Table of Contents

• Announcements
• Calendar
• Course outline
• Extra stuff: Essays
  
• Help available
  
• Instructor information
• Recommended problems
• WebAssign  The class key is: mcmaster 6637 1669
  

Instructor information
Instructor: Dr Deirdre Haskell, HH 316 x27244, haskell@math.mcmaster.ca
TAs: Marco Handa handamg@mcmaster.ca
        Adrienne Ralph ralpha@mcmaster.ca
        Harrison Winch winchht@mcmaster.ca

Help available
Instructor office hours: M Th 10:30--12:00, W 2:30-3:30 in HH 316
TA office hours (all in the seminar room of LRW-3038) 
                        Marco: W 10:30-11:30
                        Adrienne: Th 2:30-3:30
                        Harrison: TBA

Math Help Centre  will be running in HH 104 once the semester starts.

Announcements

20 April 2018 Such a long time since I posted anything! Here is  practice final exam, and here are the solutions. The review session will be Monday April 23, 10:00-12:00 in JHE-A102. This will be free from -- come with questions and I will answer them.

4 March 2018 Here is a practice midterm for your entertainment. Solutions will come eventually.

4 February 2018 Midterms are marked and will be handed back in class on Monday. Homework assignments (below and on WebAssign) have been updated.

30 January 2018 Solutions to practice midterm.

29 January 2018 Here are some recommended practice problems to prepare for the midterm. They are taken from the Review problems for Cha 11, starting on p. 784.
Concept Check: 1, 2, 3a, 4, 5a,e,f, 6, 7c, 8a,b, 9, 10a,b,c, 11, 12,
Exercises: 3, 5, 27, 41, 45, 47, 49, 55, 59

29 January 2018 The upcoming midterm will cover sections 11.1, 11.2, 11.5, 11.6 (not the root test), 11.8, 11.9, 11.10. You must know definitions and statements of theorems precisely -- an intuition about what the definitions mean is useful, but is not good enough. Go through the book, write down the definitions and memorise them! You do not need to memorise the Taylor series for any particular function, but you do need to memorise  the general formula for the Taylor series for the function f around a.

24 January 2018 Adrienne's and Marco's office hours posted above. First midterm for the winter semester coming up  on Friday, February 2 at 11:30. It will be in room T13 125. A number of people have reasons why this time is awkward for them. I will therefore have an alternate seating of the exam the day before, Thursday Feb 1 3:30-4:20. If you want to take the exam at the alternate time, please speak to me explaining your reasons and also send me an email. I can manage a limited number of people for the alternate time; please let me know by Friday Jan 26th if you want to make use of this chance.

24 January 2018 Practice midterm 3 posted here.

22 January 2018 Some of the questions on the current homework assignment ask about the interval of convergence of the power series, as well as the radius of convergence. When you apply the limit test to the power series sum_{n=0}^infty c_n (x-a)^n , you find that the series converges provided |x-a| < R. You can re-write this as saying that the power series converges on the open interval (a-R,a+R). (The number $R$ is the radius of convergence.) The ratio test does not tell you if the series converges at the endpoints of the interval. To decide this, you need to put x=a-R and x=a+R and determine if the resulting series converges. Some of the series you can tell, but some of them I have not told you how to decide. For question 4, the series diverges at x=R. For question 5, the series converges for x=R.
                        You might also need to know that lim_{n\to\infty} (1+1/n)^n = e . This is one form of the definition of the number e, and can be found on p. 222 of the textbook.

15 January 2018 Some stuff about the essay has been posted at the end of the page (follow the link Extra stuff above). I have been told that the midterms are the same day as midterms in chemistry; I will look into moving ours over by one week.

1 January 2018 Welcome to the new year and the second half of ArtsSci 2017-18. This semester we will start with something completely different -- sequences and series. Here you will discover that the kinds of questions we are asking about the objects of study are different. Instead of asking "what value does it have", we ask "does it converge". It turns out that this can give us information about how to calculate functions that arise as solutions to differential equations. Then we will return to a major topic from last semester, which is techniques of integration. For the last third of the semester, we will turn to the whole topic of considering  more than two variables. We can have one independent variable and more than one dependent variable (parametric curves), or one dependent variable but more than one independent variable. We will see that there are interesting complications in generalising the ideas of calculus that we have seen so far.

