Course home page for winter semester (see below for the archived home page for fall semester).

Table of Contents

• Announcements
• Calendar
• Course outline
• Extra stuff
• Fall webpage
  
• Help available
  
• Instructor information
• Recommended problems
• WebAssign  The class key is: mcmaster 5458 4887
  

Instructor information
Instructor: Dr Deirdre Haskell, HH 316 x27244, haskell@math.mcmaster.ca
TAs: Maddie Baker, bakermj4@mcmaster.ca
        Matthew Jordan,  jordanml@mcmaster.ca
        Max Lazar-Kurz, lazarkm@mcmaster.ca

Help available
Instructor office hours: T Th 9:30--11:00 or by appointment
TA office hours:  Maddie  F 13:30--14:20 C105
                            Matthew M 10:30-11:20 C105
                            Max Th 10:30-11:20 C105
Math Help Centre  is now (January 11 2016) running in HH 104 every weekday afternoon.

Announcements

11 April 2016 Guidelines for review and suggested problems selected from the Review Exercises at the end of each chapter.
Chapter 2: how to find limits,
                definition of continuous
                definition of derivative
                29, 39

Chapter 3: how to find derivatives
                11, 25, 65

Chapter 4: mean value theorem
                 local extreme values
                17

Chapter 5: definition of definite integral
                Fundamental Theorem
                substitution
                1, 19, 21, 27, 45

Chapter 7: integration by parts and substitution
                9, 17

Chapter 9: direction fields
                separable equations
                linear equations
                1, 9, 11

Chapter 10: how to sketch parametric curves, eliminate parameter, find horizontal and vertical tangent lines
                polar coordinates
                1, 7, 9, 21

Chapter 11: definition of convergence for an infinite series
                    tests for convergence
                    how to find Taylor series
                    radius and interval of convergence
                   True/False Quiz from the review problems
                    11, 19, 41, 49

Chapter 14: identifying picture of surface with function of two variables
                    interpreting graphs of level sets
                    continuity
                    partial derivatives
                    equation of tangent plane
                    locating extreme values (you do not need to know the second derivative test)
                    5, 7, 8, 13, 19, 33, 53

10 April 2016 and here are some solutions for the practice exam.

8 April 2016: Review session for final exam (run by Maddie, Matthew and Max) will be Monday April 18, 2:30-4:30 in HH 109. Here is a practice exam for you to look at in preparation for the final.

8 April 2016: Quiz 12 Maddie solutions   Quiz 12 Max solutions Quiz 12 Matthew solutions

28 March 2016: recommended problems for sections 14.3, 14.4, 14.7 now posted below.
Quiz 11 Maddie solutions  Quiz 11 Matthew solutions Quiz 11 Max solutions

21 March 2016: recommended problems for sections 14.1, 14.2 now posted on the calendar. There are two more WebAssign homeworks to go (21 now available). There will be a culminating assignment also available (not for credit).

10 March 2016:  Quiz 10 Maddie solutions  Quiz 10 Matthew solutions Quiz 10 Max solutions

2 March 2016: Quiz 9 Maddie solutions  Quiz 9 Matthew solutions Quiz 9 Max solutions

16 February 2016: Marks for term 2 up to and including the midterm, sorted by last five digits of student ID number.

10 February 2016: The midterm is in BSB B135 on Thursday 18:45-20:15. Here are solutions to the practice midterm.

4 February 2016: The upcoming midterm will cover everything that we have done in Chapter 11
- Know, and be able to state precisely, the definitions (convergence for a sequence/series, monotone, absolute convergence, geometric series, power series, radius and interval of convergence, Taylor series... )
- Know, and be able to state precisely, the convergence tests (divergence, integral, comparison, limit comparison, alternating, ratio ) (you do not need to know the root test)
- Know your basic series and which converge (geometric and p-series)
- Practice looking at a series and thinking which test to try (see 11.7)
- Practice finding power series to represent a function using the geometric series 1/(1-x) (integrate, differentiate, substitute different expressions for x)
- Practice using the ratio test to find the radius of convergence of a power series, and then find the interval of convergence
- Practice computing Taylor series (you do not need to know how to bound the remainder term R_n(x))

Here is a practice midterm for you to attempt. Solutions will appear at some point.
Here are some good review problems: 11.1: 27, 43; 11.2: 17, 31; 11.3: 15, 23; 11.4: 7, 15; 11.5: 11; 11.6: 3, 11, 19; 11.8: 15, 23; 11.9: 19, 27; 11.10: 11, 21

Friday's class will be either review for the midterm or review for the homework assignment -- bring your own questions!

