Mat 223 Daily Log

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Day 54:  Tuesday 4/29:   Handed out last Graded Work, and gave students time in lab to work on that, or to continue working with practice exercises from Chapter 12.  
Day 53:  Monday, 4/28:  Went through the concept of a line integral, and showed students how to develop the integral first as the concept, and then to work with this concept to get to a point where we have an integral that we can actually work with.  Worked through the example from the Mathematica material by hand so that students could get a sense of the process of creating a line integral.  
Day 52:  Thursday 4/24:  Had students work on Mathematica to create Vector Fields and curves in vector fields after briefly discussing the material.  Talked about ideas as students created the material on Mathematica.  We will talk more fully about line integrals on Monday.  
 Day 51:  Wednesday, 4/23:  Worked more on triple integrals.  Did more work with examples from section 12.8.  

Day 50:  Tuesday, 4/22:  Worked on  problem 24 from section 12.7 with triple integrals in rectangular coordinates.  Began  problem 12 from section 12.8 that we first set up in cylindrical coordinates.  Asked students to come in tomorrow with the integral set up in rectangular coordinates.

Handed out copies of the end of semester calendar with notes on it. (Extras in the box outside my door).  Handed out information on using the Success Strategy Points, with an Example of the 3 Possibilities.

 
Day 49:  Monday, 4/21:  Teacher out  
Day 48:  Thursday, 4/17:  Developed the conversion formulas and the dV component for both cylindrical and spherical coordinates.  We will work on as many problems as possible next Monday and Tuesday.  

Day 47:  Wednesday, 4/16:  Started discussing triple integrals in rectangular coordinates.  Emphasized that we enter the solid region of integration parallel to an axis, and then project the solid region into the remaining plane and revert to techniques of double integrals.

Worked through exercise 16 from 12.7.  This problem required remembering some information from earlier in the course in terms of finding the equation of a plane.

 
Day 46:  Tuesday, 4/15:  Test on optimization, chain rule, and chapter 12 sections 1 - 4.  
Day 45:  Monday, 4/14:  Had students do Evaluations at the beginning of the class.  spent 2nd half of class answering questions for the test tomorrow.  
Day 44:  Thursday, 4/10:  Spent time working on some integration, as well as reviewing some key ideas about regions of integration, and how we determine the limits of integration.  
 Day 43:  Wednesday 4/9:  Had students work on numbers 8 , 12 and 28 from section 12.4.  Also asked them to work on problem 40 and 52 from page 825  

Day 42:  Tuesday, 4/8:  Finished problem 14, and did two more problems with students.  Told students to complete the integration.  I will bring the answers to class tomorrow.

 

Day 41:  Monday, 4/7:  Began section 12.4 - Polar coordinates and double integrals with polar coordinates.  Developed the concept that dA is r dr dtheta.

We would use polar coordinates either because of the boundary region, or because of the integrand.

Started exercise 14, but didn't get to finish it.

 

Day 40:  Thursday, 4/3:  Finished section 12.3 - Worked on another example.  

 

Day 39:  Wednesday, 4/2:  Began section 12.3 - setting up definite integrals over non rectangular regions in the plane.  Discussed that depending on the region or depending on the integrand, we might find it better to work in dx dy order, or dy dx order. Worked through an example.

 

Day 38:  Tuesday, 4/1: Students continued work on GW 8 while I worked with groups as they had questions.  Extended due date to Monday, 4/7.

 

Day 37:  Monday, 3/31:Began Chapter 12.  Reviewed how we began considering definite integrals in Calculus 1.  Extended ideas to definite integrals for functions of two variables.  Completed an example of a double integral.

 

Day 36:  Thursday, 3/27:  Worked with groups as students had questions on their two assigned problems.

 

Day 35:  Wednesday 3/26:  Worked through a boundary problem, helping students see that this was just an extension of the extreme value theorem from Calculus 1.  Showed that we had to consider 3 different scenarios... general critical points, critical points on the boundaries, and endpoints.

Assigned students two problems that they need to work on for tomorrow.  Tomorrow students will meet in pairs to work through more ideas.  Graded Work 8 lays out the process.

 

Day 34:  Tuesday 3/25:  Finished our work from Monday.  Developed the 2nd derivative test, and used it for a specific example.  Handed out Practice Exercises for Unit 3.  Handed out Mathematica Instructions for working with Optimization.

 

Day 33:  Monday 3/24: Collected GW 7.

Began section 11.7 - optimization.  Discussed why we would want to consider the second order Taylor Polynomial in terms of determining the behavior we would have for a function at a critical point.  Mapped out the three options.... paraboloid, saddle,  or a cylinder.  Considered a basic quadratic in two variables, and showed how we would compute the discriminant... the value that determines which of the three scenarios we have.

