Mat 223 Daily Log
Please press F5 to refresh your page. If this page is more than two class days out of date, please send me an email reminding me to update it.
|Day 54: Wednesday, 12/4||
Worked on Vector Fields and Line Integrals. Handed out Mathematica material on this topic.
|Day 53: Monday, 12/2||
Work on two more problems using cylindrical and spherical coordinates.
|Day 52: Wednesday, 11/27||
Teacher takes a zen potato peeling day off!
|Day 51: Monday, 11/25||
Work on the conversion formulas for cylindrical and spherical coordinates. Work to help students understand that cylindrical coordinates essentially incorporate z as a function or r and theta, and then revert to polar coordinates in the domain plane. Worked on helping students visualize where the dV component for spherical coordinates comes from. Started a problem, but did not get to finish it in class.
Emailed the completed problem to students on Tuesday afternoon.
Handed out the last graded homework assignment.
|Day 50: Friday, 11/22||
Hand back tests and discuss briefly.
Continue work on triple integrals
|Day 49: Thursday, 11/21||Test.|
|Day 48: Wednesday, 11/20||
Review for test
|Day 47: Monday, 11/18||
Began Triple Integrals. Will continue this work after the test on Thursday.
|Day 46: Friday, 11/15||
Handed back quiz.
Worked through another type of problem from section 12.3 that I had not yet covered. Worked on several more Polar examples.
|Day 45: Thursday, 11/14||
Finished problem 8 and did another example of polar coordinates.
|Day 44: Wednesday, 11/13||
Answered some questions on Practice Exercises.
Began working on Polar Coordinates. Showed conversion formulas, and discussed how to find that dA for polar coordinates would be r d r d theta ( like a pirate!) Began work on exercise 8 from section 857. Will finish that problem on Thursday.
|Day 43: Monday, 11/11||
Worked through two more exercises from section 12.3, emphasizing how we decided what way to set up the integral. Problem 24 could be set up both ways, but one way was much easier to integrate. Problem 28 had a region of integration that led us to using dydx order if we wanted to avoid having to set up two separate integrals.
|Day 42: Friday, 11/8||
Worked on section 12.3, where we don't have rectangular regions of integration. Worked completely through 3 problems.
Day 41: Thursday, 11/7
Had students complete another integration problem from section 12.2
Handed back GW 6, and spent a fair amount of time talking about how to think about improving on writing about technically challenging material like what was involved in the assignment. Emphasized that the gradient vector itself does not represent a slope, nor an instantaneous rate of change. The magnitude of the gradient vector is a directional derivative, so the magnitude is an instantaneous rate of change. It is the slope of a line tangent to the curve on the surface, which is formed when we take the plane perpendicular to the xy plane, and which contains the gradient, and see where it intersects the surface. Since this line is tangent to the surface, it is also in the tangent plane.
Reviewed the integration problem students had worked on.
Day 40: Wednesday, 11/6
||Worked on 3 exercises from section 12.2. doing complete work for integration using techniques involving substitution, and integration by parts.|
|Day 39: Monday, 11/4||
Collected the GW 7 work.
Finished the problem involving LaGrange Multipliers, and reviewed the procedure and why it made sense.
Began discussing section 12.1 - Definite integrals.
|Day 38: Friday, 11/1||
Talked a little bit more about the Discriminant, and why it was essential to determine that value, rather than just relying on the second derivative signs (like we could for Calc 1). Handed out a Mathematica sheet that discussed a problem that had a critical point where the second derivatives were both positive, but which was still a saddle point because if the inputs were along the line y = x, the cross section had a maximum.
Discussed LaGrange Multipliers from section 11.8 and showed why the result was that the gradient vectors needed to be scalar multiples of each other. Began a problem involving LaGrange multipliers.
|Day 37: Thursday, 10/31||
Students had the opportunity to meet with the students who had been assigned the same problems from section 11.7 as they had.
Collected GW 6.
|Day 36: Wednesday 10/30||
Finished exercise 12 from section 11.7, and did a boundary problem from that section.
