Announcements

MATH HELP CENTRE HOURS and RECLAIMING TESTS FROM 4 DECEMBER

You can pick up any of your tests any time Math Help Centre (HH104) is open (if your TA is not there, someone else will help you). From 4 to 21 December, the Centre is open 2:30pm-6:30pm Monday-Friday.

MATH 1LS3 (AND OTHER COURSE) MARKS

Your instructor (for any course, not just 1LS3) is not allowed to reveal your final mark before it's declared official by the Registrar. At that time, all course grades will be posted on MUGSI. To find out your grades, keep checking MUGSI.

29 November: Final exam information. As well, read the information in the boxes below.

3 December: Update of marks has been posted. Make sure that all your tests marks are recorded correctly. It is your responsibility to check for errors before the day of the final exam, and to report any discrepancies to lovric@mcmaster.ca.

3 December: Due to the final exam seating arrangements, we are forced to produce four versions of the exam (which will be printed on different coloured paper). Although the order of the questions is different, all versions of the exam contain identical questions.

27 November: Test 4 grades are posted.

27 November: If you need it: review long division (needed for instance in question 3c in Assignment 21) by watching this 10-minute video tutorial.

26 November: This week we discuss applications in section 6.6 and improper integrals in section 6.7. To practice integration by parts, solve all exercises on assignment 22. To practice area questions, improper integrals, and integration using Taylor polynomials, work on assignment 24. To check your knowledge of integration concepts, work on assignment 23.

20 November: Information and link to online teaching evaluations. Please fill out the evaluations, they are very valuable to us!

26 November: Final exam information will be posted by the end of this week.

19 November: This week we finish Section 6.3, work on the Findamental Theorem of Calculus (Section 6.4) and start integration methods (Section 6.5). First, finish assignment 20. After Section 6.4 is done, work on #1 from Assignment 21. After Section 6.5 is done, finish assignment 21. Section 6.4: Skip the subsection 'The Integral Function and the Proof of the Fundamental Theorem of Calculus' (bottom of page 461 to end of section).

YOU OK? WE MISS YOU!

Please do not develop the habit of skipping1LS3 classes. Come to classes (AND tutorials), try to concentrate and follow as much of a lecture/tutorial as you can. At least, make sure you have good notes. You will definitely learn something just by listening, even if your mind is someplace else. Make sure that your lecture notes are complete. If you really need to miss a class, copy class notes from someone, or study relevant section(s) from your textbook. Do not get behind, with all work you have to do now it will be hard to catch up. Stay healthy! Try to eat something that's good for you, exercise, go out, socialize, talk to other people. Don't shut yourself off from the world, your life now is more of a team effort.

15 November: Ready for the test? What is leading behaviour? Do you know how to calculate leading behaviour at zero and at infinity? Did you study examples 5.3.8-5.3.14 from your textbook? Homework assignment 16 has lots of exercises about leading behaviour and graphing functions based on leading behaviour - go over all of them! Did you practice L'Hopital's rule? There are many solved examples in the textbook, also #4 in assignment 16. Did you practice calculating equilibrium points (assignment 17) and using the slope test for stability? Examples 5.5.4, 5.5.7, 5.6.5? Logistic system on page 386? What does an initial value problem consist of? Did you do #6 on assignment 18? What is a solution of a differential equation? Pure-time, autonomous differential equation? Did you study examples 6.1.5, 6.1.6? Question #1 on assignment 18? Do you know all antiderivatives from table 6.2.1 on page 425? Did you study Examples 6.2.11-6.2.13? Question #2 on assignment 19?

13 November: Test 3 grades are posted. The average is 70.8%!!!

12 November: This week we finish Section 6.1, work on antiderivatives in Section 6.2 and start definite integrals (Section 6.3). By the end of the week finish assignment 18 and 19. As well, you will be able to answer some questions from assignment 20.

12 November: Now that we're working on new stuff (differential equations and integrals) - come to ALL classes and tutorials, work on assignments regularly, don't get behind! It is a really good thing to finish the semester and be on top of things in math. In that case, studying for then exam will be mostly reviewing, which is easier than learning integration and at the same time studying for other exams.

12 November: Test 4 information is posted.

8 November: Teaching awards: to nominate your instructor or a teaching assistant in any course you're taking, go here.

8 November: To practice stability criteria using derivatives (sections 5.5 and 5.6) work through solved exercises (5.5.1-5.5.8 and 5.6.1-5.6.5). Ricker model (page 387 to end of section 5.6) is optional.

