Math 105, 2012W Term 2

Integral Calculus with Applications to Commerce and Social Sciences

Course information

This is the common page for all sections of MATH 105 in Term 2 of the 2012W session (January to April 2012). Here you will find the course outline, suggested homework and practice problems, course policies, exam dates, common handouts and supplementary notes, other course information, and information on available resources. For section-specific information, please follow the individual section links below or contact your instructor.

Text

The required textbook for this course is Calculus: Early Transcendentals, second custom edition for UBC, by Briggs and Cochran. The textbook is available at the UBC Bookstore. The textbook comes in three volumes. We will need volumes 2 and 3 (you used volume 1 in math 104). Some additional course material may be provided as needed.

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

Your grade will be computed based on the following formula:

Final Exam 50%
2 midterms 15% + 15% = 30%
Course-common WebWorks assignemts 10%
Other section-specific coursework (to be decided by your instructor) 10%

Please note that grades may be scaled to ensure fairness across sections.

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 duration of each midterm will be 50 minutes, regardless of whether you are in a M-W-F class or a Tu-Th class. The dates are:

Midterm 1:

Thursday, February 2 for T-Th classes.

Friday, February 3 for M-W-F classes.

Midterm 2:

Thursday, March 15 for T-Th classes.

Friday March 16 for M-W-F classes.
Midterms are non-cumulative, but the final exam is based on the entire syllabus for the course.
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. To be eligible for this arrangement, you must notify your instructor of your failure to take the test within a week of the missed midterm, and come up with a timeline acceptable to both for producing appropriate documentation for your absence. Please note that a student may NOT have 100% of their assessment based on the final examination. A student who has missed both midterms will fail the class, regardless of his or her performance in the final exam.
Missing the Final Exam: You will need to present your situation to your faculty's Advising Office 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 10 problems will be posted on WebWork as course-common homework problems every week and will be due the following week. You will need your section number, CWL login and password to access your homework set. Alternatively, you can also get to WebWork through the course site on UBC Vista . The grade you receive from WebWork will constitute 10% of your total grade. WebWork allows you seven attempts on every problem. Please be aware of this limit when you enter your answers.
The work that accounts for the remaining 10% 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 WebWork 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 midterms and the final.
Late Assignments:
- WebWork will automatically close at a previously announced time specified by the instructor, so it is important to finalize and submit your work by that deadline. It will not be possible to obtain extensions on WebWork assignments.
- There may be other hard-copy assignments that you may be required to turn in, depending on the coursework policy specific to your section. In such cases, your section instructor will inform you of the time by which this work 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 M-W-F 8-9am Buchanan A103 (Instructor: Edward Kroc, ekroc@math)
Section 202 M-W-F 8-9am Buchanan A202 (Instructor: Athena Nguyen, athena@math)
Section 203 M-W-F 9-10am Mathematics 100 (Instructor: Keqin Liu, kliu@math)
Section 204 M-W-F 4-5pm Mathematics 100 (Instructor: Malabika Pramanik, malabika@math)
Section 205 M-W-F 4-5pm Buchanan A103 (Instructor: Paul Pollack, pollack@math)
Section 206 M-W-F 4-5pm Buchanan A104 (Instructor: Keqin Liu, kliu@math)
Section 207 M-W-F 8-9am LSK 201 (Instructor: Michael Lindstrom, mlrtlm@math)
Section 208 Tu-Th 2-3:30pm Buchanan A201 (Instructor: Djun Kim, djun.kim@math)
Section 209 Tu-Th 2-3:30pm LSK 200 (Instructor: Erin Moulding, moulding@math)
Section 210 M-W-F 8-9am MATX 1100 (Instructor: Robert Klinzmann, klinzmann@math)
Section 211 M-W-F 4-5pm LSK 200 (Instructor: Erick Wong, erick@math)

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.
We will be using Piazza (www.piazza.com) as a class discussion platform. This is a question-answer forum designed for getting quick responses from classmates, instructors or TA-s. You will need to self-register for this course in Piazza using a valid ubc email address and the access code "ubc105" (without quote).
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 pramanik87613.
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.

Need a review of differential calculus?

Not sure if you remember all the material from Math 104 that we will need in Math 105? Try the following problems as a quick refresher course in differential calculus. This list is not meant to be exhaustive, but representative.

Section 1.2 : 11, 15, 19.
Section 1.3: 25, 39, 47.
Section 1.4: 29, 32, 37.

Section 2.2: 19.
Section 2.3: 26, 39, 55.
Section 2.4: 36.
Section 2.5: 21, 39.
Section 2.6: 11, 75.

