Math
103  Section 205
Integral Calculus with Applications to Life
Sciences
Winter Term 2, 2007
Instructor:
Matilde
Lalín
Classroom: Mathematics Annex 1100
Class Times: Tuesdays  Thursdays 9:30  11:00 AM
Office:
WMAX 113
Office hours:
Tuesdays 11:00 AM  12:30 PM and Wednesdays 12:00 AM  1:30 PM
in Auditorium 100A (Yum Yum's).
Phone:
(604) 8228746
email:
mlalin at math . ubc . ca
Important links:
Term Grade:
 Midterms: 30 % (15 % each)
 Homework and Quizzes: 10 % (the
lowest mark of this set will be dropped)
Note 1: A minimum mark of 44 % on the final exam
is
required to pass the course, independent of all others marks in the
course.
Note 2: I reserve the right to curve the final
marks based on statistical properties of the distribution of marks
across the entire class.
General Information:
Homework and quizzes: Homework is weekly assigned online
and generally due on Thursdays. No late homework will be accepted.
If you would like to receive credit for your
Homework, you must submit your work at the
beginning
of the class the day it is due, staple multipage submissions and make
sure that your full name and student number are clearly written on the
top of the front page.
There will be two quizzes in class. You will not
submit Homework assignment on quiz weeks. A schedule of dates for
quizzes is posted online.
The lowest mark of Homework
+ Quizzes will be dropped
Exams:
There will be two midterm exams. There will be a final exam on a date
TBA. A
schedule of dates for midterm exams is posted online.
You may use a nonprogrammable, nongraphing calculator for the
quizzes, midterms, and final. CHANGE: NO CALCULATORS OF ANY KIND WILL
BE ALLOWED.
Labs: Labs will be held in MSRC 2 (overflow in MRSC 1 if
necessary). Lab sections meet every other week with some starting the
week of the 15th (L2A,C,E,G,I,K,M) and others starting the week of the
22th (L2B,D,F,H,J,L). After the first lab, students may attend any
convenient lab session. The schedule for lab duedates is posted
online.
If you would like to receive credit for your Lab
assignments, you must submit your work at the beginning of the class on
the day it is due, staple multipage submissions and make sure that
your full name and student number are clearly
written on the top of the front page.
Independent work: You are
encouraged to work in groups and with friends on studying, on
practicing the material, and on attempting problems, sample midterms,
etc. You are also encouraged to discuss your work, labs, or other
assignments. However, by putting your name on any submission to be
graded, you are implicitly representing that submission as your own
work. A misrepresentation of another person's work as your own is
considered to be academic dishonesty.
Extra Help: Help with the
course material and problem sets can be obtained from:
 Math
Department Dropin Tutorials.
MSRC Rm #3 (west of Mathematics Annex building): Tutors are available,
at no charge, to answer questions on a dropin basis, starting the
second week of classes and continuing through the finalexam period
until the final exam.
 AMS
tutoring. The UBC student society provides
tutoring services.
Missed midterms, quizzes,
homework, and labs: If you are unable to attend one of the
quizzes or one of the midterms, you must notify the instructor in
advance with a legitimate excuse or provide professional documentation
of any medical emergency etc. within two days of the exam date. In
either of these two cases (and only in these two cases), the weight of
the final exam will be increased to compensate for the missed
midterm/quiz. Undocumented absence from midterms, and/or quizzes,
homework, and/or labs not handed in or handed in late will be given a
score of zero.
Remarking requests: If
you feel that a returned lab, homework, quiz or midterm is incorrectly
marked, you can appeal that grade by writing a note that details your
concern, attaching it to the assignment, and resubmitting. I will not
accept appeals made after one week that the assignment was returned.
Class etiquette: Use of
cell phones (including text messaging, answered or unanswered ringing
etc.), laptops, pagers, Blackberries and most other electronic gizmos
during class is highly inappropriate and disrespectful to both the
instructor and fellow students. Chit chat with neighbours, even when
whispered, is equally unacceptable. Arriving late and leaving early is
also frowned upon.
Registration: Add/drop
forms must be brought to the math department office. The instructor's
signature is neither sufficient nor necessary on an add/drop form. See here for
more
information.
Homework:
Homework is available here.
Solutions become available here. Make sure to check typos to the solutions here.
STAPLE your homework and include your LASTNAME
Homework is due IN CLASS. Please contact me BEFORE the due date to make
arrangements to submit the homework before class if
you know you won't be able to go to class the day homework is due.
PLEASE REMEMBER THAT HOMEWORK AND
LABS ARE DUE IN THE BEGINNING OF THE CLASS (9:30 AM). I'M ALWAYS FLEXIBLE
ACCEPTING ASSIGNMENTS WHILE I'M IN THE CLASSROOM, BUT ONCE I LEFT THE
CLASSROOM IT'S DEFINITELY TOO LATE.
 Due 4/10 TUESDAY: 12.3, 12.7, 12.9, 12.11, 12.13, 12.21, 12.23
(This homework is extra credit).
Suggested problems: 12.6, 12.8, 12.15, 12.16, 12.19, 12.20
Solutions to Chapter 12 problems.
 Due 4/5: 11.1, 11.3, 11.7, 11.9, 11.13, 11.15, 11.31 (ignore stability
of steady states, just find the steady states)
Suggested problems: 11.5, 11.8, 11.1012, 11.28, 11.32
The following problem was propossed by Prof. Israel. I highly recommend
it!
Problem: My bathtub has a flat bottom and vertical sides, so the volume of
water in it is Ah where A is the area of the bottom and h is the depth of
the water. When water drains out, it does so at a rate proportional to the
square root of the depth, as in section 11.5.
I start with an empty tub, stop up the drain and turn on the tap. It takes
10 minutes for the tub to fill completely. Then I turn off the tap, remove
the stopper, and the tub drains completely in 8 minutes. Now I turn on the
tap again, but (heedless of the resulting waste of water) I leave the
stopper out. The tub fills partially, approaching a constant depth as t
goes to infinity. How full will the tub get?
Hint: You don't have to solve the differential equation with tap on and
stopper out, just find a steady state solution.
Solutions to Chapter 11 problems.
 Due 3/29: 10.5, 10.11, 10.13, 10.15, 10.17, 10.21, 10.23, 10.25
Suggested problems: 10.1, 10.2, 10.4, 10.6, 10.7, 10.10,
10.14, 10.16, 10.1810.20, 10.26
Solutions to Chapter 10 problems.
 No homework is due on 3/22, there is midterm!
Solutions to Chapter 9 problems.
 Due 3/15: 8.1, 8.7, 8.13, 8.15, 8.17, 8.19, 8.21,
9.8 (a,b)
Notes: In 8.7 and 8.13(e) assume that the coins are fair.
In 8.15: "Select a sample of 3 with replacement" means consider the
following experiment: three times you randomly choose one of the 7 items
in the shipment (with equal probabilities for each of the 7 items), test
whether it's good or defective, and then put it back (so it's possible
that the same item could be chosen more than once). The question asks what
is the probability that the result of this experiment is that you choose a
good item twice and a defective item once.
In 8.13(e) you just need to graph the probability distribution (a graph
bar). The wording "probability density distribution" does not make sense
in discrete probability.
(Thanks to Prof. Israel for
these observations)
Suggested problems: 8.3, 8.6, 8.11, 8.18, 8.20, 8.22
Solutions to Chapter 8 problems.
 Due 3/8: 7.1, 7.3, 7.5, 7.7, 7.9, 7.11, 7.13
Suggested problems: even problems
Solutions to Chapter 7 problems.

