Math 105, 2010W Term 2

Integral Calculus with Applications to Commerce and Social Sciences

Course information

Text

Beginning-of-term registration information

• At last report, all sections of Math 105 were full.
• If you are not registered in a section, please do not attend it without the instructor's approval.
• Instructors do not have the authority to "fit you in". Such requests have to be processed by the math department office (Room 121 Mathematics Building).
• Math 101 and Math 103 are accepted in lieu of Math 105 as prerequisites by all faculties. You may want to check for available spots in these courses.
• The math department is conducting registration help sessions in January.
• If you need to switch from one section to another, the best way this can be done (with the sections full as they are) is to find somebody in the other section who is willing to switch with you. Then come with that person to either the main office (Room 121) or to a math department registration session.

Grading Schemes

• Final Exam 50%
• 2 midterms 15% + 15% = 30%
• Course-common hand-in homework 15%
• Other section-specific coursework (to be decided by your instructor) 5%

Exam Dates and Policies

• The final examination date for this course (to be held in April) has not yet been announced. Please do not make end-of-term travel plans before this date has been released.
• There will be two midterms in MATH 105. The dates are:
  • Midterm 1:
    • Thursday, February 3 for T-Th classes.
    • Friday, February 4 for M-W-F classes.
  • Midterm 2:
    • Thursday, March 17 for T-Th classes.
    • Friday March 18 for M-W-F classes.
• The final exam will be common to all sections of MATH 105, and will account for 50% of a student's final grade. The remaining 50% will be based on term work. The final exam generally will not be weighted higher for students who perform better on this test than they did during the term, although some allowance may be made for students who perform significantly better (an increase of 30% or more over their term mark). Such decisions are based on the sole discretion of the instructor.
• The final exam is board marked (i.e. all instructors teaching this course mark the exams together) to ensure consistency and fairness across sections.
• Grade calculation: The mark distribution of the term work of each section may be scaled based on the final exam mark distribution of that section. These adjusted term marks will then be used to compute a student's final grade. Any scaling is performed to ensure fairness in the final grades across sections. It is not expected that such scalings would result in significant grade changes.
• Exam aids: No unauthorized electronic devices will be allowed in the midterms or in the final exam. This includes calculators, cell phones, music players and all communication devices. Students should not bring their own formula sheets or other memory aids. Common formula sheets may be provided to all students depending on the material covered, in which case the content of the formula sheet will be disclosed in class prior to the exam.
• Missing midterms: If a student misses a midterm, that student shall provide a documented excuse or a mark of zero will be entered for that midterm. Examples of valid excuses are an illness which has been documented by a physician and Student Health Services, or an absence to play a varsity sport (your coach will provide you with a letter). There will be no make-up midterms, and the weight of the missed midterm will be transferred to the final examination. Please note that a student may NOT have 100% of their assessment based on the final examination. A student who has not completed a substantial portion of the term work normally shall not be admitted to the final examination.
• Missing the Final Exam: You will need to present your situation to the Dean's Office of your Faculty to be considered for a deferred exam. See the Calendar for detailed regulations . Your performance in a course up to the exam is taken into consideration in granting a deferred exam status (for instance, failing badly normally means you will not be granted a deferred exam). For deferred exams in mathematics, students generally sit the next available exam for the course they are taking, which could be several months after the original exam was scheduled.
• Please bring your student ID-s to both midterms and the final.

Coursework Policies

• About 2-4 problems will be posted on this website as homework problems every week and collected the following week. These problems will be graded by a marker assigned to this course. The grade you receive from turned-in homework will constitute 15% of your total grade.
• The worst 2 of your homework grades will be dropped. This includes the homework that you do not turn in, which will automatically be assigned a grade of 0.
• The work that accounts for the remaining 5% of your coursework grade will be decided by your instructor and may vary from one section to another. This is based on various factors such as lecture times, class size etc.
• In addition to the homework problems, a list of suggested practice problems will appear on this website every week. These are not to be turned in and will not be graded. It is however strongly recommended that you work through these problem sets as they are based on the syllabus for this course, and therefore omit problems that may be in the text but are unrelated to the course material. They also accurately reflect in terms of content and level of difficulty the problems you will encounter in quizzes (where applicable), midterms and the final.
• Late Assignments: Depending on the lecture schedule, your section instructor will inform you of the time by which homework should be turned in so as not to be deemed late. Late assignments are not normally accepted for marking and will receive a grade of 0.

Academic misconduct

• UBC takes cheating incidents very seriously. After due investigation, students found guilty of cheating on tests and examinations are usually given a final grade of 0 in the course and suspended from UBC for one year. More information.
• Note that academic misconduct includes misrepresenting a medical excuse or other personal situation for the purposes of postponing an examination or quiz or otherwise obtaining an academic concession.

