## Final Exam — Monday 15 December, 9:30-11:30am, in our usual classroom.

You are allowed to use both sides of three 8.5” x 11” sheets of paper for handwritten notes, this table of basic derivatives & integrals, this table of trigonometric integrals, and a calculator. No other notes or technology will be allowed for this exam. If you wish to use the derivative/integral table and/or trigonometric integral table, you must print out and bring your own copy.

The final exam is comprehensive; it is over all material covered this semester.

Review problems for Chapters 6-10 are posted on WebAssign. For Chapter 11, review the daily problem sets and homework 5.

A few notes:

- You will lose points for not including the differential ($dx$, $dt$, $d\theta$, etc) in your integrals.
- One of the important concepts in Calc I/Calc II is that the definite integral is arrived at through a process of “chopping and adding”. I will check whether you understand this, especially in the context of material covered in Chapter 6.
- Even though the integration method of $u$-substitution was introduced in Calc I, I consider it “testable material” for this class.
- When reviewing the material for sequences and series, pay particular attention to the following:
- Be able to derive and recognize the general formula for terms of a sequence or series, and use sum notion for series.
- Be able to recognize $p$-series and geometric series; know when they converge or diverge.
- Be able to compute a Maclaurin or Taylor series with center $c$ for a given function using the formula for the $n^{\text{th}}$ term: $s_n = \frac{f^{(n)}(c)}{n!}(x – c)^n$. When going through the review problems for computing Maclaurin and Taylor series, make sure you know how to use the formula, and be aware that this is
*not*how WebAssign is presenting the solutions (WebAssign’s solutions depend on manipulation of basic series, which is good to know, but not what I will be testing you on).

#### Wednesday 3 December

slides_12:03_sec11.4_175_14fall

Area and arc length in polar coordinates.

Review problems for Chapter 6 have been posted on WebAssign. Review problems for Chapters 7-10 will be posted tomorrow. Review for Chapter 11 on your own, by looking at the problems sets and homework.

#### A few announcements as we head into the end of the semester:

- Skills Test re-takes will be held in class on Friday 5 December. This is your last chance to re-take the Skills Test; re-takes will not be given during dead week or finals week.
- The final exam will be held in our usual classroom on Monday 15 December from 9:30-11:30am.
- There will be new material taught on the Monday of dead week, but the last two days of class will be used for review for the final exam.
- Student evaluations are open online. I appreciate constructive feedback, and take it into account when planning future classes. Please take a moment to complete the evaluation.

#### Monday 1 December

Welcome back.

slides_12:01_sec11.3_175_14fall

Polar coordinates.

#### Friday 21 November

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Arc length and speed.

#### Wednesday 19 November

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Parametric equations and parameterized curves in the plane.

#### Friday 14 November

There’s a significant possibility that the weather overnight will create hazardous driving conditions Friday morning, so I am postponing the exam until Monday (11/17). There will not be class Friday, but I will be in my office from 9:00-10:15 (if the university is open), and for regular office hours from 11:00-12:00.

Update: My office hours today are also cancelled. See you all on Monday.

#### Monday 10 November

slides_11:10_sec10.7_175_14fall (Updated Thursday 12/13.)

Taylor series.

A note about the problems sets for Taylor series: they have been broken down into two parts. The first part (#22a) involves using various substitution and multiplication techniques to derive Maclaurin series from simpler Maclaurin series. The second part (#22b) involves computing Taylor series directly.

Warning: practice another version and solutions have been disabled for #22b. The solutions presented involve algebraic manipulation of the functions instead of direct computation, and I want you to have practice with the direct computation. Following the solution steps will result in a lot of confusion.

Both problem sets #22a and #22b are due on Friday. You can ask questions about them in class on Wednesday, during office hours, help sessions, etc.

#### Saturday 8 November

Review problems for exam 2 have been posted on WebAssign. There are review problems for sections 7.8, 8.1, 9.1, 9.2, and 10.1–10.5. For sections 10.6 and 10.7, look at the current problem sets and homework.

#### Friday 7 November

slides_11:07_sec10.6_175_14fall

Power series: geometric power series, power series expansions, and integration and differentiation of power series.