No homework is due 3/1, there is quiz! NO CALCULATORS OF ANY KIND WILL
BE ALLOWED. Quiz is about
Chapter 6. Do as many problems as possible, here is a list of suggested
ones:
6.1 (a,d,f,i), 6.2 (c,d,f,m,n,o), 6.3 (a,b), 6.4 (c,d,j,k,l,m),
6.6, 6.7, 6.8, 6.10, 6.11, 6.12
Are you bored? Have nothing else to do on reading week? Try MIT's Integration
Bee!!!!!!
Please be aware that these problems are difficult (except the first one
that it's a joke). Use these problems just for fun or to tease your
instructor during office hours.
Solutions
to Chapter 6 problems.
 Due 2/15: 5.1, 5.3, 5.5, 5.7, 5.9, 5.11, 5.13
Suggested problems: 5.2, 5.4, 5.6, 5.8, 5.10 (specially fun!), 5.12, 5.14
(for 5.14, we will learn how to compute this integral on 2/13)
Solutions
to Chapter 5 problems.
 No homework is due 2/8, there is midterm! The
midterm includes what we have seen in Chapers 14. For Chapter 4, here are
some...
Suggested problems: 4.8, 4.9, 4.11, 4.15, 4.16,
4.20, 4.21, 4.24, 4.25, 4.27, 4.31
Solutions
to Chapter 4 problems.
 No homework is due 2/1, there is quizz!
However, this chapter is VERY important, so try to do the
suggested problems
Suggested problems: 3.4 (b,d,e,h,k,l,n,o,r,s), 3.5 (b,e,f,i), 3.6, 3.9,
3.11, 3.12, 3.14, 3.16, 3.17, 3.18, 3.20, 4.1, 4.2, 4.4, 4.5
Solutions
to Chapter 3 problems.
 Due 1/25: 1.3, 1.7, 1.9, 1.13, 1.15 from
Chapter
2
and 3.3 from Chapter
3.
Suggested problems: 1.4, 1.6, 1.8, 1.10, 1.16 (Chapter 2), 3.2 (Chapter
3).
BEWARE that the problems in Chapter 2 are MISTAKENLY LABELED as 1.x,
they should be 2.x.
Solutions to Chapter 2 problems.
 Due 1/18: 1.5 (only a and b), 1.6, 1.7, 1.11 (all
items), 1.13 (all), 1.19 (all) from here.
Suggested problems (do not turn these in): 1.1 (ad), 1.3, 1.4
(c,f,h,j,m,n,q), 1.810, 1.1417, 1.23.
If you feel like exploring
more, think about the Tower of
Hanoi.
Solutions
to Chapter 1 problems.
How to study:

