ARCHIVE OF PAST POSTINGS
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 firstname.lastname@example.org.
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).
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.
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.
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.
Search for the group "Math 1LS3E." Ask/answer questions, get to know your Math 1LS3 classmates, organize study groups, ask for/provide missed class notes, etc.
10 September: From Monday, 17 September, Math Help Centre in HH104 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.
6 September: Join us on Facebook! Just search for the group "Math 1LS3E"
6 September: Slides from the introductory lecture.
6 September homework: look at this web page (click on the links of the left) to make yourself familiar with what information you can find here. Work on assignment 0 from your coursepack [if you don't have your coursepack yet, download assignment 0 from here]. Solutions are posted under the SOLUTIONS link. Assignments are not collected for marks.
4 September: WELCOME !!! Classes start on Thursday, 6 September. Tutorials for 1LS3 start next week. See you all very soon!
BEEN AWAY FROM SCHOOL FOR LONGER?
What we do not use, we forget, that's normal. The longer we're away from math, the more we forget, and the longer it takes to bring it all back. Please take time now, in summer, to warm up, to recall important things and to review basic math procedures, formulas and facts. Will make a big difference. Follow suggestions given in the two boxes above.
... bit more information about the course
LIFE SCIENCES CALCULUS VS SCIENCE CALCULUS?
Both sequences Math 1A03/1AA3 and Math 1LS3/1LT3 are calculus courses. In both, we cover topics that are part of every calculus course: limits, continuity, derivatives, integrals, and functions of several variables. In 1LT3 we do not cover series and power series, but we cover differential equations is more depth that in 1AA3. As an application of calculus, we discuss basic probability and chance in 1LT3.
What is different? Math 1A03/1AA3 is geared towards Physical Science students, while Math 1LS3/1LT3 has been designed for students pursuing a degree in the area of Life Sciences. In Math 1LS3/1LT3 we focus on applications of calculus concepts that are relevant to other courses that you will be taking. For instance, we study various aspects of populations (animals, humans, cells), patterns of growth (growth of cancer), dynamics of blood flow, dating old materials, etc. There is less focus on theory than in Math 1A3/1AA3. In Math 1LS3/1LT3 you will have a chance to analyze applications in biology, medicine, and/or other disciplines, and will understand mathematics involved. You will significantly improve your quantitative reasoning skills that will be important to you, no matter which program you enter.
Upon completion of MATH 1LS3, if you wish (or need) to take further math courses, you can proceed to Math 1LT3 directly (any passing mark in Math 1LS3 will do) or to science calculus MATH 1AA3 (as long as you achieve a grade of at least 7 in 1LS3; actually grade below 7 might work, with permission).
As a prerequisite for second year math courses, for admission to various programs at Mac, for professional schools, or for any other academic purpose, the sequences Math 1LS3/1LT3, 1LS3/1AA3 are viewed as equivalent to Math 1A3/1AA3.
WHAT DO I NEED FOR 1LS3/1LT3?
IF YOU PLAN TO TAKE 1LS3 ONLY:
TEXTBOOK "Calculus for the Life Sciences: Modelling the Dynamics of Life", by F. R. Adler and M. Lovric (elephants on the cover), published by Nelson Education, 2011 and MATH 1LS3 COURSEPACK (ALL SECTIONS, 2012/2013)
IF YOU PLAN TO TAKE 1LS3 AND 1LT3:
BUNDLE Textbook: "Calculus for the Life Sciences: Modelling the Dynamics of Life", by F. R. Adler and M. Lovric and modules "Functions of Several variables" and "Probability and Statistics," published by Nelson Education, 2011 (elephants on the cover; the three texts are shrinkwrapped) and MATH 1LS3 COURSEPACK (ALL SECTIONS, 2012/2013)
Note: If you decide some time later to sign up for Math 1LT3, there will be a chance to buy the two modules that you will need separately.
WHAT ARE YOU DOING THIS SUMMER?
Warm up! A little bit of time spent preparing for your math courses over summer will help you a great deal in September.
* click on the COURSE OUTLINE link on the left; although it's from the last year, it fairly accurately describes what the course will be like in the fall (for instance, there will be the same number of tests, and the formula for calculating your final mark will be the same); follow the links GROUND RULES AND FREQUENTLY ASKED QUESTIONS and LEARNING RESOURCES for additional information.
The most important single ingredient in your success in Math 1LS3 is your background preparation. Although we do review functions, graphs, absolute value, trig, logarithms, etc., we do it fairly quickly. So, prepare yourself:
* pick up your grade 12 calculus textbook and do as many exercises as you can about functions (you do not need vectors for 1LS3): review things like domain, range, graphs; review lines, power functions, exponential and trig functions; review all differentiation rules, and practice so that you're good at it. Go over all applications of calculus that you did in grade 12.
* get a copy of Calculus: Fear No More (see the box below) and read it from cover to cover! It tells you exactly what to prepare, and what things you'll need to know for Math 1LS3. Calculus: Fear No More has solved examples, as well as exercises that help you practice things. If you need more practice, use your high school textbook (if you don't have it, see if your local library has it)
Do not worry if you did not do integrals or inverse functions or something else in high school. If you are confident in your high school background, i.e., know things that you did do in high school, you will see that learning new stuff in 1LS3 is not difficult at all. What is difficult is catching up on the background AND learning new material at the same time.
WHAT'S CALCULUS: FEAR NO MORE ABOUT?
A leap from secondary education to university environment will be, without doubt, one of the most challenging and stressful events in your life. It is a true rite of passage, with all of its anxieties, pains, hopes, frustrations, joys and rewards. You have probably created a mental image of the new environment you will be encountering soon - but it is blurry, lots of fine detail is missing. The better prepared you are, the easier it will be to adjust to new situations, demands and expectations that university life will place on you.
No matter which high school you came from, you have certain strengths and certain weaknesses. There are things that you learnt well in high school, things you know and are comfortable with. But, there are things that you forgot, or you don't know about or have very little experience with. In high school you acquired certain skills, but need to brush up on some others.
Calculus: Fear No More will tell you where you are; it will help you identify those areas of mathematics that you are good at, and those areas that you need to learn, review and work on. All you need is a little dedication, a pencil and paper, and about an hour of your (uninterrupted) time per day (say, during the last three weeks of August).
What will my first-year professors assume that I know about mathematics? The big part of Calculus: Fear No More is dedicated to answering this question. Look at the table of contents to see what areas of mathematics are covered.
We know that doing math is not the coolest thing to do in summer - BUT think a bit about the future. Change from high school to university is a big change; the better prepared you are, the easier it will be for you to adjust successfully to your new life as a university student. Student life is a busy life. It will be quite difficult for you (I did not say impossible!) to find time to do two things: learn new material presented in a lecture and, at the same time, review background material that you are assumed to know and be comfortable with. Not to mention that, without adequate preparation, you will have difficulties following lectures. Review your math now, while you have lots of free time on your hands!
One thing is certain: the more math you do, the easier it gets - experience helps! Do as many problems as you can, don't give up because the stuff looks difficult or you feel bored with it. Little investment of your time now, in summer, will make studying mathematics in the fall a whole lot easier.