Monday, February 20, 2017

lecture 12: quadric surfaces

We'll review planes (12.1) by working several examples. Then we'll turn to the more interesting quadric surfaces. We've played with several of these, including spheres, circular cylinders and cones.

As you read through section 12.1 look at the images of the surfaces. Pay attention to the curves drawn on those surfaces. These space curves are called traces, and they represent intersections between planes and the surfaces themselves. The traces help our brains interpret the images as curvy 2-dim objects living in $\mathbb{R}^3$.

Our main objective is to describe the traces with Cartesian equations and then interpret those traces as lines, circles, parabolas or hyperbolas. This is how we match a particular quadric equation with its graph. This is how we visualize surfaces.

Friday, February 17, 2017

lecture 11: planes and surfaces

We'll review the main points about differentiating and integrating vector functions by working a few examples (11.6, 11.7).

But then we have to jump into chapter 12. Before long you will be finding partial derivatives and working with the multivariable version of the chain rule. We'll start by talking about planes (12.1). I'll show how to assemble a plane equation from a point and a normal vector. Some of our examples will involve cross products and lines.

Thursday, February 16, 2017

exam one solutions

Here are my solutions to exam one. Please let me know if you find any sketchy math. We'll try to have the exams graded, and scores uploaded, by Tuesday morning.

exam one is history

Exam one began at 5:15 pm on Thursday, February 16. The exam covers only sections 11.1-11.5. No electronic devices are allowed at the exam.

We will provide you with this equation sheet. Some facts are not on the equation sheet. You need to know how to measure distance between points in $\mathbb{R}^3$, the sphere equation, and how to compute the dot and cross products. You should also know the cosine and sine of common angles like $0$, $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$, $\pi$, and $2\pi$ radians.

This exam is your opportunity to demonstrate to us that you understand the material. Be sure to read each question carefully, and draw sketches where appropriate. We expect complete solutions and correct notation. Be careful with the T/F questions; think, don't react.

Your exam room is a function of the first four letters of your last name.

  • Aaaa through Hanc, go to CR 302
  • Hans through Pont, go to CR 306
  • Post through Zzzz, go to CR 310

  • We are sharing the rooms with Calculus I and II students. Make sure you are not sitting next to another Calculus III student.

    To practice for the exam, use the problems from MyMathLab, discussion, and the mock exams and examples from the text. If you don't understand something ask questions at your discussion section and during our office hours.

    Tuesday, February 14, 2017

    homework review

    To prepare for the exam, rework the homework problems. From the MyLab page, click on MyLab Course Home, and then GradeBook.

    Monday, February 13, 2017

    lecture 10: calculus of vector functions

    We'll differentiate and integrate vector functions (11.6 and 11.7) and review a bit by writing parametric equations for tangent lines to space curves.

    week four discussion

    You'll be reviewing for exam one this week. Bring your toughest questions. Look on the discussion tab for this week's problems.

    Friday, February 10, 2017

    lecture 9: calculus of vector functions

    We'll spend more time talking about lines and curves in $\mathbb{R}^3$ (11.5). Then we will figure out how to differentiate vector functions (11.6).

    Wednesday, February 8, 2017

    lecture 8: lines and curves in $\mathbb{R}^3$

    We'll decide if two lines are parallel, intersecting, or skew (not parallel, not intersecting). Then we'll parametrize a curve or two (11.5).

    Monday, February 6, 2017

    lecture 7: lines in $\mathbb{R}^3$

    After doing one more cross product example, we'll write parametrized equations for lines in $\mathbb{R}^3$ (11.5). We'll figure out how to tell if a particular point is on the line, and we'll project the line onto one of the coordinate planes and figure out how to describe the projected line with parametric and Cartesian equations. If there is time, we'll try to decide if two specified lines are parallel, intersecting, or skew (not parallel, not intersecting).

    Friday, February 3, 2017

    lecture 6: cross products in $\mathbb{R}^3$

    We'll wrap up the dot product and look at the cross product (11.4). We'll use cross products to determine the area of parallelograms and triangles in $\mathbb{R}^3$. You'll play with additional examples in discussion next week.

    Wednesday, February 1, 2017

    lecture 5: dot product, cross product

    I'll do two examples involving the dot product (11.3). We'll calculate the work done by a constant force acting on a mass that is moving through $\mathbb{R}^3$, and we'll compute the flux of a force across a line segment in $\mathbb{R}^2$. Then, we'll define the cross product (11.4) and look at some of its properties. 

    Monday, January 30, 2017

    lecture 4: vector arithmetic, dot product

    We'll do a little vector arithmetic using basis vectors (11.1, 11.2) and, also, look at some applications of the dot product (11.3). This video shows how to use vector triangles to locate the centroid of a triangle.

    Wednesday, January 25, 2017

    lecture 2: vector arithmetic in $\mathbb{R}^2$ and $\mathbb{R}^3$

    We'll finish Monday's discussion by looking at simple surfaces (planes, cylinders and spheres) in $\mathbb{R}^3$. Then we will move on to vectors and vector arithmetic in sections 11.1 and 11.2. Basic quantities such as position, velocity, acceleration, and force are represented by vectors. We will add vectors and also scale vectors. We'll talk about basis vectors and see how to express a general vector in terms of the basis vectors.

    Monday, January 23, 2017

    no discussion sections this week

    Due to bad weather, the discussion sections will not meet this week (January 23-27).

    lecture 1: points, curves and surfaces

    We'll talk about some common objects (points, curves and surfaces) and the spaces ($\mathbb{R}$, $\mathbb{R}^2$, and $\mathbb{R}^3$) they live in. Our goal is to figure out how many Cartesian equations are required to describe the different objects in the different spaces. Also, we'll talk about how to measure distances between pairs of points in the various spaces.

    Believe it or not, this stuff will be useful throughout the semester. 

    Sunday, January 22, 2017

    office hours

    Office hours are an important part of the course; if you are not using them you are not fully participating in the course.

    My official office hours are M, W, and F from 3:10 - 5:00 pm, or by appointment. I'll post office hours for the discussion leaders (Bang and Andrew) as soon as possible. Keep checking the link at the top of this page.

    the etext is full of examples and problems ...

    if you can find it. To make your way from the WyoCourses course page to the HTML version of the textbook, look for these links:
    1. MyLab and Mastering
    2. MyMathLab with Pearson eText Course Home
    3. Course Tools
    4. HTML eBook
    5. alternate version of your eBook
    6. HTML version of your textbook
    Shame on you Pearson, shame on you!