5 November: Test 3 solutions are posted.

5 November:This week we wrap up the work on section 5.3, discuss stability of dynamical systems (sections 5.5 and 5.6) and then start integration (section 6.1). Work on assignment 16 to practice leading behaviour, and then assignment 17 for stability. Only parts of assignment 18 will be covered this week. Note: We have had some math theory and a few theorems so far, and will have more - to understand things better, read 'Mathematical Language; Mathematical Thinking and Logic' section in your coursepack (starts on page 20).

1 November: Ready for the test? Do you know the definition of a critical number (critical point)? How do we find critical points - did you do all of #4 in assignment 15? Do you know how to use Extreme Value Theorem (such as #6 on assignment 15)? Can you quote Extreme Value Theorem and explain what it's about? How do we find relative extreme values, how do we find absolute extreme values? Do you know how to find intervals where a function is increasing/decreasing, concave up/down; for instance, examples 4.6.9-4.6.12? Can you identify the cases where a function is not differentiable? Can you calculate the derivative from the definition (ie, using limits)? Can you do product, quotient and chain rules quickly? For instance, finding y' for y=tan(x^2+x^3-2) should not take you more than one minute. None of the questions 1a-f on assignment 12 should take longer than one minute (each). Same for question 4 on assignment 12. Dud you practice implicit differentiation? Do you know the formula for T_2 (quadratic approximation), and how to use it? Did you study examples 4.7.7 and 4.7.8? How about 4.7.10 and 4.7.11? Lots of questions on the test involve calculating derivatives, make sure to practice a lot!

29 October: Read below to learn how your final grade will be calculated.

29 October: This week we work on applications of derivatives: relative and absolute extreme values (Section 5.1) and leading behaviour and L'Hopital's rule (Section 5.3). Work on assignments 15 and 16.

29 October: Test 3 information is posted.

23 October: Test 2 grades are posted.

22 October: This week we discuss applications of derivatives. In Section 4.6 we graph functions using derivatives (subsection 'Acceleration' is optional). In Section 4.7 we study approximations, and in Section 5.1 extreme values (about a half of the section will be finished this week). We continue with the extreme values next week. Homework: work on assignment 14. After the last lecture this week, identify the questions on assignment 15 you can do and work on those.

22 October: The routine for test 2 pickup is the same as for test 1. You can reclaim your test starting tomorrow, according to the schedule posted under MATH HELP CENTRE AND TEST RECLAIM link.

17 October: Read the Test 2 reactions box below.

11 October: How do I improve my math marks? Read below.

TEST 2 REACTIONS ...

We have heard from some students that test 2 was "much harder than the sample tests," that "questions were nothing like the assignment questions," or that "questions were unexpected" and so on.

What do you think students told us about their tests in fall 2011, which are now in your coursepack -- and you think those are easy! What will the students in fall 2013 think of your tests when they see them as samples in their coursepacks?

If things do not go well, face the situation. Think about what you did (and did not do), and change things. Complaining, or trying to justify your performance on a test by agreeing that the test was too difficult will get you nowhere. Have you really studied as hard as you could have? If chemistry test and/or homecoming messed up your study plan, then you need to change something! Did you pay attention to the "Ready for the test?" posting? It told you almost exactly what to expect on the test.

If you already forgot what an equilibrium is, this means that you have never learned it. If you cannot recognize the per capita rate in a population dynamical system today, then you have not understood what it is. If you think that we have never done cobwebbing on a parabola, then you did not study suggested material from the textbook. Change the way you study - don't memorize, make yourself understand. Keep in mind that learning to think is difficult, takes lots of time and patience, will not happen overnight.

On a test, some students expect to see exactly the same questions as in assignments and/or sample tests (by the way, have you noticed that some questions are very close to those questions?). Why? What is the value of a course which asks you to repeat exactly what you were told in class? Honestly -- would you appreciate or value a course which asks so little of you?

Remember those slides from the start of the course about success of math students on MCAT, GMAT and other standardized tests? Why do med schools, law schools, and grad schools want to test your thinking abilities? Why don't MCAT and GMAT just test how well you can reproduce exact same information that you heard in your classes?

First year is tough for everyone -- you need all your energy, motivation and hard work to overcome the problems you're having. There is lots to be learnt from failing! If you fall and manage to get up on your own - very few things in life feel better that that! Read this excellent article from Macleans.

Above all -- don't give up!!!

HOW DO I IMPROVE MY MATH MARKS?

You got your test back and you're not happy with the mark. What can you do? First, look over the test critically and try to identify the reasons why you made mistakes, or were unable to answer question(s).

