| Day | Time | Room | |
| Lecture | TR | 8:05am-9:25am | Skiles 202 |
| Recitation | MW | 8:05am-8:55am | Skiles 202 (section B1) & 153 (section B2) |
Final Examination Thursday 13 Dec, 2:50-5:40, 202 Skiles (Our usual lecture room)
| Instructor: | |||
| Teaching Assistants: | Stephanie Sigalas (section B1) |
Peter Karasev (section B2) |
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| email: | |||
| Office: | Skiles 167 |
Skiles 230 |
Skiles 230 |
| Office Hours: | TR 10:05-10:55 |
W 12:30 - 1:30 |
F 2:00 - 3:00 |
| Math Lab Hours: | M-R 11-4 |
TBA |
TBA |
The MathLab is located in Skiles 257. Monday through Thursday there will be tutors available to help you with your Math questions. Please talk to one of us or send us an email to set up a time for an individual appointment.
Below I have posted a collection of problems from which your final exam will be selected. I reserve the right to change something minor such as a number in a problem if I see fit, but for the most part your final exam will consist of problems directly from this collection. There may be an exception for some True/False questions that will not be a part of the following collection.
Note that problems for the final exam can also be taken from any of our previous exams as well as the new problems posted.
Further note that I have been having problems with my gatech email. If you need to contact me send me a message at william.mcclain at gmail dot com
I will have office hours on Tuesday and Wednesday from 12noon until 2:30
WARNING: Given that you have access to the final exam problems prior to the exam you will be required to show all of your work in detail in order to receive credit on the exam!
Textbooks: Calculus - one and several variables, 10th edition, by Salas, Hille, Etgen and Linear Algebra From the Beginning, First edition by Carlen and Carvalho.
The topics we will cover can be broken down into the following blocks:
Block 1: Taylor Approximation and Infinite Series. Sections 10.5-10.7, and 11.1-11.6 in Salas, Hille and Etgen (6 lectures)
Block 2: Power Series and Numerical Integration, and elementary differential equations. Sections 11.7-11.8 and 8.7-8.9 in Salas, Hille and Etgen (4 lectures)
Block 3: Introduction to Matrices, Row Reduction and Solution of Linear
Systems. (7 lectures)
Block 4: Linear Independence, Kernel and Image, Gram-Schmidt
procedure, least square problems. (6 lectures)
Block 5: Volume, Determinants, Eigenvectors, Eigenvalues and Geometric Topics. (7 lectures)
There will be a homework problem to be turned in EVERY MONDAY in recitation. Homework will be due at the beginning of recitation.
There will be a 10 minute quiz EVERY WEDNESDAY except during test weeks.
Quizzes will be given during the first 10 minutes of class.These quizzes cover all the material that has been discussed in class
until and including Tuesday before the quiz.
There will be three 1 hour tests, again covering the material discussed
in class until and including lecture before the test.
Test 1: Monday, September 24.
Test 2: Wednesday, October 31.
Test 3: Wednesday, November 28.
Your grade will be based on your scores on homework, quizzes, hour tests, and the final exam.
At almost every recitation class you will either turn in one homework problem or take a brief quiz.
Your grade will be weighted as follows:
| Homework (lowest 2 scores dropped) | 10% |
| Quizzes (lowest 2 scores dropped) | 10% |
| Hour tests | 45% |
| Final Exam | 35% |
Letter grades will be based on the overall average at the end of the semester, according to the scheme
| 90 < = average | A |
| 80 < = average | at least B |
| 70 < = average | at least C |
| 60 < = average | at least D |
| average < 50 | F |
There may be a curve at the end of the semester (not for single exams or quizzes), but this will not be decided until after the final. Scores below 50% will not be curved to pass.
