Math 103 Integral Calculus with Applications to Life Sciences section 208, Winter 2012

Instructor: Eric DeGiuli
Time: 8:00 - 9:00 MWF
Location: Buchanan A 201
Main Course Website

Email: edegiuli at math.ubc.ca (Please put MATH 103 in the subject line)

Most Important Things Right Now

HW9 is due Fri Mar 30 and includes 9.1, 9.3, 9.5, 9.8, 9.11, 9.12, 9.14 from Chapter 9 Problem Set.
Solutions to Midterm 2 are available here.
Lab 6 is due Wednesday April 4.
HW10 will not be collected, but contains material which you should know for the final. From Chapter 10 Problem Set, do 10.2, 10.6, 10.9, 10.10, 10.11, 10.14, 10.15, 10.17, 10.21, 10.23.
To prepare for the final, see the links here.
Teaching evaluations are available online March 25 and should be done before April 10.
The final exam will be April 11 at 8:30am.

Overview & Motivation

Nearly all the laws of physics that we know of are differential equations, i.e., equations involving functions and their derivatives [1]. Integral calculus is the basic tool that we use to solve differential equations, and this is its most important application.

Presumably, most of you are interested in biology, where it is not always obvious how the basics laws of physics manifest themselves. Of course, the human body lives in a universe governed by the laws of physics, and so we solve differential equations on a daily basis, though we are generally unaware of this! For example, our brains essentially solve Maxwell's equations when we see. For a nice discussion of this, check out this clip by Feynman..

So integral calculus is used to understand basic physical processes. Increasingly, it is also being used phenomenologically to model higher level biological phenomena. Here are some videos which allude to this:

Can calculus cure cancer?

A Vision for Quantitative Biology

[1] One exception is the second law of thermodynamics.

Assigned Homework

HW1. Due Friday Jan 20. From Chapter 1 Problem Set: 1.2abcd, 1.4co, 1.5ab, 1.11, 1.15. From Chapter 2 Problem Set: 2.1, 2.2, 2.8, 2.11a, 2.13, 2.17. Solutions to Chapter 1 Problem Set.

Solutions to Chapter 1 Problem Set.

The average for HW1 was 42/53, or 78%. The median was 44/53.

HW2. Due Friday Jan 27. From Chapter 3 Problem Set: 3.4acfhilr, 3.5abcgj (for c assume m >= 0, for g assume x,b>0), 3.7, 3.8, 3.13, 3.14, 3.18.
Solutions to Chapter 3 Problem Set.

The average for HW2 was 35/42, or 82%. The median was 38/42.

HW3. Due Friday Feb 3. From Chapter 4 Problem Set, do questions 4.1, 4.3, 4.4, 4.5, 4.10, 4.16, 4.19, 4.21, 4.25.
Solutions to Chapter 4 Problem Set.

The average for HW3 was 24/34, or 70%. The median was 26/34.

HW4. Due Monday Feb 13. From Chapter 5 Problem Set, do questions 5.4abc, 5.5 (assume m,n>0), 5.10, 5.11, 5.15, 5.16, 5.17, 5.18.
Solutions to Chapter 5 Problem Set.

The average for HW4 was 22/32, or 69%. The median was 24/32.

HW5. Due Friday Feb 17. From Chapter 6 Problem Set, do questions 6.1hi, 6.2acego, 6.3, 6.5.
The average for HW5 was 27/35, or 86%. The median was 30/35.

HW6. Due Wed Feb 29. From Chapter 6 Problem Set, do questions 6.7, 6.10abc, 6.12 (1),(4),(7),(10),(12),(14), 6.14 (assume 0<=x<=L), 6.18, and from Chapter 7 Problem Set, do question 7.1.
Solutions to Chapter 6 Problem Set.

The average for HW6 was 40/62, or 65%. The median was 50/62, or 80%.

HW7. Due Friday Mar 9. From Chapter 7 Problem Set, do questions 7.2, 7.4, 7.16, 7.18, 7.21
Solutions to Chapter 7 Problem Set.