The key answer to many issues is - practice. Practice means to work on many problems - first the solved examples and exercises from lectures and from the textbook, and then trying some on your own. It does not help to read solutions, you are not learning! Take your notebook, read the start of an example and then try on your own. When done, make sure it is correct, and do not move right away to the next question. Think about what the example/exercise was about, and how you solved it. That's how you make yourself understand! Then move on. You cannot do math mechanically, you need to focus and constantly make sure that you know what you are doing. If you don't understand something, make a note of it, and ask a question in a tutorial or go to the math help centre.

Trying to memorize different types of questions and hoping that you'll see the same or similar questions on a test will get you nowhere. You might be able to pass tests, but you will not end up with great marks. There are too many things to memorize, under the stress of a test you might not be able to recall what you need. Or, a test question might be similar to - but not the same as - the question you memorized - trying to apply the solution from your memory is definitely not a good idea.

Math takes lots of time, patience, dedication and focus. You cannot be texting someone and learning math at the same time. You might be able to solve an exercise while looking at your facebook page, but you will very soon forget what the exercise is about (time and energy wasted, because you will need to go over it again).

Keep all your practice work, all your notes, don't trash it. You might need it later, when reviewing for the exam.

Improvement in math happens slow, it takes time to see your efforts produce results. Do don't give up just because you did not do well on one test.

Were you able to quote a definition on the test? How can you be sure that you know a definition? You should be able to explain it to yourself, or to a friend, in your own words, without looking into the textbook. As well, can you give an example of what the definition is about? If a function tells you how A depends on B (such as A=ln B, A=sin B) , then the inverse function says how B depends on A (ie, B=e^A, B=arcsinA) . This is how you understand what an inverse function is, and how you explain it to yourself.

It does not suffice to watch someone else do math, you have to do it yourself. And you need to practice a lot. You need to solve (on your own!) 5-6 exercises about any topic (say, vertical asymptotes, limits at infinity involving exponential functions, etc.) to be sure that you will not mess it up on a test.

What's the range of arcsin, is it [-pi/2,pi/2], or [-1,1]? Don't try to memorize, under stress on a test you'll probably mix things up. Remember that sin x is defined on [-pi/2,pi/2], and its range is [-1,1]. From there (using your knowledge of inverse functions) you will know what the domain of arcsin is.

Experience in transformations of graphs will tell you that 12 in arcsin(12x) does not affect the range, since it is a horizontal transformation (and the range refers to the vertical axis). Without working on several transformations questions you'll quite possibly miss this fact (and waste time trying to figure it out on a test).

As you know by now, writing a test is stressful. Practice helps here as well - the better prepared you are, the less the noise and other people freaking out will affect you.

Do you have a study plan? Such as, things I do today, tomorrow, catching-up over the weekend, ... More important - do you have self-discipline to stick to your plan? You have to have it, that's the key to your success. Keep in mind that it takes time to learn things. As well, spread it out - it makes more sense to study 2 hours or math and

Are you sleeping enough, exercising, going out, eating food other than pizza? Take care of your health, it's definitely not fun to feel drowsy from flu medication when you need to study for a math test.

Think about these things, hopefully some of it will help. Good luck on your next test!

15 October: This week we discuss derivatives and rules for computing derivatives, sections 3.5 and 4.1-4.5. Study all examples in sections 3.5 (to make yourself understand concepts), study all examples in sections 4.1 and 4.2 (to gain routine in calculating derivatives); derivations (i.e., proofs) of the product and the quotient rules in 4.2 are optional (optional means it's not on tests and/or exam). As well, go over all solved examples in 4.3-4.5. In section 4.5, the subsection 'Derivations of Key Limits' is optional. Homework: assignments 11, 12 and 13.

15 October: Solutions to test 2 are posted.

9 October: Test 1 marks are posted. Follow the TERM MARKS link. Starting today, you can reclaim your test 1. Read the RULES FOR RECLAIMING TESTS that you will find under the MATH HELP CENTRE AND TEST RECLAIM link.

9 October: Test 2 information is posted.

9 October: This week we discuss sections 3.3 and 3.4. and start section 3.5. Section 3.3: the subsection 'Application to Absorption Functions' is optional for now (will be covered later in the course) and subsection 'Limits of Sequences.' Section 3.4: read the statements of theorems 3.4-3.8; skip the subsection 'Hysteresis.' Homework: finish assignments 8 and 9. To practice concepts from chapter 3, work on assignment 10.