You will be able to view the formula sheet that you will be given in the
exam here.
Warning: the link may not work yet.
I will be out of town on April 1518. I will not be able to read my
email.
Office hours before the final: April 19 1112 and 25 in my office WMAX
113. April 20 24 in my office WMAX 113.
Don't miss my last two classes with reviews for the final!
Here are some old exams to practise. Please don't panic, start by doing
2004, and 2006.
I have just learned that you may purchase the solutions to these finals from the Math club, April
1112, 10 AM  4 PM. Their office is at Math Annex 1119. I also got a copy of the solutions if you want
to take a look during office hours. WARNING: Math Club solutions may contain mistakes.
April
2004,
April
2006,
April 2000,
April 20002,
April 20003,
April 20004,
April
2001,
April 20012,
April 20012,
April 20014,
April 2003,
April 20032,
 Quiz 2: Do as many problems from chapter 6 as possible. NO
CALCULATORS OF ANY KIND WILL BE ALLOWED
 Midterm 1: Do the suggested
homework problems in Chapters 14, and
read the topics of the notes that were covered in class for Chapters
14 (you can check
this here).
For Chapter 1 you need to know Gauss formula (1+2+...+k), the others will
be provided to you, but you need to know how to use them to compute
summations!
Keep in mind that I like problems involving areas between graphs of two
functions, like 3.8, 3.9, 3.12, 3.13. I also like problems like 4.5, 4.20,
4.21, 4.22.
Here are some practise midterms:
2000
2002
2005
2006
Note: The material covered by these midterms might not overlap
exactly with Chapters 14.
Special Announcements:
 I will be out of town on April 1518. I will not
be able to read my email. I will offer office hours April 1920, see
here.

As for today (April 2) there are two remaining homeworks and two remaining
labs. Lab 5 is due tomorrow (April 3) in class as usual, and Homework 7 is
due on Thursday (April 5) in class as usual.
Lab 6 and Homework 8 are due next week. Homework 8 is due on TUESDAY
(April 10) IN CLASS. Lab 6 is due on THURSDAY (April 12) IN CLASS.
In order to compensate that you have to turn Homework 8 and Lab 6 earlier
than usual, I will make them optional. That means that I will drop your
worst mark for the labs if you turn Lab 6 in, and the second worst mark
for Homework+Quizzes if you turn Homework 8 in (I'm already dropping the
worst mark as part of the initial deal).
 Start studying for the final here!!!
 AMS Tutoring is providing a final exam review
session for Math 103. The first session is
coming up on March 31th (this Saturday). More info.

