did in class, posted under Worksheets below).
-Section 2.2: #2, 3, 5, 7, 9, 11, 17, 19, 23, 35
-Section 2.6 (not including the IVT or complicated limits - these will come next week): 2, 9, 13, 15, 17, 71, 73
-You should be familiar with all the worksheet problems from class (solutions are posted below).
Week 2: (for quiz 2 on
Tuesday May 22 Wed May 23)
-Section 2.6 (continuity on intervals, L/R continuity): 29, 33a, 75
-Section 2.6 (IVT): 8, 49a, 79a.
-Section 2.3: 5, 10, 23, 25, 31, 32, 37, 39, 44, 45, 47, 64, 73.
-Section 1.2: 25, 26.
-Section 2.1: 3, 4, 5.
-Section 3.1: 1, 2, 4, 5, 8, 9, 11, 13, 15, 17, 21, 29, 39, 41, 42, 43, 45, 48, 51, 59, 71.
-Section 3.2: 3, 6, 7, 9, 19, 21, 23, 28, 33, 37, 41, 43, 47, 51, 68, 75
-Section 3.3: 9, 11, 13, 17, 21, 23, 27a, 29a, 46, 49, 51, 55
Week 3: (for quiz 3 on Monday May 28)
-Section 1.3: Review the properties of logarithmic and exponential functions
-Section 3.4: 6, 15, 16, 17, 19, 21, 33, 34, 50, 55 [derivatives of sin(x), cos(x), or tan(x)]
-Section 3.6: 2-7, 9, 13, 17, 19, 21, 23, 29, 39, 41, 43, 57, 59, 71, 75a, 77a [chain rule]
-Section 3.5: 7, 9, 11, 12, 20, 21, 23, 25, 29, 35, 36, 40, 41. [rates of change]
-Section 3.8: 2, 8, 9, 11, 12, 13, 15, 17, 19, 21, 35, 36, 37, 39, 45, 47, 49, 79. [derivatives of logs and exponential functions; logarithmic differentiation]
[Note: Those interested in biological applications may find problems 75-78 intriguing. If you're interested in this model for population growth, I'd be happy to discuss logistic growth with you during office hours. It will not be tested.]
-Extra Business Problems (including marginals) can be found here; solutions are here, and corrections to the solution for question 5 are here.
-The text is lacking in relative rates of change problems so here are a few additional relative rates problems and here are the answers (not full solutions, just answers). Also see the logarithmic differentiation worksheet.
-You should be familiar with all the worksheet problems from class (solutions are posted below).
Week 4: (for quiz 4 on Monday June 4)
-Elasticity: see problems from May 29 notes; also, here are some notes and problems from a different text (by Goldstein) on elasticity; try out problems 9, 10 (this one is on relative rates), 14, 15, 16, 17, 19, 20, 23; here are the solutions to the Goldstein problems.
-Section 6.8: 1, 9, 11, 13, 16, 25, 30, 40; problems #11, 12 from the Goldstein notes in the previous point (solutions included in the same document, previous point); problems from May 29 notes [exponential growth/decay].