Ready for the test? Dynamical systems - what is a solution? What is an equilibrium? Stable? Unstable? Have you looked at the cobwebbing pictures 2.2.21-2.2.31 in section 2.1? Example 2.2.6? What is the per capita production rate? Did you study the limited population model (from page 125 to end of page 127)? Can you explain the dynamics of caffeine consumption (for instance, what does d represent in the formula on page 122)? Alcohol comsumption (how is the formula for a_(t+1) on page 129 obtained)? What is average rate of change, and how do we interpret it geometrically? Did you practice calculations of limits (such as examples 3.2.4-3.2.6, 3.2.8, 3.2.10-3.2.14, 3.3.4, 3.3.9, 3.3.10)? What does direct substitution say? Can you arrange functions by how fast they approach infinity or zero as x approaches infinity? Can you write and use the definition of continuity? Did you read theorems 3.4-3.7? Did you study examples 3.4.3-3.4.8?

1 October: This week we finish dynamical systems and start limits: average rate of change (section 3.1), definition of limits (section 3.2). Thanksgiving is going to affect some sections. The plan is to cover Sections 3.1-3.4 by Friday, 12 October. Homework: study all solved examples in section 3.2 for practice on calculating limits; then work on assignment 8.

5 October: Test grades will be posted some time next week.

4 October: Starting next Tuesday, you will be able to reclaim your test 1. Read the RULES FOR RECLAIMING TESTS that you will find under the MATH HELP CENTRE AND TEST RECLAIM link. Test 2 locations are posted; sections covered, and other information will be posted by end of day Tuesday, 9 October.

1 October: Delays in delivery to Hotmail and Live accounts (message from University Technology Services). Commencing on September 25, 2012, and continuing to this point, emails sent from McMaster accounts to Hotmail and Live email accounts have experienced delays in delivery due to McMaster University being blacklisted by Microsoft mail servers. Currently the blacklist has been removed by Microsoft. However we are restricted to the number of messages that can be sent from McMaster. We are working with Microsoft to have the restriction cleared. As of this morning, we are still experiencing delays in delivering to Hotmail and Live email accounts.

1 October: Test solutions are posted, follow the SOLUTIONS link.

HOW TO STUDY MATH

(1) Come to classes and tutorials regularly and take notes; later, study notes, fill in the gaps; make sure your notes are correct and complete, as you will use them to study for every test and for the final exam. If you missed a class, borrow notes from someone and copy them, as all theory and many relevant examples are done in lectures and tutorials.

(2) The DAILY ANNOUNCEMENTS box will tell you what will be done in a given week, and what you should work on; as well, important announcements will be posted there.

(3) As your instructor finishes a section, do homework that is suggested on this webpage. As well - in your coursepack you will find suggested practice questions for each section that is covered (pages 32-34). Do as many questions as you need, to be certain that you understand the material and have sufficient routine with technical aspects (computations, powers, fractions, etc.)

(4) Solutions to an assignment are posted on this web page when all sections relevant for it are covered in lectures (usually at the end of the week).

Homework assignments are not collected for credit.

For help available from your instructor and teaching assistant and other learning resources, click on the link LEARNING RESOURCES on the left. Follow the routine outlined here throughout the course.

27 September: What's the format of test 1? Seven pages with questions (same length as test 1 last year). Test is worth 40 points. There will be two multiple choice questions, worth 6 points total, and three true/false questions, worth 6 points total. Multiple choice and true/false questions are graded all or nothing. The remaining 28 points is where you can collect part marks.

Ready for the test? Can you draw graphs based on a known graph by shifting, scaling and reflection? Did you practice finding the domain of a function, calculating composition of functions and calculating inverse function? Can you recognize the range of a function from its graph? Do you know domains and ranges of arcsin x and arctan x? Did you look at examples of linear models done in class and in the section 1.1? Did you study solved examples done in class, including applications? Can you articulate the difference between linear and non-linear? What is a proportional relationship, what is an inverse proportional relationship? Can you draw graphs of basic functions, such as powers of x, or 1/x, or 1/x^2? Can you state the horizontal and the vertical line tests; can you write down the definition of the inverse function? What are the half-life and the doubling time, did you practice calculations involving exponential growth and decay? What is a semi-log graph? Did you study the part of section 1.3 in your textbook, about inverse trig functions? Do you know how to solve logarithm and exponential equations? Did you work through assignment 5, where important concepts are covered? What is an updating function? How do we find the backwards time-discrete system? What does the backwards time-discrete system represent? What is a solution of a dynamical system? How do we find solution to a dynamical system algebraically, i.e., do you know the formulas in the boxes on pages 97 and 99? Do you know how to cobweb to find the first few values for a given dynamical system? What is an equilibrium point? How do we find equilibrium points? Did you study application examples, such as 2.1.4, 2.1.14, 2.1.16?

