| Margaret E. M. Thomas | Department of Mathematics and Statistics |
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. (This course is NOT on Avenue to Learn.)...News pertaining to this section of MATH 1ZA3 will appear here; for news about the course in general, it is your responsibility to check the Course Website regularly.
4 December 2018: Notes from the Review Lecture 37 (including lots of integral practice and volumes of solids of revolution) are now posted online.
I'm sure you have a lot to think about this week, but if you can take time for a ten-minute break and evaluate this course , to help make it better (as well as tell us what we're doing right!), then that would be much appreciated. Thanks in advance!
30 November 2018: Notes from Lecture 36 now posted online. Please send in requests for the review session by Monday (don't forget to include 1ZA3 in the subject line of the email!)!
29 November 2018: Notes from Lectures 34 and 35 are now posted online ahead of tonight's Assignment 9 deadline. Also notice the new rules (see Course Website ) about how the assignment component of your final grade will be computed (in effect, you can drop one assignment without penalty).
Please remember to email in your requests for topics/questions to be covered in the Review part of next week's lectures (don't forget to include 1ZA3 in the subject line of the email!).
23 November 2018: Notes from Lectures 32 and 33 are now posted online. Also, check out the Final Examination information on the Course Website .
22 November 2018: Notes from Lecture 31 are now posted online ahead of tonight's Assignment 8 deadline. (Notes from Lectures 32 and 33 will follow at the end of the week as usual.)
16 November 2018: Notes from Lectures 28, 29 and 30 are now posted online.
9 November 2018: Notes from Lecture 27 are now posted online ahead of the second midterm (Test 2). Good luck everyone!
8 November 2018: Notes from Lectures 25 and 26 are now posted online ahead of tonight's Assignment 7 deadline. Also, note the information on the Course Website about the REVIEW SESSIONS for the second midterm on Monday afternoon -- come along to one of them to review the material that could come up on the test.
6 November 2018: Once again, apologies, as the system didn't update properly and allow the notes from the end of last week (Lectures 23 and 24) to be available before now. They should definitely be there now. Thanks for this being pointed out to me, and please let me know if there continue to be any problems!
Also: information about the second midterm (Test 2) is now available on the Course Website .
1 November 2018: Notes from Lecture 22 are now posted online as well as the solutions to the Exercises on sigma notation set during the lecture (see below for links). At the end of the solutions file you will also find some commentary on counting the number of terms in a sequence (also useful for counting the "Sum of 1 from m to n."). Notes from Lectures 23 and 24 will be posted after the lecture tomorrow.
29 October 2018: Solution to the Optimization Problem from Lecture 20 now posted below. Also, an updated version of Lecture 21 is now posted (a small correction to the computation at the very end of the class).
26 October 2018: Notes from Lectures 20 and 21 now posted online.
25 October 2018: Notes from Lecture 19 now posted online (ahead of today's Assignment 5 deadline -- good luck!). Notes from the rest of this week will be posted after the lecture tomorrow (Friday).
19 October 2018: Lecture notes for Week 7 (Lectures 16, 17, 18) are now posted online. Marks from Test 1 are to be found on the Course Website (please also see the MSAF and Post-Test FAQ pages there for more information).
15 October 2018: The solution to the exercise set during Lecture 15 (about critical numbers) is now posted below under "Lecture 15". Good luck everyone on the test tonight!
12 October 2018: Notes from Lecture 15 now online. These should have gone up earlier but for some reason things hadn't updated properly -- I'm grateful for this being pointed out to me!
4 October 2018: All the notes for the past week are now online (Lectures 12, 13, 14). Assignment 4 deadline is tonight! And Lecture 15 will be posted at the start of the break.
28 September 2018: Information about the first midterm (Test 1) is now available on the Course Website .
27 September 2018: All the notes for the past week are now online (Lectures 9, 10 and 11). Assignment 3 deadline is tonight!
20 September 2018: Notes from Lectures 7 and 8 now posted below. Don't forget the deadline for Assignment 2 tonight!
14 September 2018: Notes from Lecture 6 now posted below. Please take a look at these, especially a commentary added about the issue at the end concerning certain types of removable singularities in the case of rational functions.
13 September 2018: Notes from Lecture 5 now posted below, because they also relate a little bit to Assignment 1. Don't forget the deadline tonight!
11 September 2018: Notes from Lecture 4 now posted below. Don't forget the first assignment is due on Thursday!
7 September 2018: Lecture notes from Week 1 (Lectures 1-3) are now posted below.
3 September 2018: This page up and running.
Summaries of lectures and notes from class will be posted here as the semester progresses. (Summaries will be posted after each lecture, if possible, and lecture notes will typically be posted all together once a week, but may be posted earlier if certain topics relate to an assignment with an earlier deadline.)
The lecture notes below are typically augmented versions of what was presented on screen during class; the augmentations are principally to be found in the form of extra comments (and corrections) written in light blue. Please send me an email if you ever find any mistakes or there are glitches in the documents.
You are strongly advised to go through these notes alongside your own notes carefully to make sure that you understand everything that was discussed!