Section 3.1: 17, 27, 45.
Section 3.2: 21, 35, 43.
Section 3.3: 10, 20, 38, 60.
Section 3.4: 19, 34, 55.
Section 3.5: 11, 31.
Section 3.6: 41, 49.
Section 3.7: 13, 21, 43.
Section 3.8: 12, 15, 45.
Section 3.9: 7, 13, 17.

Section 4.1: 15, 31, 38.
Section 4.2: 19, 31, 51, 60.
Section 4.3: 29.
Section 4.4: 11.
Section 4.5: 9.

Section 9.1: 7, 13.

Course Outline

The course is divided into three parts. Roughly speaking, we will cover multivariable calculus (Chapter 12) and start on integration (Chapter 5) before the first midterm. We will complete the theory of integration (Chapter 5) and integration techniques (Chapter 7), followed by a week's worth of probability (not in the text, but course notes will be provided) before the second midterm. The rest of the time will be devoted to discussing sequences and series (Chapters 8 and 9).
Here is a week-by-week schedule of course material based on the appropriate sections of the text. The chapter and section numbers are from the second custom edition of the textbook. 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 2--6): Functions of several variables (Chapter 12) Learning goals
  - Planes and surfaces (12.1)
  - Graphs and level curves (12.2)
- Week 2 (Jan 9--13): Functions of several variables (Chapter 12) Learning goals
  - Partial derivatives (12.4)
  - Maximum/minimum problems (12.8)
- Week 3 (Jan 16--20): Functions of several variables (Chapter 12) Learning goals
  - Maximum/minimum problems (12.8)
  - Lagrange multipliers (12.9)
- Week 4 (Jan 23--27): Integration (Chapter 5) Learning goals
  - Approximating areas under curves (5.1)
  - Definite integrals (5.2)
- Week 5 (Jan 30--Feb 3): Review + Midterm 1
- Week 6 (Feb 6--10): Integration (Chapter 5) and Integration techniques (Chapter 7) Learning goals
  - Fundamental theorem of calculus (5.3)
  - Substitution rule (5.5)
  - Integration by parts (7.1)
- Week 7 (Feb 13--17): Integration techniques (Chapter 7) Learning goals
  - Trigonometric integrals (7.2)
  - Trigonometric substitutions (7.3)
  - Partial fractions (7.4)
- Week 8 (Feb 27--Mar 2): Integration techniques (Chapter 7) Learning goals
  - Numerical integration (7.6)
  - Improper integrals (7.7)
  - Introduction to differential equations (7.8)
- Week 9 (Mar 5--9): Probability Learning goals . Please note that this week's material is not covered in the textbook. Course notes are available at the online probability module .
  - Probability
  - Continuous random variable
  - Mean and variance
- Week 10 (Mar 12--16): Review + Midterm 2
- Week 11 (Mar 19--23): Sequences and infinite series (Chapter 8) Learning goals
  - Sequences (8.1-8.2)
  - Infinite series (8.3)
  - The divergence and integral tests (8.4)
- Week 12 (Mar 26--30): Series (Chapter 8) and Power series (Chapter 9) Learning goals
  - The ratio, root and comparison tests (8.5).
  - Approximating functions with polynomials (9.1)
  - Properties of power series (9.2)
- Week 13 (Apr 2--6): Power series (Chapter 9) and review Learning goals
  - Taylor series (9.3)
  - Working with Taylor series (9.4)

Practice problems

This section contains a list of problems from the textbook and will be updated weekly. These are not to be turned in, but working through them will help crystallize the concepts covered in class. Not all parts of a textbook section will be emphasized equally in lectures, and these problems serve as guidelines for identifying the important and relevant parts that constitute the course syllabus. Exam questions will be largely modelled on these problems.

Week 1:
- Section 12.1: 2-4, 11-14, 23-24, 25-28.
- Section 12.2: 1-4, 7, 11-18, 28-33, 36, 38(b) (c), 49.
Week 2:
- Section 12.4: 1-30, 56-73. For problems 72 and 73, show differentiability using Theorem 12.5. You do not need to produce $\epsilon_1$ and $\epsilon_2$.
- Section 12.8: 15-28, 29-36.
Week 3:
- Section 12.8: 37-44, 49-52, 62.
- Section 12.9: 1, 2, 4, 5-10, 20, 21, 38-41, 45-47.
Week 4:
- Section 5.1: 3-8, 17-26, 31-33, 34(i), 49-56.
- Section 5.2: 19-50, 66-69.
Week 6:
- Section 5.3: 12, 17, 18, 19, 22, 25, 30, 32, 37, 39, 51-57.
- Section 4.8: 11, 13, 17, 19, 22, 25, 27, 28,
- Section 5.5: 35, 36, 37, 40.
- Section 7.1: 7-28, 29, 32, 33.
Week 7:
- Section 7.2: 9-32, 40-49.
- Section 7.3: 7-46, 48-55.
- Section 7.4: 5-18, 49, 51-53, 57, 58, 60-62.
Week 8:
- Section 7.6: 7-10, 35-38, 44-47.
- Section 7.7: 5-20, 27-36.
- Section 7.8: 9-20, 23-32, 53-59.
Week 9:
- Probability practice problem set .
Week 11:
- Section 8.1: 6-16, 23--30, 47--58, 60--67.
- Section 8.2: 1--4, 9--26, 35-42, 63, 67, 69.
- Section 8.3: 7-46, 59
- Section 8.4: 9-30, 44-49.
Week 12:
- Section 8.5:
- Section 9.1: 1--46, 53--64.
- Section 9.2: 1--44, 46--49, 52--57.
Week 13:
- Section 9.3: 9--28.
- Section 9.4: 21--26.