Midterms are marked. Here is how to collect your midterm:
Monday 326: I will distribute midterms at Yum Yum's 11:40 AM  12:10 PM
and 2:40 PM  3:10 PM. You can also try to find me in my office between 11
AM and 4:30 PM, but I don't guarantee that I'll be in my office all the
time.
Tuesday 327: I will distribute the remaining midterms at the END of
Tuesday class.
 I will distribute SURVEYS on
March
29. Please bring a No. 2 HB pencil and ideas, suggestions,
complaints...
 CAREERS IN MATHEMATICS + FREE
FOOD!
The Mathematics
Department will hold an informal lunchtime information
session for first and secondyear students at the time and location
below:
Mathematics Information Session
Thu. Mar. 29 from 12:30 p.m.  1:30 p.m. in Math 100
Topics to be discussed include degree programs involving mathematics at
UBC (including a wide array of combined programs), careers involving
mathematics, and general information about the Mathematics Department.
FREE PIZZA AND POP WILL BE PROVIDED.
 Midterm 2 is coming in March 22. It comprises chapters 59, and
page 1 of chapter 10. See How to study for this.
"We are looking for a few good men and women who like math a lot and love
to communicate it to their peers. Every year, we hire a few of our top
students as Math Lab TA's. These are paid positions, and you get
experience in teaching as well as job satisfaction. You would be working
on average 34 hrs per week in the math lab, helping 1st year students to
understand their lab assignments.
You MUST be a good communicator who likes and is good at explaining math
concepts. We want sociable, personable TA's who enjoy interacting
positively with other students.
Please apply by filling in a TA application form (See Verni Brown in the
Math office). It would help your application to include sample lab
assignment(s) you did
this year, as well as a transcript."
 Final Exam will be April 21, 12:00 PM in SRC A

Final Exam will be April 21, 12:00 PM

Midterms are marked. Here is how to collect your midterm:
Monday 212: I will distribute midterms at Yum Yum's 11:40 AM  12:10 PM
and 2:40 PM  3:10 PM
Tuesday 213: I will distribute the remaining midterms at the END of
Tuesday class.

Quiz 1 Solution.
Warning: there are two pages, one for version A (blue) and another for
version B (yellow)

Midterm 1 in February 8 will comprise Chapters 14. It is going to last
for
55 minutes (9:3010:25 AM).
How to study for this.

Today (January 30) I gave a survey to get
feedback
about lectures and class. If you didn't get a chance to complete the
survey, or you would like to do it again, feel free to do so, at any time
during the term. A good way
to send me the survey anonymously is to leave it with someone in the Math
department
office, writing something like "To: Matilde Lalin".
 Quiz 1 in February 1 will comprise Chapter 3 (do
the suggested problems in Chapter 3, don't worry about Chapter 4). It is
going to last 20 minutes (last 20 minutes of the class).

If you do not staple your homework, you will lose 5 points, starting with
homework #2. Homework is due IN CLASS. If you can't make it to class, you
should try to give me the homework BEFORE class. Don't leave homework in
my office or in the Math department office during the classtime of the
class the homework is due.
 Paper copies of the notes and problems are available at Copiesmart on
University Boulevard.
Important dates:
 February 1923: No classes

April 10 (Tuesday): Homework 8
 April 12 (Thursday): Lab 6
 April 21 12:00 PM : Final Exam in SRC A
Topics covered in
Class:
 4/5: 12.3, 12.6, review of some
integrals in chap 6
 4/3: 12.1, 12.2, 12.4, 12.5
 3/20: 10.4, 10.5, part of 10.6
Play
with the normal distribution.
 3/15: 9.3, 10.1, 10.2, 10.3, some of 10.4
 3/13: 9.1 (but not 9.1.1), 9.2
 3/1: 7.4, 8.1, 8.2, 8.3, some of 8.5
 2/27: 7.1, 7.2, 7.3, Problem 7.2
 2/15: 6.5, 6.6, 6.7, 6.8
Depressingly difficult problems for people who like challenges: MIT's IntegrationBee.
 2/13: 6.1, 6.2, 6.3, 6.4, some of 6.5
 2/6: 5.1, 5.2, 5.3, some of 6.1. Problem 5.5
 2/1: 4.5, Problem 1.15 from Chapter 2
 1/30: 4.2, 4.3, 4.4. Problem 4.12
 1/25: 3.7, 3.8, 4.1, some of 4.2

1/23: 3.4, 3.5, 3.6, some of 3.7
 1/16: 2.1, 2.2, 2.3, 2.4 but not 2.4.1. Idea of
problem 1.8
Area under a graph. You may choose your function here.
Other resources:
The Undergraduate
tab in the Mathematics Department website
has many resources, including recent final exams for most undergraduate
mathematics courses.
Last update: February 11, 2007