Individual section links

• Section 201 (Instructor: Siva Athreya)
• Section 202 (Instructor: Guillaume Maurin)
• Section 203 (Instructor: Malabika Pramanik)
• Section 204 (Instructor: Mark Blunk)
• Section 205 (Instructor: Alexis Guigue)
• Section 206 (Instructor: Hamid Zangeneh)
• Section 208 (Instructor: Robert Israel)
• Section 209 (Instructor: Frank de Zeeuw)
• Section 210 (Instructor: Kelan Zhai)

Help outside class

• Each instructor will hold a few (2-3) office hours per week for students in his/her section. See section website for more details.
• Drop-in Tutorials: There is a drop-in tutorial centre whose operating schedule and venue for this semester will be posted here. The tutorial centre typically starts from the second week of classes. Graduate student TAs are there to help you during specified times.
• The AMS offers tutoring services.
• MyMathLab is an online resource that is part of the textbook package. It has a rich database of problems of varying levels and provides guided help and feedback. In order to access MyMathLab, you will need to login here with the course ID pramanik71956.
• First year can be an overwhelming experience for many students. If you find yourself having serious academic difficulties in this course, it is best to talk to your instructor as soon as you can.

Course Outline

• The course is divided into two parts. Roughly speaking, we will cover the theory of integration (Chapters 5 and 7) before the first midterm, and differentiation of functions of several variables (Chapter 12) by the second midterm. The rest of the time will be devoted to discussing applications of the techniques learned above in business, economics and social sciences. This will include some material from Chapter 6 and some additional notes on random variables.
• Here is a week-by-week schedule of course material based on the appropriate sections of the text. Follow the links for each week to get a more detailed description of the concepts covered that week, and for the learning objectives that you should use as self-checks.
  • Week 1 (Jan 3--7): 4.8, 5.5, 6.7 Learning goals
  • Week 2 (Jan 10--14): 5.1, 5.2, 5.3 Learning goals
  • Week 3 (Jan 17--21): 5.4, 5.5, 7.1, 7.2 Learning goals
  • Week 4 (Jan 24--28): 7.3, 7.4, 7.6 Learning goals
  • Week 5 (Jan 31--Feb 4): Review + Midterm 1
  • Week 6 (Feb 7--11): 7.7, 7.8, 6.2 Learning goals
  • Week 7 (Feb 21--25): 12.1, 12.2, 12.3 Learning goals
  • Week 8 (Feb 28--Mar 4): 12.4, 12.5 Learning goals
  • Week 9 (Mar 7--11): 12.6, 12.7, 12.8 Learning goals
  • Week 10 (Mar 14--18): Review + Midterm 2
  • Week 11 (Mar 21--25): 12.9, Applications of integration ( notes on consumer and producer surplus) Learning goals
  • Week 12 (Mar 28--Apr 1): Applications of integration
    • notes on present and future value.
    • study material on discrete and continuous random variables
  • Week 13 (Apr 4--Apr 8): Review

Homework

• This homework is due on Wednesdays for M-W-F classes and on Thursdays for T-Th classes.
• These homework sets will consist of 2--4 long-answer exam-type problems that you will hand in to be marked.
• You will download the problem worksheet and do the problems directly on that worksheet. If there are multiple sheets, please staple all pages together. Neither the instructor nor the marker will be responsible for lost pages of unstapled homework.
• Please write up complete solutions. Use proper grammar and a readable layout. Scrap work will not be marked.
• Solutions to the homework problems will appear on this website the week after they are due.

• Homework 1 . This is due on Thursday January 13 for T-Th lectures and on Wednesday January 12 for M-W-F lectures. Solutions .
• Homework 2 . This is due on Thursday January 20 for T-Th lectures and on Wednesday January 19 for M-W-F lectures. Solutions . (A sketch for HW 2 problem 1)
• Homework 3 . This is due on Thursday January 27 for T-Th lectures and on Wednesday January 26 for M-W-F lectures. Here are pages 1, 2, 3, 4 of the solutions.
• Homework 4 . This is due on Thursday February 3 for T-Th lectures and on Wednesday February 2 for M-W-F lectures. Solutions .
• Homework 5 . This is due on Thursday February 24 for T-Th lectures and on Wednesday February 23 for M-W-F lectures. Solutions .
• Homework 6 . This is due on Thursday March 3 for T-Th lectures and on Wednesday March 2 for M-W-F lectures. Solutions
• Homework 7 . This is due on Thursday March 10 for T-Th lectures and on Wednesday March 9 for M-W-F lectures. Solutions
• Homework 8 . This is due on Thursday March 17 for T-Th lectures and on Wednesday March 16 for M-W-F lectures. Solutions
• Homework 9 . This is due on Thursday March 31 for T-Th lectures and on Wednesday March 30 for M-W-F lectures. Solutions
• Homework 10 . This is due on Thursday April 7 for T-Th lectures and on Wednesday April 6 for M-W-F lectures. Solutions