(Tues 4 September 2018) -- Introduction to course, including introduction to the Course Website . Introductory remarks about Calculus. (Thur 6 September 2018) -- App D: Review of Trigonometry (radians, special triangles, trigonometric functions, some trigonometric identities). The part about defining sin, cos, tan for general angles might have been overly confusing; sorry about that -- have a look at the notes for some more on this. Also, I await your entries in the SOHCAHTOA contest (come up with an original, local idea for this mnemonic)! (Fri 7 September 2018) -- App D: Addition formulae. 1.5: Inverse functions (finding inverse functions, horizontal line test, one-to-one functions, graphs of inverse functions). (Tues 11 September 2018) -- More on 1.5: More on inverse functions (logarithmic functions and inverse trigonometric functions); 2.5 (see also 2.2, 2.3): Start of review of limits. NB -- VERY SORRY, the graph that I drew of arcsin was not correct; please see the correction in the online notes (and we will cover this again at the start of the next class just to be sure). (Thur 13 September 2018) -- Even more on 1.5: further information about inverse trigonometric functions. More on (2.2/2.3/)2.5(/2.6): continuation of review of limits (including one-sided limits, infinite limits, limits at infinity, limit laws). (Fri 14 September 2018) -- More on 2.5: definition of continuity, types of discontinuities (including jump discontinuities, infinite discontinuities, beginnings of removable discontinuities), typical continuous functions. (Please have a good look at some extra commentary at the end of these notes about the last topic, i.e. removable discontinuities in the case of rational functions. We will aim to review this at the start of next class.) (Tues 18 September 2018) -- More on 2.5: removable discontinuities, combining continuous functions (sums, products, compositions); Intermediate Value Theorem. 2.7: Tangent lines. (Thur 20 September 2018) -- More on 2.7: Derivatives and rates of change. 2.8: The derivative as a function. (Fri 21 September 2018) -- More on 2.8: differentiability, derivative notation, higher derivatives. 3.1/3.2: Differentiation Rules (Sum Rule, Difference Rule, Constant Multiple Rule, Product Rule, Quotient Rule). 3.1: Power Rule. (Tues 25 September 2018) -- 3.1: Differentiation of polynomials and exponential functions. 3.3: Differentiation of trigonometric functions; 4.8 Newton's Method. (Thur 27 September 2018) -- More on 4.8: Newton's Method (examples). 3.4: Chain Rule. (Fri 28 September 2018) -- 3.5: Implicit Differentiation, including derivatives of inverse functions (e.g. inverse trigonometric functions). 3.6: Derivatives of logarithmic functions. (Tues 2 October 2018) -- More on 3.6: Derivatives of logarithmic functions. 3.11: Hyperbolic Functions. (Thur 4 October 2018) -- More on 3.11: Inverse hyperbolic functions. 4.1: Maximum and Minimum Values. (Fri 5 October 2018) -- More on 4.1: Maximum and Minimum Values. 4.2: The Mean Value Theorem. 4.3 Derivatives and graph shape (increasing/decreasing test). (Here is the solution to the Exercise on critical numbers set during class.) (Tues 16 October 2018) -- More on 4.3: First Derivative Test, Second Derivative Test and Concavity, Points of Inflection. Beginnings of 4.4: L'Hospital's Rule. (Thur 18 October 2018) -- More on 4.4: L'Hospital's Rule and indeterminate forms (of type $\frac{0}{0}, \frac{\infty}{\infty}$), indeterminate products ($0\cdot\infty$), indeterminate powers (of forms $1^\infty, 0^0, \infty^0$). (Note the Exercise here -- answer to be posted next week.) (Fri 19 October 2018) -- More on 4.4: indeterminate differences ($\infty - \infty$). 4.5: Curve Sketching. (Tues 23 October 2018) -- More on 4.5: Curve Sketching. 4.7: Optimization Problems. (Thur 25 October 2018) -- More on 4.7: Optimization Problems. 4.9: Antiderivatives (definition). (Here is the solution to the Optimization Problem that we discussed but did not complete during class.) (Fri 26 October 2018) -- More on 4.9: Antiderivatives. (Tues 30 October 2018) -- Appendix E: Sigma Notation. (Here are the solutions to the Exercises set during class, as well as a discussion of the "Sum of $1$ from $m$ to $n$.") (Thur 1 November 2018) -- 5.1: Areas and Distances (The Area Problem, approximation by rectangles using sample points, Riemann sums). (Fri 2 November 2018) -- More on 5.1: Areas. 5.2: The Definite Integral. (Tues 6 November 2018) -- More on 5.2: The Definite Integral. 5.3: The Fundamental Theorem of Calculus. (Thur 8 November 2018) -- More on 5.3: The Fundamental Theorem of Calculus. 5.5: Substitution Rule. (Fri 9 November 2018) -- More on 5.5: Substitution Rule. 6.1: Areas between curves. (Tues 13 November 2018) -- More on 6.1: Areas between curves. 6.2: Volumes. (Thur 15 November 2018) -- More on 6.2: Volumes. 6.4: Work. (Fri 16 November 2018) -- More on 6.4: Work. 6.5: Average Value of a Function. 7.1: Integration by Parts. (Tues 20 November 2018) -- More on 7.1: Integration by Parts. 7.2: Trigonometric Integrals. (Thur 22 November 2018) -- More on 7.2: Trigonometric Integrals (products of $\sin(x)$ and $\cos(x)$ powers, products of $\tan(x)$ and $\sec(x)$ powers, and products of sine and cosine functions with different arguments). 7.3: Trigonometric Substitution. (Fri 23 November 2018) -- More on 7.3: Trigonometric Substitution. 7.4: Integration of Rational Functions by Partial Fractions (long division, Case I (distinct linear factors)). (Tues 27 November 2018) -- More on 7.4: Integration of Rational Functions by Partial Fractions (Case II (linear factors only, some repeats); Case III (some quadratic factors but without repeats)) (Thur 29 November 2018) -- More on 7.4: Integrating Rational Functions using Partial Fractions (Case IV (some quadratic factors with repeats)). 8.1: Arc Length. (Fri 30 November 2018) -- More on 8.1: Arc Length. 7.5: Integration Strategy. (Tues 4 December 2018) -- More on 7.5: Integration Strategy. Review (of integration strategies, and 6.2 Volumes).