Monday, February 27, 2017

lecture 15: partial derivatives, and the chain rule

We'll talk more about partial derivatives (12.4) today; we'll look at implicit differentiation and we'll compute some second and third derivatives. If there is time, we'll look at the multivariable chain rule (12.5). It's a nice excuse to compute partial derivatives and, maybe, look at a total derivative.

Friday, February 24, 2017

lecture 14: partial derivatives

We'll talk more about traces and level curves and compute slopes on surfaces in various directions. And then we'll talk about partial derivatives (12.4).

Wednesday, February 22, 2017

lecture 13: functions of two variables

We'll use planes and quadric surfaces to create functions of two variables (12.2). We'll examine the domains of these functions, construct level curve maps, and compute slopes on the surfaces. We may even compute some partial derivatives (12.4).

Monday, February 20, 2017

exam one results (updated, again)

Last Thursday, 153 brave calcunauts took the first exam; four others took a make-up exam on March 2. The average is now 77.7 and the quartile scores are 70, 79, and 87. So, slightly more than 50% of you have scores of 79 or higher.

If you are unhappy with your score, talk to your discussion leader, or me. Make an appointment if you can't attend our office hours.

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.