| 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 1A03 will appear here; for news about the course in general, it is your responsibility to check the Course Website regularly.
5 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!
3 December 2018: Lecture notes from Lecture 36 are now posted online.
29 November 2018: Lecture notes from Week 13 (Lectures 33-35) are now posted online. 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 1A03 in the subject line of the email!).
22 November 2018: Lecture notes from Week 12 (Lectures 30-32) are now posted online.
15 November 2018: Lecture notes from Week 11 (Lectures 27-29) are now posted online.
8 November 2018: Lecture notes from Week 10 (Lectures 24-26) are now posted online. Also, information about the second midterm (Test 2) is now available on the Course Website . Note the REVIEW SESSIONS on Monday afternoon -- come along to one of them to review the material that could come up on the test.
1 November 2018: Notes from Week 9 (Lectures 21-23) are now posted online, as well as the solutions to the Exercises on sigma notation set during Lecture 22 (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 (useful for counting the "sum of 1 from m to n").
25 October 2018: Notes from Week 8 (Lectures 18-20) are now posted online.
18 October 2018: Notes from Week 7 (Lectures 15-17) are now posted online. Also, the results from Test 1 are now available on the Course Website (please also see the MSAF and Post-Test FAQ pages there for more information).
15 October 2018: A new version of the notes from Lecture 14 is now posted online (nothing amended, just a few extra marginal comments added). Good luck everyone on the test tonight!
4 October 2018: Lecture notes from Week 5 (Lectures 12-14) are now posted online.
28 September 2018: Information about the first midterm (Test 1) is now available on the Course Website .
27 September 2018: Lecture notes from Week 4 (Lectures 9-11) are now posted online.
20 September 2018: Lecture notes from Week 3 (Lectures 6-8) are now posted online.
13 September 2018: Lecture notes from Week 2 (Lectures 3-5) are now posted online.
7 September 2018: Lecture notes from Week 1 (Lectures 1-2) are now posted below.
6 September 2018: A remark about the lecture schedule on the Course Website : we are out of phase with all the other sections, so just keep in mind that for us a week runs from Tuesday through Monday (we have only 2 lectures in week 1, but 2 lectures as well in week 14 at the end).
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!
(Wed 5 September 2018) -- Introduction to course, including introduction to the Course Website . (Thur 6 September 2018) -- App D: Review of Trigonometry (radians, special triangles, trigonometric functions, some trigonometric identities). (Mon 10 September 2018) -- More on App D: Trigonometric addition formulae (double angle formulae), 1.5 Inverse functions (finding inverse functions, horizontal line test, one-to-one functions, graphs of inverse functions). (Wed 12 September 2018) -- More on 1.5: Exponential and logarithmic functions (natural log, change of base formula, log rules), inverse trigonometric functions. (Thur 13 September 2018) -- Even more on 1.5: Final thoughts on inverse trigonometric functions. 2.5 (also see 2.2, 2.3, 2.6): Limits (including one-sided limits, infinite limits, limits at infinity, limit laws), definition of continuity. (Mon 17 September 2018) -- More on 2.5: Types of discontinuities, combining continuous functions (sums, products, compositions); prelude to the Intermediate Value Theorem. (Wed 19 September 2018) -- More on 2.5: Intermediate Value Theorem. 2.7: Derivatives and rates of change. (Thur 20 September 2018) -- More on 2.7: Derivatives and rates of change. 2.8: The derivative as a function. (Mon 24 September 2018) -- 3.1/3.2: Differentiation rules (Sum Rule, Difference Rule, Constant Multiple Rule, Product Rule, Quotient Rule); 3.1: Power Rule and differentiation of polynomials; derivatives of exponential functions. 3.3 Derivatives of trigonometric functions. (Wed 26 September 2018) -- 4.8: Newton's Method. (Thur 27 September 2018) -- 3.4: Chain Rule. 3.5: Implicit Differentiation. (Mon 1 October 2018) -- More on 3.5: Implicit differentiation, including derivatives of inverse functions (e.g. inverse trigonometric functions). 3.6: Derivatives of logarithmic functions. (Wed 3 October 2018) -- 3.11: Hyperbolic functions. (Thur 4 October 2018) -- 4.1: Maximum and minimum values. (Mon 15 October 2018) -- 4.2: The Mean Value Theorem. 4.3: Derivatives and Graph Shape (Increasing/Decreasing Test and First Derivative Test). (Wed 17 October 2018) -- More on 4.3: Second Derivative Test, Concavity, Points of Inflection. 4.4: L'Hospital's Rule (indeterminate forms of type $\frac{0}{0}, \frac{\infty}{\infty}$). (Thur 18 October 2018) -- More on 4.4: L'Hospital's Rule (indeterminate products $0\cdot\infty$, indeterminate powers of forms $1^\infty, 0^0, \infty^0$, indeterminate differences $\infty - \infty$). (Mon 22 October 2018) -- 4.5: Curve Sketching. (Wed 24 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). (Mon 29 October 2018) -- More on 4.9: Antiderivatives. (Wed 31 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). (Mon 5 November 2018) -- More on 5.1: Areas. 5.2: The Definite Integral. (Wed 7 November 2018) -- More on 5.2: The Definite Integral. 5.3: The Fundamental Theorem of Calculus (Part I). (Thur 8 November 2018) -- More on 5.3: The Fundamental Theorem of Calculus (Part II). 5.5: Substitution Rule. (Mon 12 November 2018) -- More on 5.5: Substitution Rule. 6.1: Areas between curves. (Wed 14 November 2018) -- More on 6.1: Areas between curves. 6.2: Volumes. (Thur 15 November 2018) -- More on 6.2: Volumes. 6.4: Work. (Mon 19 November 2018) -- More on 6.4: Work. 6.5: Average Value of a Function. 7.1 Integration by Parts. (Wed 21 November 2018) -- More on 7.1: Integration by Parts. 7.2: Trigonometric Integrals (powers of $\sin(x)$ and $\cos(x)$). (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. (Mon 26 November 2018) -- More on 7.3: Trigonometric Substitution. 7.4: Integrating Rational Functions using Partial Fractions (long division, Case I (distinct linear factors, no repeats)). (Wed 28 November 2018) -- More on 7.4: Integrating Rational Functions using Partial Fractions (End of Case I; 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. (Mon 3 December 2018) -- More on 8.1: Arc Length. 7.5: Integration Strategy. (Wed 5 December 2018) -- More on 7.5: Integration Strategy. Review (of integration strategies, and 6.2 Volumes).