# Detailed schedule for Math 234.

## Math 234: Week 1

Jan 14
Lecture: Slopes and Equations of Lines (§1.1) and Linear Functions and Applications (§1.2)
HW 1 (Due Mod, Jan 28)

Without any digressions, took 35 minute to cover this, leaving 10 minutes for going over the syllabus and 5 for starting a little late. When covering distance in n-dimensions, it would be better to first compute the distance for the origin O to P and also to label the points as O and P in the 2D and 3D examples.

Jan 15
Review of Algebra Skills Worksheet.

Final exam schedule request due to Aaron.

Jan 16
Lecture: Properties of Functions (§2.1), Quadratic Functions; Translation and Reflection (§2.2).

Did not get to the derivation of the dot product formula on page 6. Also hit the dot product 40 minutes in. Next time cut something to so I will have 12.5-15 minutes for the dot product. For example, position vectors and some of the properties of vector operations.

Jan 17
Domains and Ranges of Functions, Even/Odd Functions, Functions in Word Problems (§1.2 and §2.1) Worksheet.
Notes:
Pickup syllabus if you weren’t here on Monday.
No class on Monday, Jan 21 (M.L. King Day).
If you have not received 65% or higher on the ALEKS PPL Mathematics Placement Exam some time between September 17, 2018 and January 18, 2019, then you will be automatically dropped from the course.
Quiz 1 on Tuesday covering sections §1.1, §1.2, and §2.1
Class website: http://faculty.math.illinois.edu/~iahmed8/classes/2019/234.

## Math 234: Week 2

Jan 21
Martin Luthar King Day, no class and HW 1 is due on Thursday, Jan 24.
Jan 22
Quiz 1 on §1.1, §1.2, and §2.1
Graphing Quadratic Functions (§2.2 and §2.3) Worksheet.
Jan 23
Lecture: Polynomial and Rational Functions (§2.3).

In both sections, got through the plane example but not the triple product or anything after that.

Jan 24
Discussion on Exponential and Logarithmic Functions. Worksheet.

Assign exam rooms based on current enrollments (Nathan)

Notes:
Class website: http://faculty.math.illinois.edu/~iahmed8/classes/2019/234.
Quiz 2 on Tuesday covering sections §2.2 and §2.3

## Math 234: Week 3

Jan 28
Lecture: Exponential and Logarithmic Functions (§2.4 and §2.5)
HW 1 is due at 9 am.

Got through the proof that h^2 has limit 0 at 0 in both sections, but not h^2 + 2h. In the 8am, had no time to spare, in the 9am had about 3 minutes. In both cases, started limits between 20 and 25 minutes in (closer to 20, I think). The discussion of quadric surfaces types was done quickly by showing the Interactive Gallery and referring them to the upcoming discussion section on this topic.

Jan 29
Quiz 2 on §2.2 and 2.3
Discussion on Exponential and Logarithmic Functions.
Jan 30
Lecture: Class cancel due to extrem cold weather.

In both sections, got up to the top of page 5, just before "rules for limits" with time enough to do the limit pictures Mathematica notebook and tell the sad story of the Sleipner A.

Exam 1 due.

Jan 31
Discussion on Exponential growth and decay §2.6 Worksheet.

## Math 234: Week 4

Feb 04
Lecture: Introduction to Limits (§3.1).
HW 2 is due at 9am.

The first lecture went poorly because of computer glitches. In the second lecture, I got through everything except the proof of the first theorem at the bottom of page 5. I had to keep the pace up for that to happen, however, so as usual it would be nicer if the lecture was shorter.

Exam 1 to printer.

Feb 05
Quiz 3 on §2.4 and §2.5
Discussion: Finding Limits Numerically and with Algebraic Techniques
Feb 06
Lecture: Continuity (§3.2).

In the first lecture, got through page 5 only by working at a demandingly quick pace. In the second lecture, ran out of time halfway through page 6. Overall, there's a lot to write out in this lecture, and overall the lecture is a bit long. I suspect the whole derivation of the Chain Rule is too messy for them to get much out of; on the other hand, it is a nice of example of using linear approximation theorically, which will occurs frequently in these lectures. Perhaps one should derive the single-variable chain rule and then just talk about what happens for two variables in a more heuristic fashion.