4 February 2016: Quiz 8 Maddie solutions  Quiz 8 Matthew solutions Quiz 8 Max solutions

29 January 2016: Today is the day to hand in the first draft of your essay. You can give me or any of the TAs a hard copy, or you can send it by email to me. It's OK if your draft is very rough and incomplete. We will give you feedback on what you have apparently not understood, where you should include more mathematics, or where you could lighten it up a bit. You can also hand in a draft later, but the sooner it comes in, the better the feedback will be. Other deadlines are coming up (midterm, reading week) so get this chore out of the way now!

25 January 2016: Quiz 7 Maddie solutions  Quiz 7 Matthew solutions Quiz 7 Max solutions

17 January 2016: The date of the midterm is changed to Thursday February 11, in the evening. The room will be posted later.

11 January 2016: TA office hours posted above, and essay grading rubric posted below under Extra Stuff.

4 Jan 2016: The list that I currently have of essay topics, organised by name. As threatened, if I did not hear from you, I have assigned you a topic. You can change your topic, but do not delay too long. If you have not already started researching your topic, you should start now. A draft of your essay is due on January 29. You are not required to hand in a draft, but you will get useful feedback if you do so. The final version is due the end of the week after Reading Week (Feb 26).

1 Jan 2016: Welcome back for the new semester! Changes to previously announced dates include the date for the midterm and the date for the essay -- see calendar below for details. I look forward to seeing you all in class on Tuesday.

Calendar Entries in the calendar are subject to change. See the announcements section for updates.

Week	Topic	Work due	Tutorial topic	Friday topic
Week 1 Jan 5 - 8	11.1 Sequences 11.2 series	WebAssign 12 due Monday Jan 11 at 23:59	Sequences	The problem of trisecting an arbitrary angle
Week 2 Jan 11 - 15	11.3 integral test 11.4 comparison test	WebAssign 13 due Monday Jan 18 at 23:59	Quiz 7 is on sequences Tutorial on some simple series	Constructible numbers
Week 3 Jan 18 - 22	11.4 comparison test 11.5 alternating series	WebAssign 14 due Monday Jan 25 at 23:59	comparison test	Some algebra of the constructible numbers
Week 4 Jan 25 - 29	11.6 ratio test 11.8 power series	WebAssign 15 due Monday Feb 1 at 23:59 Draft of essay due Jan 29	Quiz 8 is on the comparison test Tutorial on ratio test	Proof that the angle pi/3 cannot be trisected
Week 5 Feb 1 - 5	11.9 functions as power series 11.10 Taylor series	WebAssign 16 due Monday Feb 8 at 23:59	power series	Review for midterm
Week 6 Feb 8 - 12	9.1 intro to differential equations 9.2 direction fields and euler's method	Midterm Wednesday Feb 10 Thursday Feb 11 18:45-20:15	Taylor series	No class
Feb 15 - 19		Reading Week -- no classes
Week 7 Feb 22 - 26	9.3 separable equations 9.4 population growth	WebAssign 17 due Monday Feb 29 at 23:59 Essay due Friday February 26	Quiz 9 direction fields Tutorial on euler's method	Guest lecture: Dr. B. Bolker  "Some simple epidemiological and ecological models"
Week 8 Feb 29 - Mar 4	9.5 linear equations 9.6 predator-prey	WebAssign 18 due Monday Mar 7 at 23:59	Quiz 10 separable equations Tutorial on population growth	Cryptography
Week 9 Mar 7 - 11	10.1 parametric equations 10.2 calculus with parametric curves	WebAssign 19 due Monday Mar 14 at 23:59	parametric equations	more on cryptography
Week 10 Mar 14 - 18	10.3 polar coordinates 14.1 functions of several variables	WebAssign 20 due Monday Mar 21 at 23:59	Quiz 11 on parametric curves	Guest lecture: Dr. L. Bronsard
Week 11 Mar 21 - 25 Mar 26 no classes	14.1 more on functions of several variables 14.2 limits and continuity (review one variable limits)	WebAssign 21 due Monday Mar 28 at 23:59		Easter Friday (no classes)
Week 12 Mar 28 - Apr 1	14.3 partial derivatives 14.4 tangent planes	WebAssign 22 due Monday Apr 4 at 23:59	Quiz 12 graphs of surfaces	Julia Robinson and Hilbert's 10th problem (movie)
Week 13 Apr 4 - 8	14.7 extreme values review			Review for final

