### Final Exam Information

**Section 002: Wednesday 6 May, 10am-12pm, in our regular classroom (Education Building (EDU), Room 109).**If I have jury duty, the exam will be proctored by Dr. Harlander.**Section 004: Monday 4 May, 3-5pm, in our regular classroom (Micron Business and Economics Building (MBEB), Room 1209).**If I have jury duty, the exam will be proctored by Dr. Holmes.

More information on the final exam can be found here.

I will be checking email over the weekend. I will do my best to check email next week, but may be limited depending on how jury duty goes.

**Chelse’s weekend help sessions:**

- Saturday, May 2nd, 1:30-4:15 pm Academic and Career Services Building room 215b
- Sunday, May 3rd, 3:00-5:45 pm Library room 205

#### Thursday 30 April

**Due to illness, I need to cancel my additional office hours today (orignally scheduled for 1-4:30 pm).**

I am re-scheduling these for tomorrow, Friday 1 May. **I will be available tomorrow from 12-1:25pm and 3-5pm in MB-222D.**

I also check my email throughout the day. **Feel free to email me questions with a picture/scan of your work attached.**

**Chelse also will be holding a few more help sessions:**

- Thursday, April 30th, 12:00-1:15 pm Academic and Career Services Building room 215b
- Saturday, May 2nd, 1:30-4:15 pm Academic and Career Services Building room 215b
- Sunday, May 3rd, 3:00-5:45 pm Library room 205

#### Wednesday 29 April

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Divergence theorem.

Links from Bridge Book:

(Cancelled due to illness.)**I will have office hours tomorrow (Thursday 4/30) from 1-4:30pm in MB-222D.**

#### Monday 27 April

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Stokes’ theorem.

Links from Bridge Book:

.

#### Friday 24 April

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Green’s theorem.

#### Wednesday 22 April

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Flux integral example, continued. Vector field derivatives: curl and divergence.

Links from Bridge Book:

#### Monday 20 April

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Vector surface integrals (aka flux integrals).

Links from Bridge Book:

- Flux.

#### Friday 17 April

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The vector and scalar surface elements $d\vec{S}$ and $dS$, and scalar surface integrals.

#### Wednesday 15 April

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Parameterizing surfaces in 3-space~~; introduction to the vector and scalar surface elements $d\vec{S}$ and $dS$~~.

Links from the Bridge Book:

- Parametric surfaces.
- Surfaces.
- General surface elements (uses $d\vec{A}$ instead of $d\vec{S}$).
- (surface elements on) Graphs of functions.
- Activity: surface elements on planes, cylinders, and spheres.
- Wrap-up: surface elements on planes, cylinders, and spheres.

#### Monday 13 April

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Conservative vector fields, path independence, and the Fundamental Theorem of Conservative Vector Fields.

Links from the Bridge Book:

- Independence of path.
- Conservative vector fields.
- Finding potential functions.
- Visualizing conservative vector fields.

#### Friday 10 April

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Vector line integrals.

Review for this topic: parameterized curves (sec 13.1); vector derivatives and tangent vectors (sec 13.2); the dot product (sec 12.3).

Relevant Bridge Book links:

- Line Integrals
- Use What You Know! (evaluating line integrals). This page will give you a view of a more sophisticated way of working with the vector differential $d\vec{s}$ — denoted $d\vec{r}$ in the Bridge Book — to come up with parameterizations.

#### Wednesday 8 April

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The vector and scalar line elements $d\vec{s}$ and $ds$, and scalar line integrals.

Review for this topic: parameterized curves (sec 13.1); vector derivatives and tangent vectors (sec 13.2).

A very good explanation of $d\vec{s}$ and $ds$ can be found at the Bridge Book Wiki — note that the Bridge Book denotes the vector line element as $d\vec{r}$ instead of $d\vec{s}$.

(In fact the Bridge Book is a great reference for the rest of the class. I recommend bookmarking it.)

#### Monday 6 April

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Vector fields.

A few online vector field graphing applets:

- Vector Field Analyzer II Plots planar vector fields. By Matthias Kawski at Arizona State University.
- 2-D Vector Field Simulation and 3-D Vector Field Simulation (these are fun to play around with) by Paul Falstad.
- EquationExplorer. Vector fields, and implicitly defined and parametric curves. Simple and clear. By Kevin Mehall

#### Wednesday 1 April

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Practice with integration in cylindrical and spherical coordinates: volume integrals.

I will have additional office hours tomorrow (Thursday 4/2) from 1-3pm.

#### Monday 30 March

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Spherical coordinates and volume element (continued). Triple integrals in cylindrical and spherical coordinates.