Handed out the instructions for GW 7.
|Day 35: Monday, 10/28||
Teacher out sick. Students should continue work on GW 6 and on two problems they need drafts for on Thursday.
|Day 34: Friday, 10/25||
Gave students each two problems that they were responsible for working on from section 11.7. Gave out blue books for their preliminary work on these problems. Students will be able to meet with the other students in class who are working on the same problems in class on Thursday. At the end of class on Thursday, each student has to determine what problem they are responsible for writing up. More instructions will be handed out on Monday.
Went through exercise 4 from section 11.7, and did most of exercise 12. Will complete exercise 12 on Monday, and continue with some other examples from section 11.7
|Day 33: Thursday, 10/24||
Test on Unit 2
|Day 32: Wednesday, 10/23||
Began section 11.7 on optimization. Developed the Discriminant using the process of completing the square with a standard quadratic function in two variables. Discussed that any other quadratic function would just be some type of transformation of this basic function. Associated the function to the 2nd degree Taylor Polynomial. Showed that whether the function was a paraboloid, a saddle, or a cylinder was all based on what happened to the discriminant.
|Day 31: Monday, 10/21||
Handed out GW 6, and discussed a bit.
Review for test on Thursday.
We will begin Optimization on Wednesday.
|Day 30: Friday, 10/18||Worked on the Chain rule for multi-variable functions. Emphasized when you would use ordinary notation, and when you would use partial notation.|
|Day 29: Thursday, 10/17||Had students work on Mathematica packet entitled: Working with Gradient Vectors, Contour Diagrams and Tangent Planes. The next graded assignment will be based on this material.|
|Day 28: Wednesday, 10/16||
Handed back quiz and GW 5. Spent some time discussing answers to GW 5.
Discussed why the gradient vector was important. It is the vector that points in the direction of maximum increase. Showed why this was a natural result, based on the definition of a directional derivative as a dot product. Also worked through why the gradient vector had to be perpendicular to the level curve that it was associated with.
Announced test for this unit will be on Thursday, October 24th
|Day 27: Friday, 10/11||
Had students compute grades, and gave them their cards with the grade I have computed on it so they could check that we agreed.
Worked out another example involving directional derivatives.
Quiz on material up through section 11.3
|Day 26: Thursday, 10/10||Presented ideas on directional derivatives. Used the differential to help us make a jump from the limit definition to a more workable format. Noticed that the directional derivative could be thought of as the dot product between a vector that we called the gradient vector, and a unit vector in the direction we wanted to move.|
|Day 25: Wednesday, 10/9||
Reviewed concept of linearization, and extended it to include the concept of a differential. Discussed the difference between delta z (the change in the actual function values) and dz (the change in outputs along the tangent plane), and why the differential was important from a historical perspective and a current perspective.
Collected GW 5.
|Day 24, Monday, October 7th||
Presented information on section 11.4 Linearization (equation of tangent plane) at a point (a,b) for a function f(x,y). Discussed why linearity was important. Worked through an example of finding a tangent plane.
|Day 23, Friday, October 4th||
Worked more on section 11.3. Discussed higher order derivatives. Worked carefully through an example. Had students work through another problem in class.
|Day 22: Thursday, October 3rd||
Work on GW 5 in the computer lab.
Handed out new directions with more details on Working with Partial Derivative with respect to x (new version can be found at link in Day 20.)
Discussed how to add a particular contour to a contour diagram, how to add a point of interest, and how to add grid lines.
|Day 21: Wednesday, October 2nd||
Handed back GW 4, and discussed the last problem. Will hand out answer key for the other questions as soon as I can make copies.
Answered a question from section 9.6
Reviewed the yellow sheet on Partial Derivatives that I had handed out on Monday, using it as a way to review the ideas we had discussed.
Talked about exercise 4 from section 11.3 - and how we would approximate partial derivatives from a two way table. Discussed the meaning of the partial derivatives, as well as the units.
Began finding partial derivatives using our familiar rules for derivatives. We will do more of this on Friday.
