Lectures

This is where I will post lecture files as the course progresses. I will try to post the lectures relatively soon after I have given them. Note that ET refers to the Early Tanscendental Edition (big book) and MV refers to the Multivariable version. I HIGHLY encourage you to do as many of the suggested problems as possible because we will not have any assignments and so this is the only way you will have to practise the material. In order to view lectures you will require a PDF viewer.

1.Vectors and Quadratic Surfaces

Date     ET MV Lecture  
Comments and Suggested Homework:
May 11 12.1
12.2		 13.1
13.2		 Lecture 1
Lecture 2		 13.1:odd 1-15, 19a, 23, 27, 29, 33, 35, 37, 39
13.2:1, 3, 5, 9, 11, 13, odd 19-31, 35, 37, 39
May 12 12.3 13.3 Lecture 3 13.3:1, 3, 5, 7, 11, 13, 15, 19, 23, 25, 27, 35, 37, 47
Note:I made a typo when drawing the angles on the vectors for direction cosines. I have corrected this, make sure you update your notes. Thanks to a student for pointing this out.
May 13 12.4 13.4 Lecture 4 13.4: 1, 3, 7, 9, 11, 15, 23, 25, 41
Note:Due to some confusion about the example with three points in a plane I have included a much more thorough analysis. At the end I've also shown why |axb|=|a||b|sinθ
May 14 12.5 13.5 Lecture 5 13.5:1, 3, 5, 13, 19, 25, 27, 31, 33, 43, 45, 49, 57, 61
Note:When doing the distance the plane has equation ax+by+cz+d=0 (as is corrected in the notes) and it is not ax+by+cz=d as I wrote in class.
10.5 11.5   Note:I will not be covering much (if any) of this in class. I suggest you read the section as it may be important later on in the course/it's just a good thing to know. I won't be testing you on this material for any of the midterms.

2.Functions of Several Variables and Partial Derivatives

Date     ET MV Lecture  
Comments and Suggested Homework:
May 18 14.1 15.1 Lecture 6 15.1:1,3,5,11-20(odd),23,30,35-38(odd),39-46(odd),55,57,59,61,63
May 19       Note:Midterm
May 20 14.3 15.3 Lecture 7 15.3:1,3,5,7,9,11,15-38(odd),39,41,43,45,47,49,51-68(odd),71,72,73,81,87
Note:There are two errors from lecture that have been corrected. One was the order of the derivatives when doing mixed derivatives and one was the wave equation example. The wave equation should be utt=-a2uxx. Also the extra example has been completed.
May 21 14.4 15.4 Lecture 8 15.4:1-6(odd),11,13,15,17,19,25,27,29,31,33,37,41
Note:I've added a tiny bit more of analysis and an example for those interested in the differentiability part. Keep in mind the examples we did in class. If you don't understand the full derivation of the tangent plane that is okay as long as you're able to take partial derivatives, find the plane and understand what it is (i.e. it is a linear approximation to the function at some point (a,b)). I also missed a bit on extending to more variables. It's very straightforward but none the less good to have a quick look at.
12.6 13.6   Note:This is another section not covered. However, like the conics, it importantly describes certain quadric surfaces which will come up quite often in the course. It is important to recognize these objects. I've posted a sheet in the extra material section listing some important quadric surfaces and their representations.

3. Calculus of Many Variables and Optimization

Date     ET MV Lecture    
Comments and Suggested Homework:
May 25 14.5 15.5 Lecture 9 15.5:1-12(odd), 13, 17, 19, 21, 23, 25, 27-34(odd), 35, 39, 45, 51, 53
May 26       Note:Midterm II
May 27 14.6 15.6 Lecture 10 15.6:5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,37,39,41,43,47,53,55,61
Note:I wrote a longer comment on the temperature example with the plus and minus. The essence is that it doesn't really matter in those particular problems because I can think of cooling in one direction or heating in the opposite direction. The sign plays a more important role if I specify a direction. So if I ask for the rate of change in a given u and you get a negative it means that the function (say temperature) is decreasing in that particular direction at that point.
May 28 14.7 15.7 Lecture 11 15.7:1,3,5-18(odd)[find critical values only],19,29-36(odd),39,41,43,45,47,49,51
Note:I added a note and example at the end for anyone who was struggling with understanding how the restricted domain affects things. Make sure to take a look at it because it is a little trickier than you may think. Also if the graph is hard to read, it's the same one from your text book.
         
June 1 14.8 15.8 Lecture 12 15.8:1,3-17(odd),19,25,27-39(odd),41
Note:I reworked my inequality example at the end. Originally I chose an unbounded set which is no good, there are no guarantees about finding the maximum since y can continue on to infinity. I have now bounded x and y.
June 2       Note:Midterm III
      Taylor Series Note:This will not be tested on any midterm OR final exam. However, it is still very beneficial to know!

4.Multiple Integrals

Date     ET MV Lecture    
Comments and Suggested Homework:
June 3 15.1
15.2		 16.1
16.2		 Lecture 13
Lecture 14		 16.1:3a,11,13,17
16.2:1-22(odd),25,27,29,35
June 4 15.3 16.3 Lecture 15 16.3:1,3,5,7-28(odd),31,39-50(odd),51,55
June 8 15.4 16.4 Lecture 16 16.4:1,3,5,7-14(odd),15,17,19-27(odd),29,31,33,35,37
June 9       Note:Midterm IV
June 10 15.6 16.6 Lecture 17 16.6:1,3,5,7,9-22(odd),29,33,35
Note:Please note that I didn't format the notes correctly today. You might have to rotate the file in order to view it properly.
June 11 15.7
15.8		 16.7
16.8		 Lecture 18 16.7:1,3,5,7,9,11,13,15,17-26(odd),27,29
16.8:1,3,5,7,9,11,13,15,17,19,21-30(odd),35,37,39,44
Note:I've included (hopefully) a better drawing of the wedge. A lot of this integration section can be hard to visualize. It makes it that much more important to understand the math well.
June 15 16.5 16.5 Lecture 19 16.5:1,3-10(odd),11,13,15,17,19,27,29
16.6:37,39
16.7:25
16.8:29,32(a and b), 33
Note:The textbook covers applications throughout, since we did it all under one lecture, there are problems from other sections.