Friday, September 23, 2016

lecture 11: planes and surfaces

We're skipping over sections 11.8 through 11.9 and jumping into chapter 12. Before long you will be finding partial derivatives and working with the multivariable version of the chain rule. But before then we have to talk about surfaces in $\mathbb{R}^3$. We'll start today with 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, September 22, 2016

exam one solutions

Saturday afternoon: two people told me about the mistake in problem 3, one person told me about a mistake in 5b, and I found typos in 2c and 7. All of these are fixed but let me know if you find more mistakes.

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 ended at 7:05 pm

Exam one begins at 5:15 pm on Thursday, September 22. The exam covers only sections 11.1-11.5. 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 the 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 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.

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

  • Aaa through Iri, go to CR 302
  • Jag through Rac, go to CR 306
  • Rai through Zzz, go to CR 310

  • We are sharing the rooms with Calculus 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. Spaced practice and self-examination may produce better results than cramming. 

    Wednesday, September 21, 2016

    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.

    Monday, September 19, 2016

    lecture 9: calculus of vector functions

    After a quick review of calculus I, we will figure out how to differentiate vector functions (11.6 and 11.7).  We should always be reviewing for the next exam, so we'll talk about unit tangent vectors and tangent lines to space curves.

    Saturday, September 17, 2016

    errors in week two discussion solutions

    Thanks to the sharp eye of Samuel Kessenger, there are now fewer errors in the solutions.

    week four discussion

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

    Friday, September 16, 2016

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

    We'll decide if the two lines we examined at the end of the last hour are parallel, intersecting, or skew (not parallel, not intersecting). Then we'll parametrize a few curves (11.5). On Monday we'll do some actual calculus using parametric equations that describe curves and lines (11.6).

    Just a reminder, my office hour today is from 1:30 to 2:30 pm due to several celebrations this afternoon.

    Thursday, September 15, 2016

    office hour switcheroo

    I switched my office hour to 1:30-2:30 on Friday (September 16) due to a math department reception and the A&S honors convocation. Bang has an office hour every Friday morning at 9 am. 

    Wednesday, September 14, 2016

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

    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. We'll finish the day by trying to decide if two specified lines are parallel, intersecting, or skew (not parallel, not intersecting).

    Tuesday, September 13, 2016

    more than three attempts

    I talked to two calcunauts this week who think MyMathLab allows only three attempts per problem. Not true! After three failed attempts you are offered a chance to work another version of the problem. So, press the Similar Question button after the third failed attempt. And, don't be afraid to go back and fix incorrect answers before the final due date.

    Monday, September 12, 2016

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

    We'll look at the properties of the cross product (11.4), and compute cross products that give the area of a parallelogram and a triangle. You'll play with additional examples in discussion this week.

    It won't be long before we are integrating along lines and curves in $\mathbb{R}^3$. So, we'll return to the business of defining a line in space (11.5) using a point and a vector. Examples will be worked.

    how to evaluate a determinant

    Wednesday, September 7, 2016

    lecture 4: vector arithmetic, dot product

    We'll do a little vector arithmetic using basis vectors (11.1, 11.2). If there is time we'll look at the dot product (11.3).

    Tuesday, September 6, 2016

    office hour switcheroo

    I have to take an elderly woman to the airport this afternoon so I'm holding office hours this morning from 9 to 11:30. Drop by.

    Monday, September 5, 2016

    week 2 discussion

    This week's problems involve vectors, vector equations, and points in $\mathbb{R}^3$. Look on the discussion problems tab (above).

    Wednesday, August 31, 2016

    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.

    Tuesday, August 30, 2016

    recent updates

    Bang's discussion syllabus is available in the links to the right. The review problems for the first week of discussion are available at the discussion problems link above.

    Monday, August 29, 2016

    go to your discussion section!

    Discussion sections meet Tuesday or Thursday this week in room 120 of the Enzi S.T.E.M. Laboratory.