Tomorrow students will have time in the lab to work on GW 5.
|Day 20: Monday, September 30th||
Handed out GW 5, and spent a little time discussing it. Students should begin work on it as soon as possible, and will have the entire class on Thursday to work in lab.
Finished ideas from Hand Out on Friday.
Began section 11.3 - Partial Derivative. Reviewed ideas of derivatives of functions of one variable, and used that as a spring board to discuss partial derivatives... derivatives where we either hold x or y constant. Developed ideas for holding y constant.
Handed out a yellow sheet on Working with Partial Derivative with respect to x.
Proposed Quiz cancelled till further notice.
|Day 19: Friday, September 27th||Worked with ideas of domain and range, and then more with cross sections and contour curves using a Hand Out. Students will be completing a graded work that requires that they complete similar work.|
|Day 18: Thursday, September 26th||
In lab. Collected GW 4.
Worked with students on graphing functions in two space, and considering various view points. Also showed how we would graph the cross sections, as well as the level curves.
The Instructions also contain directions for creating a two way table. Asked students to complete this on their own.
|Day 17: Wednesday, September 25th||
Continued with section 9.6, and also section 11.1. These two sections overlap in terms of material.
Reviewed what we had covered on Monday, and continued discussion to include creating the picture of the contour (level) curves. Stressed that the cross sections are when the input variables are held constant, and the contours are when the output variables are held constant.
Students should address practice exercises from both section 9.6 and section 11.1
|Day 16: Monday, September 23rd||
Handed back tests and answer key.
Briefly mentioned the GW 4 which had been handed out on Friday, and asked if there were any questions.
Handed out Practice Exercises for Unit 2.
Began section 9.6. Discussed the domain of a function of two variables compared to the domain of a function of one variable. Discussed how to find traces (cross sections) which were parallel to the xz plane and yz plane. Discussed how these traces helped you begin to see the wire frame for the surface. We will continue with this discussion on Wednesday. Students should focus their energy on the graded work.
|Day 15: Friday, September 20th||
Test for Unit 1
Handed out GW 4 - Due at the beginning of class on Thursday, September 26th.
|Day 14: Thursday, September 19th||
Reviewed for test
|Day 13: Wednesday, September 18||
Answered some questions about some of the practice exercises.
Finished exercise 10 from section 9.5, and worked on a couple of other questions from that section. There are problems in section 9.5 which are more in depth than problems from other sections. I will be selecting a couple of these problems as a turn in assignment, and will not be putting the longer type of problems from this section on the test. The test WILL contain some of the concept type of questions from the practice sheet, but because the test is timed, I will not model questions off of the longer, more thought provoking, and many steps type of questions.
|Day 12: Monday, September 16||
Collected GW 3.
Finished material on lines, and presented how to consider the equation of a plane in space.
Worked on exercise 4, and began exercise 10. Asked students to continue thinking about how to accomplish what was asked for in exercise 10. We will pick up there on Wednesday, and continue working on some other exercises.
We will review for the test on Thursday. Test on Unit 1 on Friday, September 20th.
|11: Friday, September 13||
Handed back quizzes and answers, and talked briefly about what I was looking for on Question 6.
Announced test for unit 1 will be on Friday, September 20th.
Answered some questions students had about practice exercises.
Began section 9.5, developing the equation of a line in space. Did not quite finish that work. We will finish on Monday.
|Day 10: Thursday, September 12||
Quiz on sections 9.1 - 9.4 basic exercises.
Students had the last 20 minutes of class to work on GW 3. Gave students some specific feedback, and again reiterated that they should ALWAYS be making sure they answered the question WHY?
|Day 9: Wednesday, September 11||
Handed out back Graded Work 2, along with copies of specific answers from some student papers. Took time to explain how I grade, what I look for, what students should do if they have questions on anything I write on their paper, or feel that they should have received more credit. Spent time carefully going through answers to the questions, trying to indicate clearly where I needed more detail to answer the question "WHY?". Reminded students that one of the outcomes of the course is to ensure that students continue to develop the skills to explain complex material clearly. I will not typically spend as much class time reviewing turn in work, but since part of the objectives of this assignment was to make sure that students got up and running with the expectations of the course, it was important to spend time on this today.