 

Day 32:  Thursday 3/20:  Students continued their work on GW 7.  Again, I answered questions for students as they encountered them.

 

Day 32:  Wednesday 3/19:  Presented the Chain Rule (Section 11.5) and completed an example showing both how to generate the formula, and then how to apply it to get the final answer.

 

Day 31:  Tuesday 3/18:  Students worked in the lab on GW 7.  I worked with individuals as questions arose.

 

Day 30:  Monday, 3/17:  Handed back tests with answer key.  Talked briefly about the tests.  Results were not great.  Students MUST commit to doing the practice exercises if they want to do well in the course.

Collected GW 6.

Continued work with the gradient vector.  Reviewed the key concepts of the gradient vector, using a sheet with a contour diagram on it to help reinforce that the gradientt vector lives in the domain plane.  Found the gradient vector for 4 points.  Drew the points and the vectors on the contour diagram.  Discussed major concepts.  Looked at the gradient vector field, and discussed what it told us about the surface.

At the end of class, handed out Mathematica Instructions for working with gradient vectors, as well as GW 7.  Students will have the opportunity to work on this material in the computer lab tomorrow.   Strongly suggested that students at least read through the instructions tonight so they have a sense of what they will be workig on.

 

Day 29:  Thursday 3/6Test on Unit 3.  Happy Spring Break!!

 

Day 28:  Wednesday 3/5 Hand back GW 5, and spent some time discussing the assignment.  Students need to concentrate on doing their best work for the graded work.  Extended the due date for GW 6 until after the break so that students would make sure it really was their best work!

Answered review questions for test tomorrow.

 

Day 27:  Tuesday 3/4Teacher out sick.

 

Day 26:  Monday 3/3Worked on considering the gradient vector,and why it was important.  Showed that the maximum rate of increase is in the direction of the gradient vector, and showed that the gradient vector is perpendicular to the level curve through the point (a, b). Emphasized that the gradient vector is in the domain plane.

Did an example, and discussed how we would interpret the answer.  We always interpret derivatives as change in output per 1 unit change in input - or in this case in distance traveled in a particular direction.

 

Day 25:  Thursday, 2/27: Began section 11.6 - Directional Derivatives.  Showed how we could replace the difference in output values in our limit definition of derivative with the differential to see that the directional derivative was essentially the dot product of a vector which we called the gradient, and a unit vector in the direction we wanted to move.

Worked on two examples from the text book to compute directional derivatives.  While we worked on the first example, established that this was essentially a three step process:  1) Make sure you have a unit vector in direction you want to move.  2) Find the gradient vector at a particular point, 3) Form the dot product of the two vectors.

Test on Unit 2 will be on Thursday, 3/6

 

Day 24:  Wednesday, 2/26:Picked up where we left off.  Discussed that the increment was the actual change in function values, and the difference in output values along the tangent plane was called the differential.  By local linearity, the differential is a good approximation for the increment as long as our point is close to the point of tangency.

Completed an example that asked for finding the increment and differential for a particular function.

 

Day 23:  Tuesday, 2/25:  Collected HW 5.  Discussed what GW 6 entailed.

Worked on section 11.4 - tangent planes and linear approximations.  Had students recall information about the tangent line and local linearity from calc 1, and Euler's method from Calc 2.  Used that information to help create the equation of the tangent plane for functions of two variables.  Talked about using this equation to create a form that showed the difference in output values along the tangent plane.  Will continue with these ideas tomorrow.

 

Day 22:  Monday, 2/24:  Teacher had to be at a meeting during class time.  Sent students an email asking them to work through the tutorial instructions on Partial Derivatives.  When they have completed this work, it should be submitted in the Angel Drop box.  Here is the assignment for Graded Work 6.

I will collect GW 5 on Tuesday, and we will continue with our work in the chapter.

 

Day 21:  Thursday, 2/20:  Asked if there were any questions on GW 5.  No one had questions.

Worked on several examples of finding the first order partial derivatives after reviewing what we had discussed on Wednesday.  Extended ideas into the second order partials, and showed that there were 4 second order partial derivatives.  Through one of the examples we worked on in class, showed that the mixed order partials were actually equal.  This will always be the case as long as we have the same number of each type of variable, though we cannot currently prove that.

 

Day 20:  Wednesday, 2/19:  Handed back GW 5 with answers.  Talked briefly about the homework.  The explanations are absolutely essential...and take time and energy to make sure that the "whys" are answered. 

