Math 1512 Fall 2012 Course Information

Honors Calculus II, Math 1512 Fall 2012 Course Information

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Final information:

Final will take place in Skiles 254 (lecture room) on Wednesday, December 12, 8:00-10:50am
There will be extra office hours on Friday, Dec 7, 8:15-8:55am.
Tentatively, the test will consists of 8 problems, one of which will be ten true/false questions; in the true/false problem you will not have to justify your answer. In the other problems a justifications will be required.
On the true/false question you need not provide any explanations. For the other problems a justification is required. When explaining you should aim to be concise, and write in complete grammatically correct sentences.
Four pages (two-sided if needed) of "help sheet" will be allowed on the final; you may write/type anything there.
You must bring your Georgia Tech ID (the buzzcard) to the test and show it to the professor when you hand in the test.
No electronics (such as calculators, computers, mobile devices) is allowed on tests.
Bring your questions to the review during Friday lecture.

Basic skills/facts of the material covered since Test 3 are here.

Practice problems for the final.

7.3: 16, 20, 25, 28, 29, 30, 32, 33, 34.
7.4: 24, 26, 30, 69, 70, 72.
7.5: 16, 26 (where you not only find eigenvalues, but also find a 4x4 matrix S that that makes the matrix in 26 similar to a block matrix with two 2x2 blocks as in theorem 7.5.3).
exp(A) problems: Compute matrix exponential exp(tA) for various matrices in 7.3 (such as #28), any diagonalizable matrix in 7.4, and the matrices in 7.5 (#16, 26).
True and false in chapter 7: do as many as you can.
8.1: 6, 15, 21, 22, 29.

Have trouble visualizing solutions to systems of differential equations? Play with PPLANE developed by John Polking (click on PPLANE applet, enter your favorite linear two-by-two system and see the trajectories. The program also handles nonlinear systems, see Polking's demo.

Test 3 Information:

Test 3 solutions are here
Test 3 practice questions are here.
Test 3 will take place in recitation, on Tuesday, November 20th.
Test 3 will cover sections 5.3, 5.4, chapter 6, sections 7.1, 7.2, 7.3. and the best way to prepare is to do homeworks 9-12. For extra practice do exercises similar to those in homework.
The test will consists of 4 problems, one of which will true/false; in the true/false problem you will not have to justify your answer. In the other problems a justifications will be required.
On the true/false question you need not provide any explanations. For the other problems a justification is required. When explaining you should aim to be concise, and write in complete grammatically correct sentences.
A one-page (two-sided if needed) "help sheet" will be allowed on midterms; you may write/type anything there.
You must bring your Georgia Tech ID (the buzzcard) to the test and show it to the TA when you hand in the test.
No electronics (such as calculators, computers, mobile devices) is allowed on tests.
Bring your questions to the review during Monday lecture.

Test 2 Information:

Test 2 solutions are here
Test 2 basic skills are here
Test 2 will take place in recitation, on Tuesday, October 23rd.
Test 2 will cover Chapters 3 and sections 5.1, 5.2, and the best way to prepare is to do homeworks 5-8. For extra practice do exersices similar to those in homework. More details will be posted here closer to the test date.
Practice true/false problems for 5.1, 5.2 on pages 247-248 are 2, 5, 7, 17, 18, 19, 21, 25, 27-32, 34, 44, 45, 48.
The test will consists of 4 problems, one of which will true/false; in the true/false problem you will not have to justify your answer. In the other problems a justifications will be required.
On the true/false question you need not provide any explainations. For the other problems a justification is required. When explaining you should aim to be concise, and write in complete grammatically correct sentences.
A one-page (two-sided if needed) "help sheet" will be allowed on midterms; you may write/type anything there.
You must bring your Georgia Tech ID (the buzzcard) to the test and show it to the TA when you hand in the test.
No electronics (such as calculators, computers, mobile devices) is allowed on tests.
Bring your questions to the review during Monday lecture.

Test 1 Information:

Test 1 solutions are here
Test 1 will take place in recitation, on Thursday, September 20th.
Test 1 will cover Chapters 1 and 2, and the best way to prepare is to do homeworks 1-4. For extra practice do exersices similar to those in homework. More details will be posted here closer to the test date.
The test will consists of 4 problems, one of which will true/false; in the true/false problem you will not have to justify your answer. In the other problems a justifications will be required.
Here is a practice test:
1. Given a specific vector b, and a specific 3-by-3 matrix A that depends on a parameter k, decide when Ax=b has infinitely many solution (make your own A and b for practice).
2. Find all n-by-n matrices A such that all the entries of A equal k, and A^2=-A.
3. #40 on page 68.
4. six true false question similar in form (but not necessarily in content) to those on the homework.
On the true/false question you need not provide any explainations. For the other problems a justification is required. When explaining you should aim to be concise, and write in complete grammatically correct sentences.
A one-page (two-sided if needed) "help sheet" will be allowed on midterms; you may write/type anything there.
You must bring your Georgia Tech ID (the buzzcard) to the test and show it to the TA when you hand in the test.
No electronics (such as calculators, computers, mobile devices) is allowed on tests.
Bring your questions to the review on Wednesday lecture.