HW8. Due Wed Mar 21 and includes 8.4, 8.8, 8.9, 8.19, 8.25, 8.31 from Chapter 8 Problem Set.
Solutions to Chapter 8 Problem Set.

HW9. Due Fri Mar 30 and includes 9.1, 9.3, 9.5, 9.8, 9.11, 9.12, 9.14 from Chapter 9 Problem Set. Solutions to Chapter 9 Problem Set.

HW10. (not collected). From Chapter 10 Problem Set, do 10.2, 10.6, 10.9, 10.10, 10.11, 10.14, 10.15, 10.17, 10.21, 10.23.
Solutions to Chapter 10 Problem Set.

Grading

Homework: 8%
Labs: 7%
Clicker Participation: 5%
Midterms: 40% (20% each)
Final: 40%

Office Hours

My office is in the complex fluids lab, which is locked. Office hours will be held in LSK 100C (in the basement) Monday 1:30-2:30, Wednesday 2:00-3:00, and Friday 1:30-2:30. If you cannot make any of these times, email me.

Course Notes

This course will closely follow a set of comprehensive COURSE NOTES designed by Leah Keshet for this course. For supplementary material, take a look at MIT's course ware page..

Midterms and Final

There will be two midterms and a final exam, all of which will be common across the 6 sections of the course. The midterms will be held in the EVENINGS between 5:30pm and 7:30pm. Locations will be listed when they are available. Plan ahead and adjust work schedules, etc., as necessary, as makeup exams will not be administered. If you have a legitimate conflict, let me know by e-mail as soon as possible. Note that the last date to drop the class with a W standing is Feb 10, 2 days after the first midterm.

Midterm 1: Feb. 8 in WESB 100, covering Chapters 1-4. The midterm will be 1 hour, from 5:30pm-6:30pm.
Solutions to Midterm 1 are available here.
Midterm 2: Mar. 14
Solutions to Midterm 2 are available here.

Homework Policies

The best way to learn math is by trying to solve problems.

Homework will generally be due one week after it is assigned, and by popular request, on Fridays. All assignments will be posted on this website and I will let you know in class when a new assignment is posted. Most of the homework problems will be drawn from a PROBLEM SET associated with the Course Notes.

All homework must be turned in by the beginning of class on the due date. NO LATE HOMEWORK WILL BE ACCEPTED. Homework can be turned in at class or my office hours. Also, scanned and e-mailed homework will not be accepted.
For each assignment, selected problems will be graded thoroughly (usually on a 3, 4, or 5 point scale depending on the complexity of the problem) and the rest will be graded as either attempted or not attempted (for 0 or 1 point). Solutions for ALL assigned problems will be posted. In most cases, homework will be returned within 1 week of its due date.

Begin early. The best time may be shortly following the lecture while the material is still fresh in your mind. This is your time to determine if you understand the concepts. If not, look at the course notes. If that does not help, ask at the Math Learning Centre, or come see me in office hours. It is also useful to work with your classmates in order to share ideas and compare results. Of course, the work you submit must be your own.

Keep your work organized and legible. A correct final answer is not sufficient to receive full credit on a graded problem. All work must be shown in a clear and neat fashion. We can't grade what we can't read!

Please follow the following instructions for each homework assignment:

Full name written legibly at the top of the first page.
All pages are stapled together at the top left corner. A paper clip does not count, they easily come off and can bind your assignment to others in the stack. I will not have a stapler with me in class, so come prepared!
Write only on ONE SIDE of each page turned in. Paper tends to be see through, and writing on both sides makes it harder to read.

Labs

In the modern world, most mathematical computations are done on computers. A laboratory component has been added to this course to show how the theoretical knowledge you learn in lectures can be used in practical situations, beyond the toy problems that appear in the homework.

For a description of the labs see the lab page.