Midterm and exams

Midterm 1
- Midterm syllabus: The midterm covers everything in the course syllabus up until week 4 (refer to the week-by-week schedule above).
- A note about the midterm format: There are 4-5 problems in the midterm, one of which is a multipart short-answer question, and the others are computational. The multipart question consists of several, unrelated sub-questions designed to test your conceptual understanding of the material. The computational problems will be on multivariable calculus and modeled on WebWork and textbook practice problems.
- Books, notes and calculators are not allowed in the midterm, but this formula sheet will be provided. Any other possibly useful formulae, such as trigonometric identities or roots of a quadratic equation, have to be memorized.
- Studying for the first midterm? In addition to the WebWork problems and weekly practice problems from the text posted above in this site, here are a few review problem sets.
  - Review Problem Set 1 with solutions .
  - Review Problem Set 2 with solutions .
  - Review Problem Set 3 with solutions . (Please note that Question 3 has been modified)
- Midterm drafts: 1 , 2 , 3 , 4 , 5 .

Midterm 2
- Midterm syllabus: The midterm covers everything in the course syllabus starting from week 6 until week 9 (refer to the week-by-week schedule above).
- A note about the midterm format: Very similar to midterm 1. There are 4-5 problems, one of which is a multipart short-answer question, and the others are computational. The multipart question consists of several, unrelated sub-questions designed to test your conceptual understanding of the material. The computational problems will be on integration, differential equations and probability, and modeled on WebWork and textbook practice problems.
- Books, notes and calculators are not allowed in the midterm, but this formula sheet will be provided. Any other possibly useful formulae have to be memorized.
- Studying for the first midterm? In addition to the WebWork problems and weekly practice problems from the text posted above in this site, here are a few review problem sets.
  - Review Problem Set 1 . Solutions .
  - Review Problem Set 2 . Solutions .
- Midterm drafts: 1 , 2 , 3 , 4 , 5 .

Final Exam
- The final exam will be held on Wednesday April 11, 2012, 8:30-11 am. The venues for the different sections are:
  
  Section 201 : CIRS 1250
  
  Section 202 : HENN 201
  
  Section 203 : OSBO A
  
  Section 204 : HENN 200
  
  Section 205 : WESB 100
  
  Section 206 : OSBO A
  
  Section 207 : WESB 100
  
  Section 208 : CIRS 1250
  
  Section 209 : WOOD 2
  
  Section 210 : WOOD 2
  
  Section 211 : WOOD 2
- The final exam is cumulative.
- A copy of the formula sheet that will be provided in the final exam.
- A review problem set will be posted on WebWork by the end of this week. This is not a homework assignment and does not count towards your grade. Its only purpose is to offer a comprehensive selection of problems covering the range of topics discussed in this course.
- Here is a link to an online module that may be helpful in reviewing the material on sequences and series.
- There will be three back-to-back review sessions (not all of them necessarily lecture style) on Tuesday April 10 in Room 100, Mathematics Building. They will be led by Michael Lindstrom (10 am-12 noon), Malabika Pramanik (12 noon - 2pm) and Erin Moulding (2-4pm). We recommend you attend at least one review session by an instructor different from your own section instructor.
  
  Michael Lindstrom is conducting an online survey to assess the suitability of various topics for his review session. You are welcome to provide him feedback before the survey closes on April 9 at 10 am.
  
  Problem set from Mike Lindstrom's review session on April 10.
  
  Problem set from Malabika Pramanik's review session. Correct answers are indicated in the problem set. Detailed solutions will be discussed during the review session, but due to time constraints, typed-up solutions will not be provided.
- Math exam resources wiki is a wiki of solutions to previous final exams prepared by math graduate students. There are currently solutions for most of the April 2011 and 2010 exams, and the Math 101 and Math 103 exams may also be useful.