Practice problems

• Week 1: (A few problems in this set contain definite integrals. Just compute their indefinite counterparts for the moment, and return to them again next week when we talk about definite integrals.)
  • Section 4.8: 8, 9, 13, 15, 17, 21, 25, 35, 36--38, 40--42, 45--48, 76--79, 84--87.
  • Section 5.5: 9--34, 52--64, 78--93.
  • Section 6.7: 11--22, 46--54.
• Week 2:
  • Section 5.1: 17--20, 23--26, 31--32, 53--56, 58--59.
  • Section 5.2: 15--18, 19-22 (replace Δx_k by Δx), 23--30, 35--44, 51--55, 65--73.
  • Section 5.3: 11--16, 19-22, 25--40, 51-57, 62--63, 74--82, 87-90.
  • Back to Chapter 5.5: 35-44, 59-64.
• Week 3:
  • Section 5.4: 9-14,16,18, 19-22, 24, 27, 33-36.
  • Section 5.5: 31-34, 37,39,41-43, 48-50, 52-64,79,80.
  • Section 7.1: 10, 11, 14, 17, 19, 20, 25, 26, 31, 33, 34, 50 ,51, 68, 70.
  • Section 7.2: 10, 11, 15, 17, 22-26, 30-32, 34, 35, 40-43, 46, 56, 58.
• Week 4:
  • Section 7.3: 8, 10, 13, 14, 16, 23, 34, 29, 30, 38, 43, 44, 50, 53.
  • Section 7.4: 9--18, 34, 48, 49, 51, 52, 53, 56, 57, 58.
  • Section 7.6: 7, 11, 12, 14, 15, 17, 18, 40 and 42 [only for n=4,8].
• Week 6:
  • Section 6.2: 15-26, 33-38.
  • Section 7.7: 5-18, 27-33, 52-54, 43, 46, 67, 70, 71.
  • Section 7.8: 15-18, 23-32, 33, 52, 59.
  • A list of supplementary word problems. The answers to the supplementary word problems.
• Week 7:
  • Section 12.1: 11-13, 33-34,63, 74-77.
  • Section 12.2: 13-16, 28-34.
  • Section 12.3: 11-24, 27-33, 49, 52-54, 56-58, 60(a), 63.
• Week 8:
  • Section 12.4: 7-30, 42, 47-53.
  • Section 12.5: 7-16, 27-32, 36-37, 49-52, 54.
• Week 9:
  • Section 12.6: 3, 4, 9-14, 21-26, 33-36.
  • Section 12.7: 5, 21-26, 31-34, 53 (b) (c).
  • Section 12.8: 9-36.
• Week 11:
  • Section 12.9: 5--10, 19--21, 27--30, 45--47.
  • Practice problem set on consumer and producer surplus
• Week 12:
  • Practice problem set 1 on present and future value of a continuous income stream.
  • Practice problem set 2 on present and future value of a continuous income stream.
  • Section 12.1 of study material on discrete random variables (see course outline above):1-10.
  • Section 12.2 of study material on continuous random variables (see course outline above):1-38.
  • Answers to the practice problems above.

Midterm and exams

Midterm 1 study material

• Studying for the first midterm? Here is the link to the math department's archive of past exams. Note that not all the earlier versions of Math 105 followed the same textbooks or covered the same material, or covered the common topics in the same order as we are doing now. On the other hand, Math 101 and Math 103 in spite of being different courses, have quite a large overlap with Math 105 in terms of course content. Here is a list of problems from the past exams that covers the syllabus of the first midterm, and that should help you prepare for the test.
• Here is a sample midterm 1 with solutions .
• Here you can find another practice midterm with solutions.
• This formula sheet will be provided to all students during the first midterm. Do not bring your own!

Midterm 2 study material

• If you are preparing for the second midterm, here is a list of practice problems from past math exams. Note that not all of the midterm material is adequately represented in this problem set. See also the sample midterms below.
• Sample midterm 1 with solutions.
• Sample midterm 2 with solutions.
• Sample midterm 3 with solutions.
• Note that a formula sheet will not be provided in this midterm, nor will you be allowed to bring your own. Please memorize any formulae or mathematical expressions that you feel might be relevant to the material.

Final Exam study material

• This formula sheet will be provided to all students during the final exam. Do not bring your own! It is your responsibility to go through the formula sheet before the exam, be clear about the notation used and memorize any formula not on the sheet that you may need.
• Sample exam 1 with solutions . (Prepared by Kelan Zhai)
• Sample exam 2 with solutions. (Prepared by Mark Blunk)
• Sample exam 3 with solutions . (Prepared by Frank de Zeeuw)
• The Math Club has printed past exam packages with solutions and they will be on sale this week (Apr 4-8) at the Math Club in MATX 1119 at the following times:
  • Monday, Wednesday, Friday from 10am-2pm
  • Tuesday, Thursday 9:30am -3:30pm
  The exam packages are $5 for members and $10 for non members.