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 4-5	Sequences - definition, convergence Read Stewart  11.1		No tutorials this week.	Regular lecture
Week 2 Jan 8 - 12	series, geometric series, convergence, alternating series (lectures given by TAs this week) Read Stewart 11.2, 11.5	WebAssign 13 due  Monday Jan 8 at 23:59 Homework 5 due Friday Jan 12	Talk about Homework #5 on sequences	No class
Week 3 Jan 15 - 19	ratio test, power series Read Stewart 11.6, 11.8	WebAssign 14 due  Monday Jan 15 at 23:59	Quiz 6 on convergence	Cryptography I
Week 4 Jan 22 - 26	Taylor series Read Stewart 11.10	WebAssign 15 due  Monday Jan 22 at 23:59 Homework 6 due Friday Jan 26	Talk about Homework #6 on series	Cryptography II
Week 5 Jan 29 - Feb 2	Review fundamental integrals, integration by parts Read Stewart 7.1, 7.2	WebAssign 16 due  Monday Jan 29 at 23:59 Submit draft of essay for comment by Friday	Review for midterm	Midterm 3 covers chapter 11
Week 6 Feb 5 - 9	More integration by parts, trigonometric integrals Read Stewart 7.3	WebAssign 17 due  Monday Feb 5 at 23:59 due date changed to Feb 12 Homework 7 due Friday Feb 9	Talk about Homework #7 on integration	This Friday will be a regular class. The guest lecture by Lia Bronsard is moved to next Tuesday
Week 7 Feb 12 - 16	Partial fractions, integration strategy, improper integrals Read Stewart 7.4, 7.5, 7.8	WebAssign 18 due  Monday Feb 12 at 23:59 due date changed to Feb 19	Quiz 7 on integration	Integration bootcamp
Reading Week
Week 8 Feb 26 - Mar 2	Parametric curves, calculus Read Stewart 10.1, 10.2	WebAssign 19 due  Monday Feb 26 at 23:59 Essay due on Friday!	Talk about Homework #8 on Parametric curves	Julia Robinson and Hilbert's 10th Problem (movie)
Week 9 Mar 5 - 9	More on calculus for parametric curves, polar coordinates Read Stewart 10.2, 10.3	WebAssign 20 due  Monday Mar 5 at 23:59	Review for midterm	Midterm 4 covers chapter 7, 10.1, 10.2
Week 10 Mar 12 - 16	Area in polar coordinates, Functions of several variables Read Stewart 10.4, 14.1	WebAssign 21 due  Monday Mar 12 at 23:59	Quiz 8 on parametric curves	More on JR and Hilbert's 10th
Week 11 Mar 19 - 23	Limits and continuity, partial derivatives Read Stewart 14.2, 14.3	WebAssign 22 due  Monday Mar 19 at 23:59	Talk about Homework #8 on polar coordinates	Guest lecture: Megumi Harada "A glimpse of Hamiltonian mechanics and geometry"
Week 12 Mar 26 - 30	Tangent planes Read Stewart 14.4	WebAssign 23 due  Monday Mar 26 at 23:59	Quiz 9 on partial derivatives	Good Friday (no classes)
Week 13 Apr 2 - 6, 9	Local maxima and minima, review Read Stewart 14.7	WebAssign 24 due  Monday Apr 2 at 23:59	Review for final	Review