#### Wednesday 5 November

slides_11:05_sec10.6_175_14fall

Introduction to power series. Convergence of power series.

A note on daily problems sets: I’ve broken the problem set for power series (sec 10.6 in the text) into two separate assignments: #21a and #21b. Both are due next Monday. However, everything needed to complete problem set #21a was covered in class today, and I highly recommend that you complete it before Friday’s class.

#### Tuesday 4 November

Vote.

#### Monday 3 November

slides_11:03_sec10.5_175_14fall

Ratio and root tests.

#### Friday 31 October

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Alternating series test, ~~ratio test, and root test~~.

#### Wednesday 29 October

slides_10:29_sec10.3-10.4_175_14fall

Absolute and conditional convergence.

Note: for problem set #19, you will only have one try for the multiple choice questions (#4-12).

#### Monday 27 October

slides_10:27_sec10.3_175_14fall

Positive series.

#### Friday 24 October

slides_10:24_sec10.2_175_14fall

Introduction to series.

#### Wednesday 22 October

slides_10:22_sec10.1_175_14fall

Sequences: computing convergence and limits.

#### Monday 20 October

slides_10:20_sec10.1_175_14fall

Introduction to sequences.

#### Wednesday 15 October

Slides and the worksheet from today’s lesson on probability — thank you, Rachael!

Unfortunately, there were not any good probability problems on WebAssign…

Also: Rachael’s help session times have been updated in the sidebar.

#### Monday 13 October

Very few people did problem 4b correctly. You will have a chance to improve your score during the first ten minutes of today’s class. This will be your only opportunity to improve your score on this problem.

These are the expectations for the Skills Test on Friday 10/17

#### Friday 10 October

slides_10:10_sec9.1_175_14fall

Introduction to differential equations. Separable differential equations.

#### Wednesday 8 October

slides_10:08_sec8.1_175_14fall

Applications of the integral: arc length and surface area.

#### Monday 6 October

slides_10:06_sec7.8_175_14fall

I have decided to let error bounds go for now. We will see them again when we talk about sequences and series. On today’s problem set, I’ve set part (b) on problems #3 and #4 to zero points. You can try them if you’d like — it will not affect your score. We will talk about arc length and surface area on Wednesday.

#### Monday 29 September

Improper integrals, continued: limit comparison tests, and $p$-integrals.

Here is the worksheet on $p$-integrals.

And, because I tried to hurry the wrap-up, here are notes on part 3 of the worksheet — tying the convergence/divergence behavior of $p$-integrals to the value of $p$.

#### Friday 26 September

slides_09:24_sec7.6_175_14fall

Improper integrals.

We covered everything you need to do the problem set today.

#### Wednesday 24 September

slides_09:24_sec7.5_175_14fall

Techniques of integration: method of partial fraction decomposition – quadratic terms. Completing squares.

#### Monday 22 September

slides_09:22_sec7.5_175_14fall

Techniques of integration: method of partial fraction decomposition – linear terms.

Help Sessions: Rachael’s help sessions for the next week will be:

- Wednesday (9/24) 10:30-11:45 AM in Library Room 205
- Thursday (9/25) 4:30-5:45 PM in Multipurpose Building Room 210
- Tuesday (9/30) 9:00-10:15 AM in Multipurpose Building Room 210

~~Monday 15~~ Friday 19 September

slides_09:19_sec7.3_175_14fall

Techniques of integration: trigonometric substitution.

A heads-up on today’s problems set (#09 Trigonometric Substitution) — you only get 3 chances on the multiple choice.

~~Monday 15~~ Wednesday 17 September

slides_09:17_sec7.2_175_14fall

Techniques of integration: trigonometric integrals.

#### Monday 15 September

slides_09:15_sec7.1_175_14fall

Techniques of integration: the method of integration by parts.

Reminder: the first homework assignment is due on Wednesday (5 minutes before class). Rachael is holding a special LA help session today from 12-1:15pm in the Multipurpose Building, Room 207A.