24 September: For core section 1 only: in test weeks, we switch monday lecture and wednesday tutorial; so, on 1 October (Monday) we'll have a tutorial (in BSB/147), and on Wednesday (3 October) there we'll have a lecture (in CNH/104).

24 September: This week we finish chapter 1 and discuss discrete-time dynamical systems, sections 2.1, 2.2 and 2.3. We will see how to use math to model things such as population growth and caffeine and/or alcohol consumption and absorption. Section 2.1: the material from start of Example 2.1.8 on page 100 to end of example 2.1.9 on page 102 is optional. Homework: assignments 6 and 7.

24 September: Test 1 information has been posted, follow the TERM TESTS link. NOTE: In the case of a discrepancy in the test information (say, as it appears on facebook, or some gossip floating around as compared to this web page) WHAT IS POSTED ON THIS PAGE IS TAKEN AS ACCURATE AND OVERRIDES ANY OTHER INFORMATION.

Note: No information that appears on this webpage is deleted. If you don't see it, check the archive under PAST POSTINGS link

20 September: Test 1 room information is posted, follow the TERM TESTS link. For now: read carefully all information about tests which is posted there. Make sure to know where you write your test. If you have a scheduling conflict, follow directions. Learn how absences from tests reflect in your grades. Read FREQUENTLY ASKED QUESTIONS about tests. It's all there. Test 1 will cover chapters 0 and 1 for sure (this includes assignments 0-5). Could be a few more sections. Details will be posted under TERM TESTS link early next week.

20 September: For three days next week, Math Help Centre has to relocate: 25 September (Tuesday) 2:30-4:30pm in BSB/B119, from 4:30-close back in HH/104; 26 September (Wednesday) 2:30-5:30pm in BSB/B155, from 5:30-close back in HH/104; 27 September (Thursday) 2:30-5:30pm in HH/217, from 5:30-close back in HH/104.

19 September: Consider coming to McMaster Innovation and Discovery Lecture Series.

17 September: This week we study sections 0.3, 1.2 and 1.3 (composition of functions, transformations of graphs and inverse functions, exponential and logarithm functions, trig and inverse trig functions). Here is a link to an applet that lets you practice transformations of trig graphs.

17 September: Related to exponential growth and decay: half-lives of some drugs, doubling time of breast cancer growth. These slides are for your information, no need to memorize anything that's there.

17 September homework for this week: (1) Start by working through questions on assignment 2. Assignment 3 will help you review and gain routine with exponential and logarithm functions. For trig and inverse trig, work on assignment 4. To make sure you understand all concepts in chapter 1, work on the remaining assignment 5 questions. (2) Work through solved examples in your textbook, in particular 1.3.10. and 1.3.11 about inverse trig, as this is new to almost everyone; if you understand the table on page 82, you understand transformations of graphs; study example 1.2.15.

This is lots of homework, but we do it because we want you to learn this stuff. Make an effort now - the things that come next will be lots easier if you know laws of exponents and logarithms, graphs of trig functions, inverse trig, etc.

17 September: Math Help Centre in HH104 opens today. It is open Monday-Thursday 2:30pm - 8:30pm and Friday 2:30pm - 6:30pm. Come whenever you wish, and stay as long as you need. No appointment needed.

14 September: Solutions to assignments 1 and 5 are posted. Click on the SOLUTIONS link.

12 September: Conversion of units - this sheet tells you which conversions you need to know, and which conversions will be given on a test if needed.

10 September: For students in Erin Clements' class: powerpoint notes of the lectures are here.

10 September: This week we discuss the material from sections 0.1, 0.2 and 1.1. We will say what a model is, give many examples and review basic properties of functions and graphs.

10 September homework for this week (routine): (1) By the end of the week, finish assignment 1 and questions 1-7, 8a and 8b from assignment 5. As well, go over assignment 2 questions to see much you can do on your own. (2) Study solved examples from the three sections in your textbook.

10 September homework part 2 (one-time thing): (3) Read HOW TO STUDY MATH box below. As well, read about learning mathematics on page 7 in your coursepack. Be aware of learning resources (pages 8-9), especially the part about keeping notes. Read the section 'Why Background Knowledge Matters' in your coursepack, pages 11-13. (4) For your information, read the short version of the article "Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better" which is in your coursepack (pages 15-19) or, read full version online from this website.

19 September: Test 1 information will be posted by the end of the week. We are waiting for the bookings office to give us locations of test rooms. Tests will be written in two shifts, 5:45-6:45pm and 6:45-7:45pm according to the schedule which will be posted. As well, test times for students with schedule conflicts will be posted.