Had students individually recapture what they remembered about derivatives of functions of one variable.  Had students share ideas with each other.  With student input, reviewed key concepts of derivative of f(x).  Used this information to springboard into the concept of partial derivatives with respect to x and y.  Developed the geometric and algebraic concepts for the partial derivative of f with respect to x.  Worked through an example of finding the partial derivatives.

 

Day 19:  Thursday, 2/13:  Snow Day  Students should work on the instructions for graphing in 3 space (see link on day 18).  These need to be submitted in Angel, Learning Modules, Graded Work, GW 5 - Preliminary Tutorial, and will count as 5 points towards GW 5.

Sent students GW 5 over email.  Please get this started soon!

 

Day 18:  Wednesday, 2/12:  Discussed another function completely using a Mathematica generated Handout.  Considered domain and range from an analytical point of view.  Considered the cross sections.  Considered the contour diagram.  Used this information to fully discuss the function behavior.

Handed out Mathematica instructions for Beginning Graphing in Three Space

Students should complete the work from these instructions as 5 points towards their next homework grade.

 

Day 17:  Tuesday, 2/11:  Continued discussion of the function we worked with yesterday.  Talked about and computed the rates of change, and discussed what that told us about the function.  Created the contour curves (level curves) for z = 0, 2, 4, 6.  Graphed these, and observed the behavior of the contour diagram.

 

Day 16:  Monday, 2/10:  Handed back tests and answers.  Emphasized how important it is to make sure that students read through the notes, and see how the notes pretain to the practice exercises.  Encouraged students to do a Test Analysis for Success Strategy Points.

Started Section 9. 6.  Emphasized the domain of a function of two variables is a set of ordered pairs in the plane.  Did an example of a finding a domain. 

Began looking at cross sections of a function to help create a "wire framework" for the surface.  We will continue to work tomorrow.

 

Day 15:  Thursday, 2/6:  Test on Unit 1.

Handed back Graded Work 3 with answers (pink)

Handed out Graded Work 4 - Due on Wednesday, 2/12

 

Day 14:  Wednesday, 2/5:  Snow day!  DCC cancels all classes.

 

Day 13:  Tuesday, 2/4:  Review for test.

 

Day 12:  Monday, 2/3:  Handed back quizzes with pink answer key.  Reminded students that they could do a quiz analysis for Success Strategy Points.  Check on my web site for further details for this option.  It is NOT just redoing the questions (since you now have the answers!), but rather analyzing what went right or wrong.

Handed out answers to GW 2 (yellow), and encouraged students to look at the answers carefully in terms of understanding what I am looking for in terms of written explanations.

Discussed a strategy for working on exercise 19 in section 9.4 on page 661.

Reviewed quickly the equation of a line in space, and showed how we could move from the parametric form to the symmetric form.

Showed how to derive the equation of a plane given a point in the plane and a vector perpendicular to the plane.  Did a quick example of writing the equation of a plane given a point and a perpendicular vector.  Worked on exercise 24 on page 671.  Students should finish up this question for tomorrow, and need to work on some of the practice exercises for this section.

Reminder:  Test on Unit 1 on Thursday, 2/6.

 

Day 11:  Thursday 1/30: Discussed how to create an equation for a line.  Tried to have students see that all the key information was in the beginning of section 9.5, and used the picture from the book, and read through the discussion, actively showing students how to go back and forth from text to picture to help understand what is written.  Ended with an example of finding the parametric equations for a line given two specific points. 

Students should work on exercises 1 - 19 odd.  I will cover the rest of the material in the section early next week.

Test on Unit 1 will be on Thursday, 2/6.

Last half of class, students took a quiz on the basics from sections 1 to 4.

 

Day 10:  Wednesday 1/29:  Discussed again the importance of having the beginning points of the vectors coinciding when you are determining the angle between the two vectors.  Reviewed how you could be getting the angle which is the exterior angle of a triangle rather than the angle you are intending to get.

Showed how to use the geometric definition of dot product to find the angle between the two vectors.  This is the formula that Mathematica is actually employing when you use VectorAngle command.

Reviewed how to determine if two vectors were parallel.  There are 3 different approaches that you can use:  1) scalar multiples, 2) using ideas from dot product, 3) Using ideas from cross products.

Showed that the magnitude of the cross product was the area of the parallelogram formed by the two vectors as sides.

Emphasized how important it is for students to be reading the examples in the text book, and making sure they are completing the practice exercises and asking essential questions.

 

Day 9:  Tuesday, 1/28:  Handed back GW 2, and asked students to make sure they shared the results with the group.

Checked that students had complete the work from the sheet of instructions for Mathematica with vectors.  this will add 5 points to the GW 3 assignment, so that the assignment will truly be out of 40 points, rather than 35.