Announcement: If you are interested in providing one-on-one mentorship to a low-income high school student, helping them navigate the college application and financial aid process, contact boise@striveforcollege.org. This is a volunteer organization. My understanding is that the time commitment is one hour per week, and mentors are particularly needed this week and next.

#### Friday 12 September

#### Wednesday 10 September

slides_09:10_sec6.5_175_14fall

Application of the definite integral: work.

#### Monday 8 September

slides_09:08_sec6.4_175_14fall

Computing the volume of solids of revolution using the method of cylindrical shells.

Announcement: Help sessions with Rachael have been scheduled. See the sidebar for times and locations.

#### Friday 5 September

slides_09:05_sec6.3_175_14fall

Computing the volume of solids of revolution using the disk/washer method.

#### Thursday 4 September

I am extending the deadline for the third problem set until midnight tomorrow (Friday 9/4). The last half hour of tomorrow’s class will be open for questions about the assignment.

~~Monday~~ Wednesday 3 September

slides_09:03_sec6.2_175_14fall

Applications of the definite integral: computing the volume of solids whose cross-sectional area can be written as a function of a single variable.

Worksheet (corrected): volumes of solids sec6.2 175 14fall

Notes on the example and the worksheet problems:

- Color notes — blurry due to file-size-reduction: volume_of_solid_notes_9:3_sec6.2_175_14fall
- Black-and-white notes: volume notes (black and white) sec 6.2 175 14fall

The notes give a more linear presentation of the examples and worksheet problems from this morning’s class.

#### Friday 29 August

slides_08:29_sec6.1_175_14fall

Applications of the definite integral: area between curves, and mass (integrating linear mass density functions).

Announcements:

- I spoke with a WebAssign representative about the problem of being forcibly logged out by WebAssign when trying to access homework. He suggested clearing the cookies and cache of the web browser. Apparently, this fixes several WebAssign issues, so it’s worth trying first when you run into problems. Ideally, you should be logged out of WebAssign when you do it.
- Have a great weekend.

#### Wednesday 27 August

slides_08-27_integration_review_175_14fall

Review of antiderivatives, definite integrals, and the method of $u$-substitution.

Announcements:

- You can check Blackboard to see if your clicker registered in today’s class.
- Please fill out the survey for finding days and times for help sessions with Rachael.
- The first help session with Rachael will be on Friady 29 August from 7:30-8:45am in Albertosns Library Rm 205.
- We will begin class on Friday with questions about WebAssign

#### Monday 25 August

slides_08-25_welcome_175_14fall

There was a clear preference for daily problem sets to comprise 15% of the course grade, and homework to comprise 5%. The syllabus will be updated to reflect this.

The first help session with Rachael will be on Friady 29 August from 7:30-8:45am in Albertosns Library Rm 205.

See you on Wednesday

#### Welcome to Math 175

Welcome to Math 175, section 001, Fall 2014. Our class meets MWF 9:00–10:15am, Interactive Learning Center (ILC), Room 302.

In this course, we continue to study the integral, learning new techniques of integration, exploring a few applications of the integral, and defining indefinite integrals. This will be followed by an introduction to sequences and series. Finally, we will briefly consider parameterized curves in the plane.

Please take a few minutes to familiarize yourself with the course website, which includes: announcements, course slides, and notes (which will be posted on this home page throughout the course); the syllabus (this is where you can see how grades will be calculated); information about the textbook and WebAssign (the online homework platform); and exam information.

My email address and links to the log-in pages for Blackboard and WebAssign can be found in the sidebar at the top right side (or, on tablets, at the bottom) of each page of this site.

Blackboard will be used to register clickers, host a class discussion board, and post grades (except for homework and daily problem set grades, which will be posted on WebAssign).

Information on registering for WebAssign can be found here. Information on registering clickers can be found here.

**Please mark the following dates in your calendar**:

- Exam 1: Friday 10/3, during class.
- Exam 2: Friday 11/14, during class.
- Final Exam: date and time TBA, in our regular classroom.
- Basic Skills Test (first iteration): Friday 10/17, during class.

Please feel free to contact me via email at shariultman@boisestate.edu with any questions.