Note: there are three problem sets associated with the material covered in today’s class:

- “#22: Intro to Cylindrical and Spherical Coords” — due before class on Wednesday 4/1.
- “#23: Triple Integrals in Cylindrical Coordinates” — due before class on Friday 4/3 (day of Exam 3).
- “#24: Triple Integrals in Spherical Coordinates” — due before class on Friday 4/3 (day of Exam 3).

#### Friday 20 March

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Cylindrical and Spherical coordinates, and volume elements.

#### Wednesday 18 March

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Triple integrals in Cartesian coordinates.

Regions of integration for problem set #21:

#### Monday 15 March

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More double integrals in polar coordinates.

#### Friday 13 March

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Double integrals in polar coordinates.

#### Wednesday 11 March

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Applications of double integrals.

#### Monday 9 March

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Double integrals.

#### Monday 2 March

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Optimization subject to a constraint: the method of Lagrange multipliers.

#### Friday 27 February

*A life is like a garden. Perfect moments can be had, but not preserved, except in memory. LLAP*

— Leonard Nimoy

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Local extrema, saddle points, and the second derivative test.

#### Wednesday 25 February

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Critical points~~, local maxima and minima, and saddle points~~.

#### Monday 23 February

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Directional derivatives and the chain rule(s).

General Announcement:

- You will be responsible for learning how to do the chain rule in more than one variable. I have created an extra credit assignemnt on WebAssign to help you do this. Please try it before you attempt problems 6–8 on Problem Set #15. The assigment is set up to give you 100 attempts, with practice another version and solutions available after the first attempt.You may want to read/reference Chapter 16.4 in the course text. And remember, Chelse can help you with this during her help sessions.

Announcement for Math Majors (and anyone else who may be interested):

- There is a colloquium today at 3:00-3:50pm in ILC303. There will be refreshments at 2:40pm in MB 226.

**Speaker**: Michael Dorff, Brigham Young University

**Title**: Analytic functions, harmonic functions, and minimal surfaces

**Abstract**: Complex-valued harmonic mappings can be regarded as

generalizations of analytic functions and are related to minimal surfaces which are beautiful geometric shapes with intriguing properties. In this talk we will provide background material about these harmonic mappings, discuss the relationship between them and minimal surfaces, present some new results, and pose a few open problems.

#### Friday 20 February

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The gradient vector field and its properties. Directional derivatives.

Online app for graphing surfaces and level curves: Surface/level curve grapher.

Online app for graphing 2-d vector fields (including gradient fields): Vector Field Online Graphing (link changed after Section 002 found a better grapher!).

(Also, an online app for graphing tangent planes: Tangent Plane Applet.)

Annoncement: If you are a Math major, you may be eligible for a scholarship through the Math Department. Check it out.

#### Wednesday 18 February

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Applications of differentiability: two linear approximations (the local linearization and the function differential).

#### Friday 13 February

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Second order partial derivatives. Tangent planes.

#### Wednesday 11 February

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Level curves and contour maps. Partial derivatives. How are they related to the derivatives you learned about in Calc 1? Jedi mind tricks.

#### Monday 9 February

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Introduction to functions of more than one variable. Domain and range. Evaluating functions. Graphs. Level curves and contour maps.

Two links for graphing functions and level sets/contour maps:

- WolframAlpha
- Surface/Level Curve Grapher (D. Ensley, B. Kaskosz).

#### Friday 6 February

The first midterm is today, in class. For more information, check the Exams page.

#### Monday 2 February

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The unit tangent vector $\hat{T}$ and the principal unit normal vector $\hat{N}$. Briefly, the unit binormal vector $\hat{B}$, the moving frame $\{\hat{T}, \hat{N}, \hat{B}\}$, and curvature $\kappa$.

Announcements:

- WebAssign problem set #08, problem 4: the score for this problem has been set to zero. This is an example of a problem where you need to use parenthesis for the argument of a trig function — e.g.: $\sin(6t)$ (not $\sin\!6t$).
- On homework #2, problem #6: use $s$ for the parameter (not $t$).
- Review problems for Chapter 12 have been posted on WebAssign. Review problems for Chapter 13 will be posted soon.
- Check the Exams page of the course website for information about Friday’s exam. The equation sheet is posted there. Look at it before the exam, so you know what is (and is not) included. If you have suggestions for equations that you think should be included on the sheet, let me know. You are also allowed one side of an 8.5” x 11” sheet of paper for handwritten notes.
- Wednesday is review. I will not have anything prepared, so come with questions!

#### Friday 30 January

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Derivatives of vector-valued functions. Tangent vectors. Velocity, speed, and acceleration.

