MATH 105, Section 207, January to April 2016
Integral Calculus with Applications to Commerce and Social Sciences
 Course title: Integral Calculus with Applications to Commerce and Social Sciences.
 Instructor: Reza Sadoughian.

Where and when:
MondayWesdnesdayFfriday 89am MATX 1100.
 Instructor's office:
Auditorium Annex 126.
 email:
rsadoughi at math dot ubc dot ca

Office Hours for 1115 April (last week):
Monday, 1213 in LSK300b, and Wednesday, 1012 in Math Learning Center (MLC).
(LSK300b it is a small room besides the MLC one)
All the information about the course is at
the common course website.
Grading Schemes:
Your grade will be computed based on the following formula:
Final Exam 50%
2 midterms 17% + 17% = 34%
Coursecommon WebWorks assignemts 10%
Weekly quizzes 5%:
2.5% for your attendance + 2.5% for your average marks (The worst mark will be dropped.)
Assignments 1%
MATH 105 FINAL EXAM NOTICE
Math 105 final exam will be held on April 18 (Mon) from 8:30 am to 11:00 am, in LSK 201.
The information about math 105 final exam is HERE .
A sample final exam is HERE ,
and Math 105 final exam for 2015 is HERE .
There will be two problem session to prepare you better for the final exam:
 Friday 1317 at MATX 1100 : lectures given by Shaya Shakerian, instructor of the section 202.:
He has plan to review on "Sequences, Series and Power series " (chapters 8 and 9) from 13 to 15. After a break, he will review previous chapters, based on students' need.
 Saturday 1315 at Math 100 (main building of math department), lectures given by me. (I may continue after 15 if students request)
I focus on "Sequences and Series" then "Probability". If there are enough interests, I will continue after 15 to review previous sections.
Midterm2
Midterm exam 2 held on March 17 (Thursday) in MATX 1100.
The SOLUTIONS to midterm 2 ( version 1).
The SOLUTIONS to midterm 2 ( version 2).
The SOLUTIONS to midterm 2 ( makeup).
For Midterm 2 you will be expected to know the material from the following sections: 4.8, 5.1, 5.2, 5.3, 5.5,
7.1, 7.2, 7.3, 7.4, 7.5, 7.7, 7.8 and 7.9. This FORMULA SHEET will be provided for midterm 2.
Below, you find some sample midterms. I strongly suggest you to first solve problems yourself rather than reading solutions;
in case you spend enough time on a problem but don't find the correct solution, then open the link to solutions and read it.
 Midterm2 in 2015: here,
whose solution is here.
 Midterm2 in 2014: here, whose solution is here.
I put more sample problems below. But note that the model for your midterm 2 is the one of the common page (the above links).
I take no responsibility if the samples below are a different difficulty than the one next week.
Midterm1
Midterm exam 1 held on January 28 (Thursday), from 6:30pm to 7:30pm in MATX 1100.
The SOLUTIONS to midterm 1 ( version 1).
The SOLUTIONS to midterm 1 ( version 2).
Below, you find some sample midterms. I strongly suggest you to first solve problems yourself rather than reading solutions;
in case you spend enough time on a problem but don't find the correct solution, then open the link to solutions and read it.
 A sample midterm 1 is here, whose solution is here.
 An old midterm 1 is here, whose solution is here.
I put more sample problems below. But note that the model for your midterm 1 is the one of the common page (the above links).
I take no responsibility if the samples below are a different difficulty than the one next week.
Math 105 Webwork site link
About 10 to 17 problems will be posted on
WebWork as coursecommon homework problems every week and will be due the following week.
You will need your CWL login and password to access your homework set.
Math Learning Center (MLC)
The MLC is a space for undergraduate students to study math together, with friendly support from tutors, who are graduate
students in the math department. The MLC is located at LSK310 and LSK302 and is open 5 days a week. Every undergraduate student
studying Math is welcome here! Please note that while students are encouraged to seek help with homework, the MLC is not a place
to check answers or receive solutions, rather, our aim is to aid students in becoming better learners and to develop critical
thinking in a mathematical setting. For additional information please visit its website.