-Section 3.7: 2, 3, 5, 7, 9, 15, 19, 21, 23, 27, 31, 47, 49, 51, 53, 61, and the problems from the Implicit Differentiation Worksheet [implicit differentiation]
-Section 3.10: 3, 6, 11, 13, 17, 18, 23, 38, and the problems from the Related Rates Worksheet. Here are some additional business-oriented related rates problems and their solutions. [related rates]
-Section 4.1: 1, 4, 5, 7, 8, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 37, 44, 45, 53, 55, 57. [maxima/minima]
-You should be familiar with all the worksheet problems and activities from class (solutions are posted below)
Weeks 5 and 6:
-Section 4.2: 1, 2, 3, 4, 15, 17, 21, 30, 31, 33, 35, 37, 39, 57, 59, 61, 77, 79. [classifying max/min]
-Section 4.4: 1, 2, 3, 4, 7, (note that #10c was our worksheet problem) 11, 13, 15, 17, 23, 25, 31, 33, 57. [optimization]
-Section 2.4: 6, 9, 11, 17, 19, 23, 36. [infinite limits: vertical asymptotes] answers to #36: aD, eA, fE, bC, cF, dB
-Section 2.5: 9, 21, 23, 25, 39, 43, 53, 54. [limits at infinity: horizontal asymptotes]
-Section 4.3: 3, 4, 11, 13, 15, 17, 19, 22, 29, 31, 32, 43, 55. [graphing]
-Section 4.2: 69, 71, 73. [more graphing]
-Section 4.5: 2, 3, 7, 9, 12, 17, 19, 39, 43, 47. [linear approximation]
--Here are some pencast examples (created by a colleague) of linear approximation, including error estimation:
Linear approximation of e^0.05, with error estimation
Linear approximation of 12-(2.1)^2, with error estimation
Linear approximation of cos(-0.01), with error estimation
-Section 4.5: 23, 25. [linear approximation]
--More pencast examples for linear and quadratic approximations:
Linear and quadratic approx of ln(1+x)
Linear and quadratic approx of cube root of 65
-Section 9.1: 1, 2, 7, 9, 15, 19, 27, 31, 33, 37, 65. [quadratic approx., Taylor polynomials]
-Practice problems: graphing and word problems. Answers. A few full solutions. Both Math 184 summer sections (us and 921) are using this for practice.
-Past final exams are available on the department website.
-The Chapter Review sections in your textbook at the end of each chapter have a good mix of questions, if you're looking for more practice problems.
Additional class notes will be posted here on occasion, either to supplement or clarify your in-class notes.
Logarithm rules and properties (May 8)
Clarification of how to find the demand equation in the UBC farm example from class (May 9)
This document provides a basic summary of revenue, cost, and profit. (May 9)
This document provides notes and an example for continuously compounded interest. (May 10)
Filled-in notes and worksheets for May 29 (price elasticity of demand, exponential growth).
Worksheets and activities
Worksheets and in-class activity solutions will be posted here.
Solutions to the first-day skills test (May 7)
Solutions to the exponents, logs, and inverse function worksheet (May 8)
Solutions to 'A Business Problem' oPad worksheet (May 9)
Solutions to the compound interest worksheet (May 10)
'The Paint Store' worksheet and
solutions (May 11)
Intermediate Value Theorem worksheet and
solutions (May 15). A complete and correct solution is indicated in blue font. Red is additional notes.
Tax rate worksheet (May 16)
Graphing derivative worksheet solutions (May 17)
Calculating derivatives worksheet (May 18) This was NOT collected for marks. <---posted May 18. Ignore sin and cos derivative questions!
Chain rule worksheet and solutions (May 24).
Marginals worksheet and solutions (May 25). This was NOT collected for marks.
Logarithmic differentiation worksheet and solutions (May 25). This was NOT collected for marks.
See 'Class Notes' above for filled-in notes and worksheets for May 29.
Implicit differentiation worksheet, split into two parts: basic questions solutions and elasticity of demand answers (May 30). This was NOT collected for marks.
Related Rates worksheet, split into two parts: in-class question solution and extra problem solutions with diagrams (May 31).
Maxima/minima worksheet and solutions (June 1). This was NOT collected for marks.
Optimization worksheet and solutions - scan quality is a bit poor for some reason, but still legible (June 5).
Graphing worksheet and solutions (June 7).
Linear approximation in-class worksheet (June 8). This was more of a notes outline than a worksheet, and it was NOT collected for marks.
Taylor polynomials worksheet and solutions (June 13).
Timed practice problems: graphing and a word problem, 45 minutes (June 14).
Selected practice problems and solutions (June 15).
Solutions to the four quizzes will be posted here.
Quiz 1 (May 14, Week 1 material) grading comments and solutions: average 77%
Quiz 2 (May 23, Week 2 material) solutions and grading comments: average 68%
Quiz 3 (May 28, Week 3 material) solutions and grading comments: average 52%
Quiz 4 (June 4, Week 4 material) solutions, and grading comments: average 58%
For a thorough algebra review, including practice problems and solutions, check out this document from the Stewart textbook website.
Past final exams are available on the department website.