Thursday, March 5, 2015

exam two approaches

Exam two is scheduled for Thursday, March 12 at 5:15 pm. The exam covers sections 13.1, 13.2, 14.1, and 14.3-14.7. No electronic devices are allowed at the exam.

We will provide you with an equation sheet. You can find the equation sheet on the last page of each mock exam. Some facts are not on the equation sheet. Among other things, you need to know the definitions of the dot and cross products.

Your exam room is a function of your discussion section. If possible, leave an empty seat between you and the next calcunaut.

  • Section 20, Berry Center 138
  • Section 21, Berry Center 138
  • Section 22, Classroom Bldg 214
  • Section 23, Geology (old part) 216
  • Section 24, Classroom Bldg 214
  • Section 25, Geology (old part) 216

  • To practice for the exam, use your WebAssign, discussion, and mock exam problems. Solutions are available for these problems. The mock exams include questions from section 14.8 but section 14.8 is not covered on this exam.

    If you don't understand something ask questions at your discussion section and during our office hours. Spaced practice and self-examination may produce better results than cramming.

    Wednesday, March 4, 2015

    lecture 17, the directional derivative

    We'll use differentials and the chain rule to assemble the directional derivative (14.6). Then we'll calculate some rates of change and investigate the properties of the gradient vector.

    Tuesday, March 3, 2015

    discussion, week 6

    This week's discussion problems involve partial derivatives, tangent planes, linear approximations, differentials and the chain rule.

    The quiz has questions about space curves and the surface they lie on (13.1), the geometric relationship between $\vec{r}(t)$ and its derivative (13.2), and about the domains of functions of two variables (14.1).

    Monday, March 2, 2015

    20 dollars!

    Dr. Meredith Minnear (mminear2@uwyo.edu), from the Psychology Department, has a 20 dollar bill (tax free!) with your name on it. To get the money you'll have to spend an hour answering questions that test your spatial reasoning ability. The minimum wage in Wyoming is 7.25 dollars/hour.

    Sunday, March 1, 2015

    lecture 16, the chain rule

    We'll start by looking at the similarity of tangent planes, linear approximations and differentials. Then we'll turn to the multivariable version of the chain rule (14.5). 

    This version of the chain rule is more complicated and more powerful than the single variable version. We'll work examples that involving a space curve, a change of variables from Cartesian to polar coordinates, and a peculiar case where the variables obey a constraint equation.

    A team of engineering students could, as a senior project, vastly improve the WyoCast system. Start with an infrared light source that could be placed on the board, that the camera would pan toward and focus on. 

    Friday, February 27, 2015

    no office hours this afternoon

    I've been fighting an infection all week and the antibiotics are not working as fast as I hoped. So I'll be snoozing on the couch this afternoon and watching my email in case you have questions.

    lecture 15, differentials

    We'll practice partial differentiation today by working on tangent plane, linear approximation, and differential examples. 

    Wednesday, February 25, 2015

    lecture 14, partial derivatives and tangent planes

    I'll do one more tangent line problem and then show that our slope measurements can be made more easily using partial differentiation (14.3). If there is time, we'll use the tangent lines to create a tangent plane to the surface.

    More low-res video.

    Monday, February 23, 2015

    exam one results

    If you took this exam you may view your score and current total score in WebAssign by clicking on the Grades link. If you are taking the makeup exam don't click on the Grades link - the view will terrify you.

    We graded 179 exams. The quartile scores are 71, 80, and 90. So 50% of the group scored 80 or higher and 25% of the group scored 90 or higher. The median scores on the ten problems are 16/20, 18/20, 11/15, 5/5, 4/8, 4/8, 12/12, 8/8, and 7/8.

    For comparison, last semester the quartiles were 67, 77.5, and 90.

    Of course 17.9% of the group scored 67 or below. If your score is not as high as you would like, give some thought to these lists of good and bad study habits: ten things to do and ten things not to do.

    Each full size rectangle represents four brave calcunauts.

    discussion, week 5

    Exams will be passed back, so no quiz this week. The discussion problems cover material from 13.1, 13.2 and 14.1.

    Low-res video from WyoCast.

    lecture 13, functions of several variables

    I'll work examples today from sections 14.1 and 14.3 (we skip 14.2). We'll use quadric surfaces to create functions of two variables. We'll figure out what the domains of these functions look like, and we'll create contour maps to help visualize the functions. Also, we'll see that, unlike curves, these functions do not have a single slope at a particular point. This observation will lead us to partial derivatives and directional derivatives.

    Friday, February 20, 2015

    lecture 12, velocity and acceleration

    It is past time to finish chapter 13. We'll start with a position vector and compute the velocity and acceleration vectors for a point moving on a sphere. We'll also start with an acceleration vector and integrate to get velocity and position vectors. 

    Thursday, February 19, 2015

    exam one solutions

    Take a look at my solutions while the exam is still fresh in your mind. And, let me know if you find any errors. I'll make you famous.

    exam one is history!

    Exam one starts this afternoon (Thursday, February 19) at 5:15 pm. The exam covers only chapter 12. No electronic devices are allowed at the exam.

    We will provide you with an equation sheet. You can find the equation sheet on the last page of each mock exam. 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 the definitions of the dot and cross products.

    Your exam room is a function of your discussion section. If possible, leave an empty seat between you and the next calcunaut.

  • Section 20, Berry Center 138
  • Section 21, Berry Center 138
  • Section 22, Classroom Bldg 214
  • Section 23, Geology (old part) 216
  • Section 24, Classroom Bldg 214
  • Section 25, Geology (old part) 216

  • To practice for the exam, use your WebAssign, discussion, and mock exam problems. Solutions are available for these problems. If you don't understand something ask questions at your discussion section and during our office hours. Spaced practice and self-examination may produce better results than cramming.

    Wednesday, February 18, 2015

    lecture 11, calculus with vector functions

    We'll integrate and differentiate vector functions today (13.2). Along the way we'll compute the slope of a space curve, compute the angle of intersection of two space curves, compute the velocity and acceleration of a point traveling on a circle, and solve an initial value problem to determine the position of a point traveling on a space curve. You might be amazed at how much reviewing we can do while working on new problems.

    Monday, February 16, 2015

    lecture 10, calculus of single variable vector functions

    We'll parametrize (13.1) another space curve or two and then talk about how to differentiate vector functions (13.2) constructed from those space curves. Our goal is compute the slope of a space curve.

    week 4, discussion

    There is no quiz this week due to the exam on Thursday. This week's problems cover material from all of chapter 12; use the discussion to review for the exam. You are welcome to attend as many discussion sections as you like. 

    Friday, February 13, 2015

    lecture 9, traces and space curves

    We'll work one more example of a quadric surface, the hyperbolic paraboloid, from 12.6. Except for spheres, please don't memorize the equations of specific surfaces. I do want you to know how to construct traces for a given surface in horizontal and vertical planes, and be able to identify the traces as lines, parabolas, ellipses and hyperbolas. The mock exams are a good example of the questions you might be asked on the exam. After working the example we'll talk about how to parametrize space curves (13.1).

    Low-res video from WyoCast.

    Wednesday, February 11, 2015

    lecture 8, quadric surfaces and cylinders

    As you look at the images of the surfaces in section 12.6, 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 them as lines, circles, parabolas or hyperbolas. This is how we match a particular quadric equation with its graph. This is how we visualize surfaces.

    Monday, February 9, 2015

    week 3, discussion section quiz

    Expect a short quiz in your discussion section. You'll need to know how to describe the coordinate planes and axes using Cartesian ($x$, $y$, and $z$) equations. And you'll need to know how to compute dot and cross products.