Piazza
Piazza is a discussion board that everyone in the class is expected to join. It is a good place to ask/answer questions that you
or your classmates have regarding the course/assignments, and for me to give announcements. I already sent you a link to join my
section, 207, in Piazza. You can also search "Math 105 Section 207" and follow the instructions.
Quizzes
There will be weekly or biweekly Quizzes to prepare you for midterms and final exam. I'll post answer keys/hints for each quiz after it is taken. After each
quiz, you are strongly recommended to discuss the problems with your friends and find solutions on your own.
Quiz 1: Friday, 8 January: Answer Key: 1)a 2)d 3)b 4)c 5)d 6)d 7)b
Quiz 2: Friday, 15 January: Answer Key: 1)b 2)d 3) b 4)a 5)c 6)c 7)b 8)d 9)d 10)b
Cordelia found out that the problem 4 was wrong. The inequality in choice a) has to be x^2+y^2<4:
Quiz 3: Friday, 22 January: Answer Key: 1)c 2)c 3)a 4)b 5)d 6)c 7)d 8)b 9)c 10)b
There was a mistake in problem 3. I will give its mark to everybody: The equation was supposed to be z^2x^2=z+z^2+y^2.
Quiz 4: Friday, 5 February: Answer Key: 1)c 2)d 3)d 4)b 5)d 6)b 7)c 8)c
Quiz 5: Friday, 12 February: Answer Key: 1)a 2)c 3)a 4)d 5)a 6)c 7)b
Quiz 6: Monday, 22 February: Answer Key: 1)c 2)d 3)b 4)a 5)d
Quiz 7: Friday, 26 February: Answer Key: 1)c 2)c 3)a 4)c 5)c 6)a 7)c
The questions 4 and 5 had typos and were wrong. The corrected version is given here.
Quiz 8: Friday, 4 March: Answer Key: 1) c 2) d 3) b 4) c 5) b 6) d 7) c
Quiz 9: Friday, 11 March: Answer Key: 1) a 2) d 3) b 4) b 5) c 6)  7) a 8) d
(Takehome) Quiz 10 .
Assignments
The assignments are aimed to improve your writing skills together with practicing the content of the course.
Therefore, I will post solutions after the assignments are turned in so that you can compare your solutions with mine.
(and in case you have a better, shorter or just different solution to a problem than mine, do not hesitate to share it with me. I then post your solution too)
Assignment 1  Solutions .
Assignment 2  Solutions .
Assignment 3 (Review problems for chapter 5)  Solutions .
Assignment Policies
There will be 2 or 3 assignments, in total.
Assignments will be collected at the beginning of the class. Late or missed assignments will result in a mark of zero.
Students are allowed (and encouraged) to collaborate on assignments but make sure that the work submitted is your own.
Lecture notes
Lecture notes, From Monday 4th January to Friday 8th January.
Lecture notes, Monday 11th January.
Chapter 12, section 12.8 Till the second derivative test.
Chapter 12, section 12.8 Part 2.
Chapter 12, section 12.8 Part 3.
Review notes for derivatives
Solutions.
Chapter 12, section 12.9 Lagrange Multipliers.
Example done on Friday 22th Jan.
Work sheet #1: Review exercises  Solutions .
Chapter5, Integration, part 1.
Chapter5, Integration, part 2.
Work sheet #2: Integration problems 1  Solutions.
Work sheet #3: Integration problems 2  Solutions.
Work sheet #4: Integration problems, sections 7.3 and 7.4  Solutions.
Work sheet #5: Integration by parts, sections 7.2  Solutions.
Work sheet #6: together with: Lecture notes, 7.5 Partial Fractions.
 Solutions for Work sheet #6
Work sheet #7: Differential equations  Solutions.
More examples for Substitution method.
More examples for Substitution method, part 2.