Recommended problems

Week	Recommended problems by section of Stewart	Challenge problems
Week 1 Jan 5 - 8 Stewart: 11.1, 11.2	11.1: 9, 15, 27, 41, 53, 57 11.2: 5, 17, 25, 31, 33,	11.1: 64 11.2:
Week 2 Jan 11 - 15 Stewart: 11.3, 11.4	11.2: 45, 59, 63, 71 11.3: 3, 5, 11, 23, 27, 29, 37, 39	11.2:81 11.3: 34
Week 3 Jan 18 - 22 Stewart: 11.4, 11.5	11.4: 3, 9, 15, 21, 29 11.5: 5, 9, 13, 19	11.4: 37, 39 11.5: 35
Week 4 Jan 25 - 29 Stewart: 11.6, 11.8	11.6: 3, 9, 15, 23, 39 11.8: 3, 13, 25	11.6: 32 11.8: 37
Week 5 Feb 1 - 5 Stewart: 11.9, 11.10	11.9: 3, 7, 13, 17, 27 11.10: 7, 17, 21, 29, 33, 37, 53, 61	11.9: 41 11.10:84
Week 6 Feb 8 - 12 Stewart: 9.1, 9.2	9.1: 3, 7, 9, 11 9.2: 1, 7, 13, 19, 23	9.1: 15 9.2:
Feb 15 - 19
Week 7 Feb 22 - 26 Stewart: 9.3, 9.4	9.3: 5, 9, 13, 17 9.4: 3, 5, 11	9.3: 9.4:21, 25
Week 8 Feb 29 - Mar 4 Stewart: 9.5, 9.6	9.5: 7, 11, 13, 17 9.6: 3, 5, 11	9.5: 38 9.6:
Week 9 Mar 7 - 11 Stewart: 10.1, 10.2	10.1: 3, 5, 7, 11, 13, 15, 27, 33 10.2: 5, 7, 17, 19, 25, 27	10.1: 44 10.2:73
Week 10 Mar 14 - 18 Stewart: 10.3, 14.1	10.3: 1, 3, 7, 9, 15, 19, 31, 39 14.1:	10.3: 53 14.1:
Week 11 Mar 21 - 25 Stewart: 14.1, 14.2	14.1:5, 7, 9, 19, 27, 32, 33, 37, 47, 61 14.2: 5, 7, 9, 11	14.1: 79 14.2: 39
Week 12 Mar 28 - Apr 1 Stewart: 14.3, 14.4	14.3: 3, 11, 17, 23, 35, 37, 55, 57, 75 14.4: 1, 3, 5, 13, 15, 23	14.3: 102 14.4:46
Week 13 Apr 4 - 8 Stewart: 14.7	14.7: 1, 3, 5, 9, 15	14.7:39

Extra stuff

A description of the essay and list of the available topics. essay-topics.pdf

If anyone wants to learn LaTeX (mathematical typesetting program), the TAs will be very happy to help you. Matthew offers the following sample to illustrate the vast superiority of LaTeX over Word equation editor, with a sample .tex file to follow in order to get started.
Word vs. LaTeX.docx    Word vs. LaTeX.pdf    Word vs. LaTeX (Code).pdf

Essay grading rubric: the essay will be marked out of 10 points. The points are distributed as follows.
    1/10 for correct grammar, reasonable style, appropriate length
    2/10 for being interesting/engaging/makes the topic approachable
    2/10 for the degree of clarity of the mathematics   
    2/10 for the degree of correctness of the mathematics
    3/10 for the level of difficulty of the mathematics and the degree to which you understand the mathematics (If you try to explain something very difficult, then you will not be penalised for not totally understanding it. On the other hand, if you are explaining something pretty easy, you will be expected to fully understand it.)