# MATH 184

Differential Calculus for Social Science and Commerce

Topics as for Math 104; intended for students with no previous knowledge of Calculus. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414. Not for credit for students with AP Calculus AB, AP Calculus BC, or a passing score on the UBC-SFU-UVIC-UNBC Calculus Challenge Examination.
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## 24HR Notes for MATH 184

Available 24 hours after each lecture

### Keqin Liu

#### MATH 184 Syllabus for Keqin Liu — Fall 2018

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MATH 184, 2018W
Differential Calculus with Applications to Commerce and Social
Sciences
Course information
This is the common page for all sections of MATH 184 in Term 1 of the 2018W session (September to
December 2018). 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.
There will be common weekly webwork assignments, and these can be accessed on this page. For section
specific assignments and information please go to your own section site linked at the bottom of the page.
There will be three examinations (two midterm exams and one final exam), and the exams will be common to all
sections of MATH 184. See the information below for examination dates. For section-specific information,
MIDTERM EXAM NOTICE
Midterm exam 1 will be held on October 16 (Tuesday). The time is from 7:00pm to 8:00pm.
A sample midterm 1 is HERE . You should try to do the sample midterm 1 before you use THE SOLUTION
TO THE SAMPLE MIDTERM 1.
For Midterm 1 you will be expected to know the material from 1.3, 2.1, 2.2, 2.3, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5,
3.6 ( p171- p177) in the textbook, the marginal cost, the marginal revenue, the marginal profit and the Notes on a
Basic Business Problem on online. Midterm 1 will NOT cover Elasticity in section 3.6. The weekly learning
goals, and the accompanying suggested problems, outline precisely what you are expected to know. Midterm 1
consists of 6 questions, and you will have one hour to do it. No memory aids are allowed. No calculators. No
communication devices. You need to bring your student ID to do Midterm 1.
Midterm 1 Room Assignments: Note that Math 184:XYZ means the section XYZ of Math 184
Math 184:101 is in ESB 1013
Math 184:102 is in ESB 1013
Math 184:103 is in SCRF 100
Math 184:104 is in SCRF 100
Math 184:105 is in CHEM B150
Math 184:106 is in MacMILLAN Room 166
The locations of the rooms can be found in this webpage.
Midterm exam 2 will be held on November 15 (Thursday). The time is from 6:00pm to 7:00pm.
Math 184 FINAL EXAM NOTICE
Math 184 final exam will be held in December. More information about it will be given in November.
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Textbook
The required textbook for this course is Calculus: Early Transcendentals with student solutions manual, Volume
1. Fourth custom edition for UBC, by Briggs, Cochran and Gillett. The textbook is available at the UBC
Bookstore. ISBN 10 digit: 1-269-91047-7. ISBN 13 digit: 978-269-91047-7. This book is available at the UBC
Bookstore.
Note that there may be differences in page number references and problem numbering between different
editions if you use a different edition of the Briggs, Cochran and Gillett textbook. It is up to you to deal with any
such potential inconsistencies if you use a different edtition of the text.
Beginning-of-term registration information
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). The math department is conducting registration
help sessions in September.
MATH 184: Your grade normally will be computed based on the following formula: 50% Final Exam +
25% 2 Midterms + 10% Math 184 Workshops + 10% Webwork Homework + 5% other (section specific).
A student must get at least 40% on the final exam to pass this course. A student who gets less than 40% on
The webwork problems will be posted on MATH184-ALL 2018W1 as course-common homework problems
every week and will be due the following week. Note that students need to access Webwork through Canvas.
There are no workshops during the first week. All workshops will begin on September 10, 2018. The basic
information about the Math 184 workshops and also the weekly problems with their solutions can be found on
Math 184 Workshop page .
Exam Dates and Policies
THE FINAL EXAM for this course will be common to all sections of MATH 184. The exam will take
place in December at a date to be announced. Please do not make end-of-term travel plans before this
date has been released. The final examination is board marked (i.e. all instructors teaching this course
mark the exams together) to ensure consistency and fairness across sections.
THE MIDTERM EXAMS for this course will be common to all sections of MATH 184. There will be
two midterms in MATH 184. The midterm examinations are board marked (i.e. all instructors teaching
this course mark the exams together) to ensure consistency and fairness across sections. The duration of
each midterm will be 60 minutes. The dates are as follows:
Midterm 1: October 16 (Tuesday), 7:00pm-8:00pm
Midterm 2: November 15 (Thursday), 6:00pm-7:00pm.
Midterms are non-cumulative, but the final exam is based on the entire syllabus for the course.
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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. Formula sheets and other memory aids will not be
allowed.
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 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 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.
Coursework Policies