Feb 07
Discussion: Continuity
Notes:
The first midterm exam will be on Tuesday, Feb 12 from 7:15–8:30pm.
See here for complete details, including how to register for the conflict exam.

## Math 234: Week 5

Feb 11
Lecture: Rates of Change (§3.3) and Definition of Derivative (§ 3.4).

This lecture is a nice length and I was able to get through it all without working too hard.

Feb 12
Discussion on Derivatives. Midterm the First: 7:15–8:30pm.
Feb 13
No class.
Feb 14
Discuss Midterm 1
Notes:
Different tutoring and office hours this week.

## Math 234: Week 6

Feb 18
Lecture: Techniques for Finding Derivatives (§4.1).

In the first hour, I got through the top of page 6 fine and then tried to cram the last example into 3 minutes. In the second hour, I skipped the top of page 5 and so had more like 5-6 minutes for the last example, which was still too little to cover it completely. Also, in both sections, I forgot about the Mathematica visualization.

Feb 19
Quiz 4 on §4.1
Derivative Rules
Feb 20
Lecture: Product and Quotient rules, Marginal Average Cost function, Marginal Average Revenue function (§4.2).

This lecture is a good length. In the first section, I even got through a reasonably complete discussion of why the local max is the absolute max. In the second section, I didn't have time for the absolute max discussion, but I didn't have everything (including the contour plot) up beforehand as I was answering questions during the break.

Feb 21
Product rule, Quotient rule and Marginal Average Cost

## Math 234: Week 7

Feb 25
Lecture: Composite functions, Chain Rule §4.3

This lecture is actually slightly short for once. I padded it out with a discussion of what the integral of x over the 1/4 circle C is means in terms of an area, and also said that "ds" is called the "arc-length element", which is at the beginning of the next notes. Should have included that the integral of 1 is the length.

Feb 26
Quiz 5 on §4.1 and §4.2
Practicing Derivatives of Composite Functions and Word Problem Applications

Exam 2 draft due (Patrick and James)

Feb 27
Lecture: Derivatives of Exponential and Logarithmic Functions (§4.4 and §4.5).

This lecture is a good length. It was 3-4 minutes short for the first hour and exactly right for the second. In the first lecture, I padded it out by extending the last example with a parameterization of the same curve going the opposite direction.

Feb 28
Multi-Layer Derivatives and Interpreting Word Problems

Should learn date of final now. Decide on format, that is, all multiple-choice or not, and announce to all involved.

Notes:
The date of the final exam for Math 234 will be announced here.

## Math 234: Week 8

Mar 04
Lecture: Increasing and Decreasing Functions (§5.1) and Relative Extrema (§5.2). Higher Derivatives, Concavity and the Second Derivative Test (§5.3).-->

In the first hour, I did everything except the last example on page 6. In the second hour, I did everything with 3 minutes to spare. One minor thing: on page 2, the example is not quite the same as in Lecture 18: they differ by a factor of 2.

Mar 05
Quiz 6 on §4.3, §4.4, and §4.5
Finding Min/Maxes and Intervals of Increase/Decrease

Exam 2 to printer.

Mar 06
Lecture: Higher Derivatives, Concavity and the Second Derivative Test (§5.3). HW 21 (Due Mon, Oct 22)

As written, this lecture is a little short. In the first hour, even after padding out the dicussion of why averages over shorter and shorter paths converged to the value of the function at the fixed endpoint, I actually ended class 5 minutes early. In the second hour, I did take the whole period, but I was definitely moving more slowly than usual. Also, this is among the most theoretical lectures of the whole semester.

Mar 07
Discussion-recitation: Understanding relationships between f(x), f'(x), and f''(x)
Notes:
The second midterm exam will be Tuesday, March 12 from 7:15–8:30pm.
See here for complete details.

## Math 234: Week 9

Mar 11
Lecture: Absolute Extrema (§6.1) and Applications (§6.2). .

Got through notes as written.

Mar 12
Midterm the Second: 7:15–8:30pm.
Mar 13
No class.
Mar 14
Discussion-recitation: Discuss Midterm 2
Notes:
Different tutoring and office hours this week.

## Math 234: Week 10

Mar 25
Lecture: Absolute Extrema (§6.1).

This lecture is fine, I had a few minutes to spare in both sections, and that's with an extended answer to a question that came up in both sections, namely is why phi only goes from 0 to pi.