Review of Riemann sum.
Some Review examples.
Probability : (these aree lecture notes written by Professor Keqin Liu.)
Probability, some remarks. (read these notes together with the above notes)
Lecture notes for sections 8.18.4. (read these at the same than the textbook)
Lecture notes for section 8.5.
Lecture notes for section 8.6.
Lecture notes for sections 9.1 and 9.2.
Updated: Lecture notes, 8.15.
Summary for series convergence. (Updated on Wednesday 13th April)
Lecture notes, geometric series. (uploaded on Friday 8th April)
Lecture notes, Review on limit
of sequences, together with an important example for Taylor series. (Reuploaded on Friday 10th April)
Lecture notes for section9.3. (uploaded on Friday 8th April)
Practice problems
Section 11.2: 3,5,7,8,45,46,71
Section 11.3: 3,4,9,12,15,16,17,18,80
Section 12.1: 1, 3, 11, 13, 29, 31, 33.
Section 12.2: 1, 3, 5, 11, 13, 14, 15, 16, 17, 21, 23, 25, 29, 33, 37, 41, 43, 47.
Section 12.4: 1, 3, 5, 17, 21, 23, 25, 29, 33, 37, 41, 43
Section 12.8: For "Analysing critical points": 13, 19, 21, 23, 25, 27, 35, 37
For "Finding Absolute extrema": 43, 45, 47, 49, 51
Section 12.9: 5, 11, 13, 27, 29, 35, 37, 47, 49 "Lagrange Multipliers"
Find the absolute maximum and minimum of f(x,y)=1+xyxy on the set D, a region bounded by the parabola y=x^2 and the line y=4.
Using Lagrange multiplier method, find the maximum and the minimum value of f(x,y)=x(y^2) subject to x^2+y^2=1.
 Solutions
Section 5.1: 5, 7, 21, 23, 27, 31, 33, 35, 39, 41, 55, 57, 59, 61, 63
Section 5.2: 3, 5, 9, 21, 23, 27, 31, 33, 35, 37, 39, 41, 43, 45, 47, 51, 69, 71
Section 4.8: 11, 13, 15, 17, 19, 21, 25, 27, 29, 39, 41.
Section 4.8 . and
the solutions
to the Practice problems in section 4.8.
Section 7.2: 7, 9, 11, 15, 17, 19, 25, 27, 31, 35, 37
Section 7.3: 13, 15, 21, 25, 35, 37, 41, 53, 59, 61
Section 7.4: 7, 9, 17, 25, 27, 35, 37, 47, 59, 63, 65.
Section 7.5: 1, 3, 15, 19, 21, 27, 29, 63, 65, 67, 71, 77, 79
Section 7.7: 7, 9, 11, 13, 15, 17, 39, 41, 49, 51, 59
Section 7.8: 9, 11, 15, 17, 27, 43, 45, 69, 71, 73
Section 7.9: 17, 19, 25, 27, 29, 31, 33, 39, 63, 65, 67
Probability Appendix 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. The solutions are HERE . .
Section 8.1: 3, 7, 9, 15, 19, 21, 23, 29, 31, 35, 57, 69, 71, 73, 75, 77
Section 8.2: 3, 5, 9, 11, 17, 29, 45, 47, 49, 75, 79, 81
Section 8.3: 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 33, 35, 37, 39, 49, 61, 63, 69
Section 8.4: 3, 5, 9, 13, 21, 23, 25, 29, 31, 45, 47, 49, 53, 55, 57
Section 8.5: 9, 11, 13, 15, 17, 27, 29, 31, 33, 35, 37.
Section 9.1: 49, 51, 53, 61, 63, 65, 67, 69
Section 9.2: 17, 19, 21, 23, 25, 27, 29, 31, 33, 41, 45, 47, 49, 63, 65, 67
Section 9.3: 9, 11, 15, 23, 25, 29, 33, 35
Section 9.4: 25, 27, 29, 31, 55, 61