Answered some questions from some of the practice exercises.
Quick Quiz tomorrow in lab. Students will then have the time in lab to talk to each other, or to me, about Graded Work 3. Extended the due date for graded work 3 to Monday, 9/16.
|Day 8: Monday, September 9th||
Finished work on section 9.3. Did not do a specific example of projection, but asked students to make sure they asked questions if they had difficultly connecting the notes to the exercises.
Announced Quick Quiz (no more than 15 minutes) on Thursday, September 12th. This quiz will cover the basic material from the practice exercises in sections 9.1, 9.2 and 9.3, as well as computing a cross product from section 9.4.
Began section 9.4 - Defined a cross product and worked through two examples to find cross products (# 6 and 8).
Began talking about area of a parallelogram, but will complete this material on Wednesday.
|Day 7: Friday, September 6||
Handed out Practice Exercises for Unit 1 (Purple).
Began section 9.3 - Dot Products. Got through most of the core material up to Projections. Worked on several of the even numbered exercises. Will complete section 9.3 on Monday.
|Day 6: Thursday, September 5||
Discussed briefly, again (see note from Day 5) why I had broken the exercise sets out into Basic, and Concept. iHad students work through a package that contained tutorial instructions on working with vectors in Mathematica (Tan).
Handed out Graded work 3,(Green) due on Thursday, September 12. Students began that assignment in the lab.
|Day 5: Wednesday, September 4||
Reminded students about GW 2. Answered some questions about question 10, giving students hints about how to think about the situation when they get a negative number.
Discussed the core material in section 9.2. Walked thru the section, pointing out some things that students should read, but which I did not emphasize as part of the practice material.
Explained clearly that tests and quizzes really come directly from practice. Quizzes will be based on the "skill builders", while tests will also include the questions that require applying the skills. Graded homework either asks for verbal explanations, or uses problems that I would not put on a test. Therefore, students need to be doing the practice in order to ensure they are prepared for tests. Doing the graded work is not sufficient to learn all the nuances of the course.
|Day 4: Friday, August 30th||
Quickly reviewed the answers to the lab assignment. Reminded students that GW 1 is due in today by 5 PM.
Handed out the Success Strategies Grade Sheet (green), and spoke briefly about it.
Handed out GW 2(green) and briefly discussed the purpose of the assignment.
Had students get together with others to discuss their answers to Practice Exercises. Circulated and answered some specific questions. Did a whole class review of # 39, and discussed how to convey the "Whys" to the approach.
|Day 3, Thursday, August 29th||
Gave students an assignment modified from one I had given to my Calculus 2 students last semester as a base to work from as they "reclaimed" their Mathematica skills. Had copies of the manual available for students to reference as needed to remember the core skills.
Worked with students as they discussed the ideas involved. The assignment reviewed defining functions, graphing functions, solving equations, finding derivatives, finding a general antiderivative, finding definite integrals, and using text regions to discuss ideas.
|Day 2: Wednesday, August 28th||
Handed out print out of sections 9.1 and 9.2 since the book is not available yet in the bookstore.
Finished discussing questions from Class Work sheet. Gave students the opportunity to get together again with some people they did not know to discuss some of the ideas from the sheet, as well as the practice exercises from 9.1
Students should continue working on the practice exercsise from section 9.1, doing the work in their Blue Book (each question on a separate page), and need to bring this work with them on Friday.
Tomorrow, we will be in the computer room, and will work on activities that help reclaim (or learn) essential skills with Mathematica.
|Day 1: Monday, August 26||Handed out General Information package (gold) and Graded Work 1 (green) which is due no later than 5 PM on Friday, August 30th.
Had students fill out Course Information cards. Discussed some of the questions on Day 1/ Class Work and Homework.(yellow) Students should do work For Wednesday indicated on the back of the sheet. Work should be done in the Blue Book provided.