#### Wednesday 28 January

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Introduction to parameterized curves.

Being able to graph these curves is very useful. There are online applets for graphing parameterized curves, for example: this one. You can also download a graphing app for your computer or tablet. See the Resources page for a few options.

#### Monday 26 January

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Planes in 3-space.

#### Friday 23 January

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The cross product, area, and normal vectors.

Announcements:

- I am extending the number of attempts on Homework 1 from three to five. This is for Homework 1 only. The remaider of the homework assignments will have only three attempts.
- If you are a math major and are interested in attending a math seminar (getting an idea of what higher math looks like), you may want to condiser attending the topology seminar this afternoon. The information is:

Date: Friday, January 23

Time: 3:00-3:50pm

Location: MB 139

Speaker: Uwe Kaiser, Boise State University

Title: Contact Topology and Legendrian Knots I

Abstract: This will be the first in a series of elementary lectures on contact topology of 3-dimensional manifolds. A contact structure is a topological structure on a 3-manifold that allows to define refined invariants both of the 3-manifold and of links in the 3-manifold. It is related to open book decompositions of 3-manifolds and grid diagrams. The final goal of the lecture series will be to explain how contact topology is used to prove some remarkable theorems in the skein theory of links in 3-manifolds.

#### Wednesday 21 January

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Class notes 01/21. In general, I will not post my notes from class. Today is a special case: between President Obama’s visit, and not finishing the example on orthogonal decomposition, it makes sense to post these. These are the notes from the morning class (section 002). The example on orthogonal decomposition is worked out on pages 8-10.

The dot product, continued. Projections, orthogonal decompositions, and work.

Announcements:

- We do have class today.
- If you are attending President Obama’s speach, do not worry about clicker scores. I will not count them today. However, you are responsible for learning the material covered today. Check the slides posted on the course website, and read section 12.3 in the course text.
- Chelse has a help session today from
~~2:30~~4:30-5:45pm in the Simplot Micron Technology Center, room 106. - Beginning this Friday, Dr. Ultman’s office hours will be Mondays, Wednesdays, and Fridays from 12-1pm in MG-222D. These are drop-in office hours; you do not need an appointment. Office hours and help session times are posted on the sidebar (or bottom, depending on window size) of every page of the course website.

#### Friday 16 January

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The dot product. Computing the dot product. The dot product, angles, and orthogonality.

#### Wednesday 14 January

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Magnitude of vectors; vector algebra (vector addition and scalar multiplication); vector parameterizations of lines; unit vectors and basis vectors; ways of representing vectors.

#### Monday 12 January

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Welcome to Math 275. Introduction to vectors. Component form ~~and magnitude~~.

We will begin with magnitude on Wednesday. You can either try the magnitude problems in problem set #01 now, or wait until after class on Wednesday. (Recall that problem set #01 is not due until Wednesday 1/21.)

Results of voting:

- 93% of students voted for having daily problem sets worth 15% of the final course grade, and homework worth 10%. By section, the vote was 93% in section 002, and 91% in section 004.
- 76% of students voted to not to set fixed percentages at which to assign +/- to grades when computing the final course grade. By section, the vote was 79% in section 002, and 71% in section 004.

I have updated the syllabus to reflect the results of the votes.

#### Welcome to Math 275

Welcome to Math 275, sections 002 and 004, Spring 2015.

- Section 002 meets MWF 10:30-11:45, in the Education Building (EDU), Room 109.
- Section 004 meets MWF 1:30-2:45, in the Micron Business and Economics Building (MBEB), Room 1209.

In this course, we will see how the mathematics learned in Calculus I and II generalizes to higher-dimensional settings, and develop new tools to deal with new situations. In particular, we will explore the mathematics of space-curves (one-dimensional objects sitting in two- or three-dimensional space), surfaces (two-dimensional objects) and volumes (three-dimensional objects).

Please take a few minutes to familiarize yourself with the course website. This page will be used for posting announcements and class notes/slides. The menu at the top will take you to pages with course information, including: the course syllabus (this is where you can see how grades will be calculated, information on academic honesty, course learning objectives, etc); the projected course schedule; exam information; links to useful resources; and information about the textbook, WebAssign (the online homework platform), and clickers and ResponseWare.

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).

Follow these links for more information on:

- The syllabus.
- The textbook.
- Registering for WebAssign.
- Registering clickers or ResponseWare (you need one or the other, not both).

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

- Exam 1: Friday 6 February (in class).
- Exam 2: Friday 6 March (in class).
- Exam 3: Friday 3 April (in class).
- Final Exam:
- Section 002: Wednesday 6 May, 10am-12pm
- Section 004: Monday 4 May, 3-5pm.

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