Assigned and recommended problems

Week	WebAssign Problems	Homework Problems	Recommended problems (practice)	Challenge problems
Week 1 Jan 4-5 Read Stewart 11.1			11.1: 1, 5, 11, 16, 19, 27, 35, 49, 65, 75	11.1: 83, 91
Week 2 Jan 8 -12 Read Stewart 11.2, 11.5	WebAssign 13 due  Monday Jan 8 at 23:59 11.1: 16, 23, 30, 38, 64	Homework #5 11.1: 66, 67	11.2: 3, 16, 17, 33, 53, 61 11.5: 5, 7, 25	11.2: 77, 81 11.5: 35
Week 3 Jan 15 - 19 Read Stewart 11.6, 11.8	WebAssign 14 due  Monday Jan 15 at 23:59 11.2: 3, 17, 18, 28, 52 11.5: 4, 8		11.6: 7, 17, 19 11.8: 7, 11, 21, 29	11.6: 11.8: 33
Week 4 Jan 22 - 26 Read Stewart 11.10	WebAssign 15 due  Monday Jan 22 at 23:59 11.6: 8, 10, 18, 11.8: 5, 9, 24	Homework #6 11.2: 72	11.10: 3, 13, 21, 27, 31, 30, 53	11:10: 84
Week 5 Jan 29 - Feb 2 Read Stewart 7.1, 7.2	WebAssign 16 due  Monday Jan 29 at 23:59 11.10: 4, 12, 22, 31, 40, 46		7.1: 7, 9, 21, 27, 37 7.2:5, 9, 17, 23, 47, 57	7.1: 74 7.2:70
Week 6 Feb 5 - 9 Read Stewart 7.3	WebAssign 17 due  Monday Feb 5 at 23:59 due date changed to Feb 12 7.1: 6, 10, 24, 34, 40 7.2: 2, 10, 34, 51	Homework #7 7.1 68 7.2 66	7.3: 5, 13, 19, 37 7.4: 7, 9, 13	7.3: 40 7.4: 67
Week 7 Feb 12 - 16 Read Stewart 7.4, 7.5, 7.8	WebAssign 18 due  Monday Feb 12 at 23:59 due date changed to Feb 19 7.3: 4, 12, 18, 34 7.4: 8, 12		7.5: 3, 17, 19, 43 7.8:5, 11, 19, 25	7.5: 7.8: 63
Reading Week
Week 8 Feb 26 - Mar 2 Read Stewart 10.1, 10.2	WebAssign 19 due  Monday Feb 26 at 23:59 7.5: 4, 8, 16, 22, 28 7.8: 6, 14, 18		10.1: 3, 7, 11, 15, 21, 25 10.2: 3, 5, 9, 17,	10.1: 10.2:
Week 9 Mar 5 - 9 Read Stewart 10.2, 10.3	WebAssign 20 due  Monday Mar 5 at 23:59 10.1: 4, 10, 14, 18, 32 10.2: 7, 22, 30		10.2: 31, 41 10.3:1, 3, 7, 9, 15, 21, 31, 37	10.2: 10.3:
Week 10 Mar 12 - 16 Read Stewart 10.4, 14.1	WebAssign 21 due  Monday Mar 12 at 23:59 10.2: 32, 42 10.3: 3, 5, 8, 12, 19, 25, 32, 42, 58		14.1: 5, 7, 9, 11, 13, 27, 33, 35, 43, 63	14.1: 77
Week 11 Mar 19 - 23 Read Stewart 14.2, 14.3	WebAssign 22 due  Monday Mar 19 at 23:59 14.1: 2, 17, 22, 24, 32, 36, 42, 52, 62	Homework #8 10.3: 52	14.2: 1, 5, 11, 15, 31 14.3: 3, 5, 15, 21, 29, 37, 53, 63, 77, 91	14.2:39 14.3: 97
Week 12 Mar 26 - 30 Read Stewart 14.4	WebAssign 23 due  Monday Mar 26 at 23:59 14.2: 2, 18, 26, 38 14.3: 6, 10, 24, 36, 42, 56		14.4: 3, 5, 13, 15, 23 14.7:3, 9, 15, 19, 21	14.4: 46 14.7:57
Week 13 Apr 2 - 6, 9 Read Stewart 14.7	WebAssign 24 due  Monday Apr 2 at 23:59 14.4: 6, 11, 22 14.7: 3, 10, 12, 20

Extra stuff
Essay topics

Here is the list of who has signed up for which topic. You are welcome to discuss your topic with the other people who have chosen the same one. You might also ask each other to read and advise on your essays. Those of you who do not yet have a topic should choose one!
Essay grading rubric: the essay will be marked  out of 10 points (with a possible extra credit point), distributed as follows.
    2/10 for correct grammar, reasonable length, appropriate formatting, relevant references (any referencing style will do)
    2/10 for being interesting/engaging/making the topic accessible
    2/10 for the degree of clarity of the mathematics
    2/10 for the degree of correctness of the mathematics
    2/10 for the degree of difficulty of the mathematics (with an extra credit point for a really difficult topic)
If anyone wants to learn LaTex (mathematical typesetting program), you can talk with me or the TAs. The following samples were written by Matthew Jordan to illustrate the vast superiority of LaTex over Word for writing mathematics (or anything for that matter, in my opinion).
Word vs. LaTeX.docx    Word vs. LaTeX.pdf    Word vs. LaTeX (Code).pdf