HW12 There will be no quiz based on this homework but it will be used in the test 3. Skip section 7.1 (except for definitions of eigenvector and eigenvalue, and Examples 1-4). Read sections 7.2, 7.3. Do the following problems 7.1: 2, 18, 19, 22, 36, 38. 7.2: 2, 10, 16, 32, 35. 7.3: 16, 20, 25.

HW11 Read sections 6.3, and all chapter 6. Do the following problems 6.3: 2, 3, 13, 16, 18; True or false on page 292: 2, 3, 11, 13, 16, 31, 32, 34, 38. Quiz 10 will be given on Thursday, November 15st, at the beginning of the recitation.

HW10 Read sections 6.1, 6.2. Do the following problems 6.1: 18, 36, 50, 54, 56; 6.2: 8, 30, 41, 42, 53. Quiz 9 will be given on Thursday, November 8st, at the end of the recitation.

HW9 Read sections 5.3, 5.4. Do the following problems 5.3: 26, 31, 38b, 40; 5.4: 4, 17, 18, 24, 30, 32, 37. Quiz 8 will be given on Thursday, November 1st, at the end of the recitation.

HW8 Read sections 5.1, 5.2. Do the following problems 5.1: 10, 11, 14, 16, 17, 28, 30, 35, 36; 5.2: 4, 34, 36, 39, 44, 45. There will be no quiz on this material due to the Fall break (which we will enjoy on October 15-16). Still 5.1-5.2 will appear on Test 2 which takes place on Tuesday, October 23, so you have to digest the material by then.

HW7 Read sections 3.3, 3.4. Do the following problems 3.4: 48, 52, 54, 58, 62, 70, 71; True or False on page 151: 12, 19, 20, 30, 32, 42, 50. Quiz 7 will be given on Thursday, October 11th, at the end of the recitation.

HW6 Read sections 3.3, 3.4. Do the following problems 3.3: 24, 28, 30, 34, 36, 44, 58, 76; 3.4: 14, 22, 28, 38, 40, 44. Quiz 6 will be given on Thursday, October 4th, at the end of the recitation.

HW5 Read sections 3.1, 3.2. Do the following problems 3.1: 10, 15, 36, 39, 40, 44; 3.2: 6, 20, 36, 44. Extra problem: let A be a 2x2 matrix such that Ae_1=e_1=Ae_2. Is the kernel and the image of A orthogonal? Explain. Quiz 5 will be given on Thursday, September 27th, at the end of the recitation.

HW4 Read section 2.4. Do the following problems 2.4: 10, 30, 32, 36, 42, 45, 70, 82, 106; True or False on page 98: 8, 20, 42, 44, 52. Quiz 4 will be given on Tuesday, September 18th, in the beginning of the recitation. Note that Test 1 is on Thursday, September 20th, and it will be based on material of Chapters 1-2.

HW3 Read sections 2.1, 2.2, 2.3. Do the following problems 2.1: 4, 14, 26, 40, 43, 44, 50; 2.2: 14, 17, 32, 33, 44; 2.3: 14, 38, 48, 66. Quiz 3 will be given on Thursday, September 13th, in the beginning of the recitation.

HW2 Read sections 1.3. Do the following problems 1.3: 22, 24, 30, 34, 46, 58, 64; True or False on page 38: 3, 10, 18, 23, 30, 38, 44. Quiz 2 will be given on Thursday, September 6th, in the beginning of the recitation.

HW1 Read sections 1.1, 1.2. Do the following problems 1.1: 10, 12, 18, 24, 26. 1.2: 4, 6, 18, 24, 30, 44, 46. Quiz 1 will be given on Thursday, August 30th, in the beginning of the recitation.

Please check out the School of Mathematics free tutoring center: Math Lab. Strictly speaking math 1512 is not among the courses listed (because it considered too theoretical). The reality is that this course is not much different from math 1502, and you will not be turned away. In case of trouble mention that Klara Grodzinsky, the TA coordinator, has given all math 1512 a permission to come to Math Lab. All those in the lab should be able to help you, but those teaching 1502 should have everything on their fingertips, and grad students will as a rule have a better grip on theoretical issues.

Instructor: Igor Belegradek
office hours: Monday and Wednesday: 8:05-8:55am, or by appointment.
office: Skiles 240B.
phone: (404) 385-0053 (please do not leave messages as I do not check voice mail).
Email: ib at math dot gatech dot edu
This is the best way to contact me. Please include 1512 in the subject header. Please email me from the Georgia Tech address: this would ensure your message won't end up in the spam folder, and besides, I shall not discuss more private matters, such as grades, to someone with non Georgia Tech email address.
Course homepage: http://www.math.gatech.edu/~ib/1512.html

Lectures: Skiles 254: MWF 11:05-11:55.

TA's email and office hours: Robert Krone: rkrone3 at math dot gatech dot edu, office hours: TBA.

Textbooks:

Linear Algebra with Applications (4th Edition) by Otto Bretscher. This is on reserve in the library.