Students worked on GW 3, and I offered help as questions arose. 

Reminder:  Quiz is on Thursday! 

 

Day 8:  Monday, 1/27:  Answered a question from the practice exercises (# 23 from section 9.2) and extended the results.

Handed out GW 3, and emphasized that I needed students to have completed the work on the yellow sheet, and show me that they had completed that before they could begin the work on GW 3 in lab tomorrow.

Continued discussion about Dot Products, and discussed how to use dot products to find projections of one vector on another.  Emphasized that we had a scalar component, and that we then multiplied this scalar component by a unit vector in the same direction as a.

QUIZ on Thursday - Will cover sections 9.1, 9.2, 9.3, and forming a cross product from section 9.4.

 

Day 7:  Thursday 1/23:  Answered a question from the practice exercises.  Presented the geometric definitions for Dot product and cross product. (Section 9.3 and 9.4)  Presented algebraic approaches to create both of these products.  Emphasized that the dot product is a scalar, while the cross product is a vector.  Worked with students on a specific example for each.  Emphasized that if two vectors are perpendicular (orthogonal, or normal), then the dot product of the two vectors should be 0.

Students should work on the beginning level practice exercises for these sections.  I will present more material from each of these sections on Monday.

Handed out instructions for using Mathematica for vectors (yellow sheet ) extra copies in the folder outside my door.  Students need to complete this work by Tuesday.  The next turn in homework will involve using the patterns laid out in this material.

 

Day 6:  Wednesday 1/22: Collected GW 2.  Presented material from section 9-2:  Vectors.  Reiterated that students should be reading the textbook after I presented material in class, and working with the practice exercises for that section.   Remember:  Practice Exercises are listed by section on the purple Practice Exercise sheet.

 

Day 5:  Tuesday 1/21: Hand out new Success Strategy Grade sheet (pink) with holes punched correctly!  Extras are in the bin outside my office.  Handed out How to Save to the Angel Toolbox instructions (gold).  Hand out Issue with Automatic Positioning (gold) for Mathematica.  Hand out my updated schedule (see my webpage).  I had to move one of my office hours.

Discussed information from section 9.1 in the text book.  Asked students to read the text book, and to work on practice exercises.  I will hand out Practice Exercises for Unit 1 tomorrow.  I could not get to the copy machine this morning!

Homework:  Section 9.1, page 638, 3 - 11 odd, 21, 27, 29, and then 19, 39

 

Day 4:  Thursday 1/16:  Work in lab on GW 2.  Showed students how to create a table of values.  Reinforced that students need to make their presentation clear, with a minimum of command lines.  Function definition and solve commands should be included in the body of the report, but the definitions to create graphs and tables should be moved to a "Background Page". 

Homework:  Continue to work together on project.  No class on Monday.  GW 2 is due at the beginning of class on Wednesday.

 

Day 3:  Wednesday 1/15: 

Discussed textbook, and encouraged students to consider options.  We ARE using the 2010 edition of the textbook, as listed on the syllabus.

Had students check and make sure they have appropriate material in their blue books.  Gave them a few minutes to meet a few more people.  Gave about 15 minutes to meet with their group for GW 2, and make a plan for getting the most accomplished tomorrow.  Tomorrow, students will be given the time to work in the lab on the assignment.

Started discussing some of the key ideas in Chapter 9 section 1.  Discussed inputs, outputs, points on graph, axes, and Right hand rule for 3 space.  We will continue this discussion next week. 

Homework:  Students need to continue to reclaim their Mathematica skills ( or gain them if they have not used Mathematica before).  Students need to focus on how they will explain the material for GW 2 so that they can blend their voices with the time in the computer lab tomorrow. 

 

Day 2:  Tuesday 1/14: 
Put students in groups of 3 at the computer based on whether they had said they had No, Low, Medium or High Mathematica skills.   Hand out GW 2 (green), and have students begin working on it - with 2 using the computers, and one "supervising".  The end goals are to have all students become familiar with how to use Mathematica for the skills listed on the assignment, and to work together to blend their "voices" into one coherent assignment.  Each group will be submitting one assignment. 

 

Day 1: Monday  1/13:   Handed out syllabus (white) General Information package (gold) and Graded Work 1 (green) which is due no later than 5 PM on Friday, January 17th.

Had students fill out Course Information cards.  Had students meet some other students in class, and begin to discuss Remembering Some Calculus. (yellow)  Students should have notes in the blue books provided for each of these questions.

Homework:   Students should complete working on the questions on the Remembering Calculus sheet in their blue book, and bring that material with them tomorrow.  Students need to also review the core Mathematica material that they should know listed at the top of the yellow sheet.

 
   
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