The section specific 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 WebWork problems, a list of suggested practice problems is at the end of this webpage.
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.
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
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.
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Section 101 of MATH 184 M-W-F 12-1pm Buchanan A102 (Instructor: LIU, KEQIN)
Section 102 of MATH 184 M-W-F 3-4pm MATH 100 (Instructor: LIU, KEQIN)
Section 103 of MATH 184 M-W-F 4-5pm Leonard S. Klinck 201 (Instructor: CASTO, KEVIN)
Section 104 of MATH 184 M-W-F 12-1pm Leonard S. Klinck 201 (Instructor: CASTO, KEVIN))
Section 105 of MATH 184 T-R 3:30-5pm MATH 100 (Instructor: DEMIRBAS, SECKIN)
Section 106 of MATH 184 M-W-F 3-4pm Leonard S. Klinck 201 (Instructor: HUXOL, TOBIAS)
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
The AMS offers tutoring services.
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
MATH 184 are courses in diî€€erential calculus, with applications and examples drawn primarily from
business and economics. These courses 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 184 is Single Variable
Calculus: Early Transcendentals , First Edition, by Briggs and Cochran. Any supplemental notes for speci c
topics will be posted on the main course website.
Please note that ``Week" below typically means 3 lecture hours, but this will vary. There are two common
midterms scheduled in the term, and both will take place in the evening. This course is heavily
coordinated, but individual instructors will have their own style. Be assured that the content taught will be
the same across all sections in spite of this, and that all sections will be prepared for the common
midterms and common nal exam.
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 0 Introduction: Review of Exponentials, Logarithms, and Inverse Functions. Chapter 1.3
Week 1 A standard business problem from managerial economics. (Notes). An Introduction to
Limits. Chapter 2.1, 2.2, and 2.3 (to the end of Quick Check 3 on p. 74)
Week 2 Continuous Functions. Chapter 2.6 (to p. 101 plus the definitions on page 103 and the
intermediate Value Theorem). The Derivative. Chapter 3.1, 3.2
Week 3 Rules of Differentiation. Chapter 3.3, 3.4. Chapter 3.5: only the table of derivatives
Theorem 3.13 on p. 167. (We return to this section at the end of the course.)
Week 4 Derivative as rate of change. Chapter 3.6. The Chain Rule. Chapter 3.7
Week 5 Implicit Diî€€erentiation. Chapter 3.8 to the end of the section on Slopes of Tangent Lines,
plus material on te power rule with rational exponents. Derivatives of Logarithms and Exponentials.
Chapter 3.9
Week 6 Derivatives of Logarithms and Exponentials Continued. Chapter 3.9. Applications:
Elasticity of Demand (Notes to be posted online. Instructors will cover the first two pages in the
note on Elasticity of Demand and do some examples from the other pages. Students should read the
remaining examples in this note.). Exponential Growth and Compound Interest. (Chapter 6.8 to the
end of Example 3 plus online notes. ).
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Week 7 Related Rates. Chapter 3.11. Maxima and Minima. Chapter 4.1
Week 8 Information in the rst and second derivatives. Chapter 4.2. Asymptotes from Chapter 2.5.
Graphing functions. Chapter 4.3
Week 9 Optimization problems I. Chapter 4.4
Week 10 Optimization Problems Continued. Chapter 4.4. Linear Approximation. Chapter 4.5
Week 11 Approximating Functions with polynomials Chapter 9.1
Week 12 Approximating Functions with polynomials Continued Chapter 9.1. Inverse Trigonometric
Functions. Chapter 3.10
Week-by-week detailed learning goals
Supplementary notes
A business problem for week one
Here are some notes on Elasticity of Demand , notes on Compound interest and section 6.8 for week 6
Here are some (for week 6 and week 7)
problems on Elasticity of Demand and on Continuous Compound Interest(with answers) ,
Practice problems
This section contains a list of problems from the textbook. 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.
Section 1.3: 3, 5, 11, 15, 17, 19, 25, 27, 29, 41, 43, 45, 53, 55, 70, 71, 72, 73, 79, 81, 91.
Section 2.1: 3, 5, 7, 11, 15, 29.
Section 2.2: 2, 5, 10, 11, 21, 23, 27, 29, 43.
Section 2.3: 5, 10, 26, 29, 33, 34, 37, 40, 41, 46, 47, 51, 68.
Section 2.6: 8, 10, 18, 23, 39, 58, 65, 84, 85.
Section 3.1: 2, 10, 23, 49, 51, 56, 63.
Section 3.2: 9, 10, 15, 19.
Section 3.3: 19-24, 28, 33, 36, 38, 41, 54, 62, 72, 79.
Section 3.4: 7-14, 15, 31, 34, 51, 54, 59, 60, 72, 85, 87.
Section 3.5: 6, 17-28, 46, 62, 66.
Section 3.6: 7, 10, 11, 12, 20, 21, 35, 41, 42, 46, 47.
Section 3.7: 2, 4, 5, 6, 35, 36, 38, 50, 51, 52, 79, 81, 82, 88, 93, 99, 100.
Section 3.8: 2, 3, 10, 12, 18, 24, 27, 28, 51, 54, 56, 60, 61, 75,
Section 3.9: 1, 2, 6, 12, 16, 19, 54, 57, 60, 65, 68, 97, 105.
Section 6.8: 1, 10, 11, 13, 16, 25, 30, 38
Section 3.11: 3, 10, 15, 19, 22, 24, 29, 46.
Section 4.1: 1, 4, 5, 7, 8, 10, 13, 14, 20, 24, 30, 31, 33, 52, 54, 58, 61, 62, 66, 79.
Section 4.2: 1, 2, 3, 12, 16, 22, 34, 40, 46, 47, 50, 60, 64, 68, 70, 79, 80, 97, 98, 100.
Section 2.4: 9, 11, 17, 19, 21.
Section 2.5: 28, 32, 52, 53, 57, 68.
Section 4.3: 2, 3, 8, 13, 19, 25, 30, 35, 36, 48, 49, 70.
Section 4.4: 2, 3, 4, 6, 15, 17, 21, 22, 26, 29, 31, 37, 39, 54, 61, 63.
Section 4.5: Quick Checks: 1-4; Exercises: 2, 3, 4, 15, 16, 18, 24, 26, 30, 37, 38, 47, 51, 57, 61, 63.
Section 9.1: 1, 2, 6, 9, 11, 17, 21, 31, 39, 42, 43, 73.
Section 3.10: 7-12, 22, 26.
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Notes
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