It is a good idea to have access to the solution manuals for Bretscher's forth edition containing solutions to odd-numbered exercises.

At the end of the semester we shall discuss infinite series, and for that purpose any calculus book will do, such as Salas-Eitgen-Hille: Calculus in One and Several Variables.

Content and Course Objectives:

The material will parallel that in Math 1502, but will be covered in greater depth. The main emphasis will be on linear algebra, including the solution of systems of linear equations; least-squares solutions of over-determined systems; vector spaces and linear transformations; eigenvalues, eigenvectors, and diagonalization of matrices. Topics from single variable calculus such as Taylor polynomials, infinite series, and differential equations, will be covered when they arise naturally in this discussion. Math 1512 is an excellent choice for those seeking a deeper understanding of linear algebra. It is an ideal bridge course to more advanced courses in pure and applied mathematics, and is especially valuable for entering mathematics majors and other students who will be taking advanced mathematics courses.

We plan to cover the first seven chapters of the book, which will keep us busy for most of the term at the end we shall cover infinite series and other calculus topics.

Linear Algebra concepts and methods are fundamental in many problems of Sciences and Engineering where non-linear equations and functions are studied through linear approximation.

The intellectual goal of the course is to teach you to solve specific problems in the above-mentioned topics, and help you understand the ideas behind the solutions. An education goal to to help you transition from "elementary" math based on rote learning to "higher" math with more abstract ideas and methods.

Prerequisites: This course is designed for students who have had a serious single variable calculus course in high school.

Homework:

The homework assignments will be posted on the course webpage. Be sure to check it for new homework and announcements.
For most students doing homework is necessary to prepare for tests.
Homework will of course be discussed in recitaions.
Homework will be usually assigned weekly on Monday, and will not be graded or collected.

Quizzes:

There will be weekly quizzes in recitations, usually every Thursday (but rare changes are possible due to holidays, and those changes will be announced on the course webpage.).
Each quiz will consists of 1-2 problems from the homework assigned on Monday of the previous week.
All quizzes are closed-book and closed-notes. No "help sheet" is allowed on quizzes. No electronics (such as calculators, computers, mobile devices) are allowed on quizzes.
Three quizzes with the lowest score will be dropped.
The quizzes will be graded by the TA. All questions about grading quizzes should be first addressed to the TA. (I shall deal with whatever cannot be resolved by him).
There will be no makeup quizzes. If your excuse for missing a quiz seems valid to me, then the other quizzes will be given higher weight. To arrange for this you need to contact me promptly (by email).

Tests:

There will be three in-class midterms and one (cumulative) final.
All tests are closed-book and closed-notes. A one-page (two-sided if needed) "help sheet" will be allowed on midterms; you may write/type anything there. A four-page "help sheet" (again, two-sided) is allowed on the final.
No electronics (such as calculators, computers, mobile devices) are allowed on tests.
There will be no makeup tests. If your reason for missing a test seems valid to me, then the corresponding part of the final will be given a higher weight; to arrange for that you must contact me as soon as possible. With rare exceptions acceptable reasons for missing a test are limited to illness, court appearance, and taking part in a Georgia Tech events. In particular, the popular excuse ``alarm clock malfunction'' will not be honored: please stock up alarm clocks beforehand.
Midterms will be graded by the TA/Instructor team with a detailed grading key provided by the Instructor. Questions about grading midterms should be asked within one week after the graded test is handed out.
Midterm test dates: September 20 (Thursday), October 23 (Tuesday), and November 20 (Tuesday). All midterms are in recitations. The last midterm is the Tuesday before Thanksgiving.
Final date is: December 12 (Wednesday), 8-10:50am.

Random thoughts on how to do well in this course:

Read the textbook and think about what you have read. I hear that its style is somewhat terse, and Bretscher tend not to repeat things twice.
do all homework.
attend lectures and recitations; while some rare individuals can do well without going to class, there is a strong evidence that those who attend most lectures and recitations get a better grade.
join a study group: explaining ideas to others helps clarify them for yourself, not to mention that your peers may have something to teach you too, and most importantly to tell you when you are wrong.
always go to review sessions.
do not hesitate to ask questions, come to the office hours etc.

Needless to say that cheating will not be tolerated. Please report all cheating to me or your TA, and do so promptly (if you wait till after the end of the term, there will be little I can do). What constitutes cheating on a test or quiz? Examples are use of unauthorized materials, use of electronic devices, and getting outside help including talking, and looking in other students' papers. See the Georgia Tech Honor Code for your rights and obligations.

Grading:

Quizzes will count for 10% of the final grade. Each of the midterms is worth 20%, and the final is worth 30%. No test score will be dropped.
All grades will be recorded in T-square, but we will not use T-square for any other purpose.
I shall not follow the standard 90-80-70-60 grading scheme (for it feels claustrophobic). Instead, after every midterm I shall tell the cutoffs for a particular test. For quizzes the cutoffs are A=85%, B=70%, C=55%, D=45%.

How to get help: any concerns should be promptly discussed with me. All feedback on teaching and administrative issues is appreciated. Let me help you before it is too late.

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