Mar 26
Absolute Extrema
Mar 27
Lecture: Applications of Extrema (§6.2).

This lecture is also fine, namely a few minutes short. I was feeling a little under the weather, so I skipped the straightforward calculation of the integral on page 3.

Mar 28
Applications of Extrema
Notes:

## Math 234: Week 11

Apr 01
Lecture: Implicit Differentiation (§6.4) and Related Rates (§6.5).

Note: The 7th and last page of the notes is for reference only.

In both sections, I was unable to get through the general form of change of coordinates for triple integrals, even skipping the detailed evaluation of the integrals in the extended examples.

While personally I find the discussion of linear approximation for functions from R2 to R2 very satisfying, my guess is that it goes over their heads given how little exposure they have had with linear transformations.

Apr 02
Quiz 7 on §6.1 and §6.2
Worksheet on Related Rates.

Exam 3 draft due (Nathan and Patrick)

Apr 03
Lecture: Linear Approximation (§6.6) and Antiderivatives (§7.1).

This lecture is fine, even with the 5 minutes at the beginning for the general 3D change of coordinate formula.

Apr 04
Worksheet on Linear Approximation
Notes:
Note that there are two quizzes next week; Quiz 8 on Tuesday (§6.4 and §6.5) and Quiz 9 on Thursday (§6.6)

## Math 234: Week 12

Apr 08
Lecture: Antiderivatives (§7.1) and Integration by Substitution (§7.2)

This lecture was fine, maybe even a little short.

Apr 09
Quiz 8 on §6.4 and §6.5
Indefinite Integrals

Exam 3 to printer.

Apr 10
Lecture: Approximating Areas under Curves (§7.3) and Fundamental Theorem of Calculus (§7.4).

This lecture is too long as written, even assuming all the "previously" bits are up before the starting bell rings. In one lecture, I skipped page 6 and in the other the "Case 2" of non-simple curves the proof of Green's Theorem. Certainly the latter should be skipped, but even then page 6 will be rushed.

Apr 11
Quiz 9 on §6.6
Integration by Substitution
Notes:
The third midterm exam will be Tuesday, April 16 from 7:15–8:30pm.
See here for complete details.

## Math 234: Week 13

Apr 15
Lecture: Approximating Areas under Curves (§7.3) and Fundamental Theorem of Calculus (§7.4).

Even going quickly, I could only devote 10 minutes to the heat equation stuff at the end, which isn't enough time to get through it all. If you slow down a bit, the first four pages of the notes can fill basically the whole 50 minutes.

Apr 16
Discussion-recitation:
Midterm the Third: 7:15–8:30pm.
Apr 17
No class
Apr 18
Discussion-recitation:
Notes:
Different tutoring and office hours this week.

## Math 234: Week 14

Apr 22
Lecture: Area between Two Curves, Consumer Surplus, and Producer's Surplus (§7.5).

Draft of part 2 of final, covering roughly midterm 3 and after. (Mostly Nathan and TBA?)

Apr 23
Taking and interpreting integrals
Apr 24
Lecture: Integration by Parts (§8.1) and Average Value of a Function (§8.2).

This lecture is a good length.

Apr 25
Discussion-recitation:

This worksheet was split in half from the corresponding one in 2016.

Final exam to printers

## Math 234: Week 15

Apr 29
Lecture: Functions of Several Variables (§9.1 and §9.2).

This lecture is intensionally short so that there is time to do the ICES survey. It took me 40 minutes when I skipped the second half of the last page.

Apr 30
Quiz 10 on §7.4, §8.1, and §8.2
Finding Mins/Maxes of two variables functions

This is the second half of the Stokes' theorem worksheet from 2016.

Final exam to printers

May 01
Lecture: Maxima/Minima of two variables functions(§9.3)

Skipping the second half of page 2 and simplifying Ampere's law to the case when the current is 0 made the notes as written take 35 minutes, leaving 15 minutes for a stirring summary the integral theorems and a hint at the general form of Stokes' Theorem.

May 02
May 03
Finals begin.
May 04
Saturday.
Notes:
Extra office hours and tutoring later in the week, see here for complete details.

## Week 16

May 06
Monday Conflict Final Exam (7 - 10 pm)
May 07
Tuesday Final the Ultimate. (8 - 11 am)
Notes:
For office hours and tutoring this week see here for complete details.