You must be registered in a lab section as well as the lecture section. If you have trouble getting into a lab section, come to the Math Department registration sessions.
You are responsible for completing six computer labs (see the lab page for more information). You can do the labs at home or in Leonard S. Klinck (LSK), Room 121 at any time.
If you are unfamiliar with the labs or do not have an account, you should visit the labs in the second week of classes (first week of labs). Your MATH 102 account from last term will probably still work but try it to make sure.
Any difficulties with the labs should be directed to the lab instructors, not me.
Labs should be handed in to me in class on the due date. All policies which applied to the homework outlined above apply to the labs as well. Be sure to put your full name, section number (the lecture section number, 208, not the lab section number), and the number of the problem that you did, at the top right of the page you hand in.

Clicker Usage

Clickers are a great innovation in teaching that give the lecturer feedback on how the class is doing with new material. They allow the lecturer to adjust the pace of teaching to make lectures most effective for students.
We will be using clickers for this course and every enrolled student is required to have one. These can be purchased at the bookstore and any technical issues regarding them or defects should be dealt with at the bookstore. More information regarding clickers can be found at the UBC e-learning website . Note that you must tie your clicker to your student number through the Vista system. If you do not do this, I will not know you participated and you will not recieve credit.

Please have your clicker out at the beginning of every lecture. The frequency code needs to be set to 'BC', so that your clicker will be recognized by the reciever in the room. I will try to give you a reminder and this code will be posted at the beginning of every lecture (though it will be the same for every lecture).

Clicker participation will count for 5% of your final grade. A few questions will be posed throughout each lecture. These are not quizzes and you will not be graded on correctness, only on participation. If you participate in 75% of the clicker questions throughout the term, you will recieve full marks.

The use of clickers is intended to enhance your classroom experience. So please, be honest with your responses.

Other Important Notes

Passing mark is 50%. In addition at least 41% is needed in the final exam.
There are no make-up midterms but if you miss a midterm for a legitimate reason (e.g. illness, with a doctor's note), allowances will be made.
Homework and labs must be handed in to me (either in class or at my office hours).
Calculators are not allowed on midterms and final exam.
All marks are subject to scaling. This ensures fairness of the final grades across the sections.
Further information can be found at the main course website.

Extra Assistance

New this year is the Math Learning Centre, in the basement of Klinck (LSK Room 100). On most weekdays, throughout the day, there are grad students from the Math Department available to help with conceptual questions or homework. From 15:00-19:00 Mon-Thurs, there is also AMS Tutoring (which also includes Physics, Chemistry, and Economics tutoring) in the learning centre. AMS tutoring also runs in Totem Park and Place Vanier on Tuesday and Thursday nights, and online. Both services are free. In addition, you are highly encouraged to form study groups, share notes, discuss homeworks, etc.

Course Outline

Week	Lecture Topic	Notes
Jan. 4-6	Areas, volumes and simple sums	We skipped 1.8 from the notes, the problem about lungs.
Jan. 9-13	Areas in the plane & The Fundamental Theorem of Calculus
Jan. 16-20	The Fundamental Theorem of Calculus & Applications	Jan 20: HW1 due.
Jan. 23-27	Applications: rates, velocities and densities	Jan. 27: HW2 due & Lab 1 due.
Jan. 30-Feb. 3	Applications: volume and length	Feb. 3: HW3 due.
Feb. 6-10	Techniques of Integration	Feb 6: Lab 2 due. Feb. 8: Midterm 1.
Feb. 13-17	Techniques of Integration, Discrete probability	Feb 13: HW4 due. Feb. 17: HW5 due.
Feb. 20-24	Midterm break
Feb. 27-March 2	Discrete probability	No class Monday Feb 27. Feb 29: HW6 & Lab 3 due.
March 5-9	Continuous probability	March 9: HW7 due
March 12-16	Continuous probability & Differential Equations	March 14: Midterm 2. March 16: Lab 4 due.
March 19-23	Differential Equations	March 23: Lab 5 due
March 26-30	Infinite series, improper integrals, and Taylor series
April 2-6	Review	April 4: Lab 6 due