| Due | Problem | Comments |
| M 08/27 | SHE 11.6: 42 |
Recall that these problems are to have a very neatly written solution and be turned in. |
| M 09/10 | SHE 12.8: 28 |
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| M 09/17 | SHE 9.1: 17 |
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| M 10/01 | CC 1.1: 11 |
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| M 10/15 | Find the point on the plane x + 2y - z = 1 closest to the point p = (2,1,2). |
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| M 10/29 | Find the best fit quadratic to the following data points using the method of Least Squares: .. (1,2) (2,5) (4,8) (7,6). (Recall a quadratic is just a function of the form a(x^2) + b(x) + c ) |
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| M 11/5 | Is the solution set to the equation 2x + y +3z = 0 a subspace of R^3? If it is SHOW that it satisfies the definition of a subspace. If not, show a contradiction to the definition of a subspace. |
The problem as written before had a typo. It is now correct and you will be able to turn it in on Wednesday. |
| M 11/12 | Find the matrix of projection onto the line parameterized by t(1,2,1). |
(1,2,1) represents the column vector with top coordinate 1, middle coordinate 2, and bottom coordinate 1. |
| M 11/19 | Let A be the matrix of problem 3.8.11. Find an orthonormal basis for the image of A. |
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| M 11/26 | Let u = (1,0,2), v = (1,1,1), w = (6,2,6). Find the volume of the parallelopiped spanned by u,v and w. |
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| M 12/03 | Find the eigenvalues and eigenvector for the matrix, A, with first row (1 -2 0), second row (1 2 0) and third row (0 2 -1). |
| Lecture | Problems | Comments |
| T 8/21 | SHE 11.5: 3, 12, 23 SHE 11.6: 5, 6, 13, 28, 51, 54 SHE 11.7: 1, 3, 8, 9, 22, 45, 51 |
In class I misspoke; I stated we were in section 10.5 - 10.7 when in fact we were in those same sections of chapter 11. I.e. 11.5 - 11.7. |
| R 8/23 | SHE 12.1: 8, 13, 18, 23, 25 SHE 12.2: 1, 3, 7, 9, 12, 22, 28 SHE 12.3: 1, 2, 4, 10, 16, 21, 27, 29, 33, 36, 50 |
In section 12.2 we'll go over problems 12 and 28 in recitation but still attempt them on your own. Same for problems 33 and 50 in 12.3. |
| T 8/28 | SHE 12.4: 1, 5, 6, 8, 16, 26, 28, 30, 36 SHE 12.5: 2, 4, 6, 7, 9, 18, 27, 32, 33, 34, 35, 41 |
:) |
| R 8/30 | SHE 12.6: 1, 2, 5, 9, 11, 14, 19, 30, 32, 53, 56 |
There will be no homework problem to be turned in Monday 03/09. Have a good weekend. |
| T 9/04 | SHE 12.7: 23, 24, 27, 29 SHE 12.8: 3, 4, 5, 16, 23, 24, 26, 29, 31 |
:) |
| R 9/06 | SHE 12.9: 1, 6, 7, 8, 10, 14, 17, 19, 20, 24, 25, 27, 28, 36, 39, 41, 42, 43, 44, 45, 56 |
See above for homework problem to be turned in on Monday. |
| R 9/13 | SHE 9.1: 12, 15, 18, 20, 25, 37, 42 SHE 9.2: 6, 7, 15, 18, 24, 28 |
I'll post a practice exam soon. Also, see above for HW to be turned in Monday. |
| R 9/06 | For the following integral: Integral (e^x * 1/x) from 1 to 3 [that is read in English as E to the power of X times 1 over X integrated from 1 to 3] (a) using n=6 estimate the integral using the right-endpoint, left-endpoint and midpoint rules. (b) approximate within 1/100 error using the trapezoidal rule. (c) approximate within 1/100 error using Simpson's rule. |
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| T 9/25 | CC 1.1: 1, 5, 6, 9, 11 CC 1.3: 1, 2, 3, 4 |
Note that we are now using the Linear Algebra text. See above for HW to be turned in on Monday. There is no quiz on Wednesday this week |
| R 9/27 | CC 1.2: 1, 3, 4, 7, 9, 10, 11, 19, 21 |
Exams were handed back in lecture today. |
| T 9/25 | CC 1.4: 1, 3, 5, 6, 11, 14, 16 CC 1.5: 3, 5, 6, 11 CC 1.6: 1, 3 |
No Homework to be turned in Monday since it is Fall Break. |
| R 9/27 | CC 2.1: 1, 5, 6, 7, 9, 10, 11, 13, 18, 21 |
There will be a quiz Wednesday next week. |
| R 10/11 | CC 2.1: 28, 29, 30 CC 2.3: 1, 2, 8, 9, 4, 7 |
For problems 8 and 9 in section 2.3, PARAMETERIZE THE SOLUTION SET. |
| T 10/16 | CC 2.3: 11, 12, 13, 14 CC 2.4: 1, 4, 8, 9, 12 |
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| R 10/18 | CC 2.4: 14 CC 2.5: 1, 2, 3, 4, 8abc, 10, 11 |
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| R 10/18 | CC 2.5: 5 CC 3.1: 1, 2, 5, 6, 8, 11, 12 CC 3.2: 1, 2 |
for 6 and 8 just parameterize the image. |
| R 10/18 |
CC 3.2: 1, 2, 3, 5ab, 6, 7 |
for 5 just find the best fit line and quadratic. practice exams are posted below. |
| R 11/01 |
CC 3.3: 1, 2, 6, 9, 11, 14, 15 |
for 5 just find the best fit line and quadratic. practice exams are posted below. |
| R 11/08 |
CC 3.5: 1, 2, 3, 5 CC 3.6: 1, 2 What would be different if A had full rank? (i.e. rank=4) |
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| T 11/13 |
CC 3.6: 4, 5, 6, 9, 11, 13 CC 3.7: 1, 4, 8 |
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| R 11/15 |
CC 3.8: 1, 2, 7 CC 4.1: 1, 2, 3 |
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| T 11/20 |
CC 4.2: 1, 2, 3, 4 CC 4.3: 1, 2, 3, 4, 5 |
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| R 11/29 |
CC 5.1: 1abc, 2abc, 3abc, 8, 9 CC 5.2: 1, 2, 3, 6, 9, 11, 12, 16 |
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| T 12/4 |
CC 5.3: 1, 3, 5, 6, 7 |
Links to some sample exams for exam 3. Pay no attention to problem 4 from each exam. We have not yet covered the material required. Also, be prepared to work out a change of basis problem and be able to reprent vectors with respect to different bases. Here are the links: ( Sample 1 Sample 2 Sample 3)