| Time |
MWF 11:30 AM -- 12:20 PM The class meets starting on Monday, August 25. The final exam will be Friday, Dec. 12, 12:30-2:30 PM |
| Location |
276 Lockett Hall |
| Leonard Richardson |
Office 386 Lockett Hall |
| Office Hours |
12:30 PM--1:20 PM, MWF, in 386 Lockett. I can also meet individually with students on request on Tuesdays and Thursdays via Zoom at this link:
https://lsu.zoom.us/j/7111204773.
There is a Zoom Waiting Room in case more than one person comes at the same time. I am available at many other times. Email first to make sure I'm able meet with you. I answer email many times daily---usually quickly. |
| Office phone |
578-1568 |
| E-Mail |
rich@math.lsu.edu |
| Text |
Richardson, L., Advanced Calculus: An Introduction to Linear Analysis, John Wiley & Sons, 2008. ISBN 978-0-470-23288-0. There is a list of errata. If you find an error not on this list, please tell me. The text is also available as a free e-book through the LSU Library at this
link. |
| Syllabus |
We will cover most of Chapters 8, 9, 10, and 11. |
| Graduate Assistant |
You will turn in homework in class on the due-date. If you must be absent on the due-date, you may email the scan files of your homework to the grader directly by class-time: TBA at TBA@lsu.edu , who will grade those homework problems that are to be turned in---the ones
that are assigned in red boldface in the table below.
The grader will be available to answer questions about the homework grading at at TBA on TBAday from TBA to TBA.
Please be sure to write your solutions neatly and carefully so that they can be read. |
Math Major Requirements and Recommendations
Math 4031, followed by either Math 4032 or Math 4035, satisfies the Advanced Calculus requirement for the Mathematics major with a mathematics concentration. It prepares students for graduate study of mathematics and its applications. The Department strongly recommends that Mathematics majors planning graduate study in Mathematics take all three Advanced Calculus courses: Math 4031, 4032, and 4035.
Prerequisites
Mathematics 4031 and 2085 or the equivalent.
Homework
Problems, mainly proofs, will be assigned frequently. These will be collected on paper in class, corrected, and returned to you at the next class meeting, if possible. You are encouraged to seek hints to help you get started with these problems! Please turn in every assignment! The key to learning to prove theorems lies in how you study Advanced Calculus. It is very important to understand thoroughly how and why the proofs presented in the book and in class work. Please read the Introduction to your textbook! We will go over every collected homework problem in class, to help you prepare for tests. At the end of the course, you will have the benefit of whichever of the following two final average adjustments gives you the best final average.
- Adjustment #1: Add your average homework score on a 10-point scale to the average of your 3 hour tests with the final exam. For example, if your average on the homework is 5 points out of 10, and you have an 85% exam average, Adjustment #1 raises your final average to 90%, which is an A-.
- Adjustment #2: Replace your lowest hour-test grade with half of your 200-point final exam score.
Please turn in every homework assignment!
Proofs assigned for homework are a very important learning experience. Some students try an easier technique - copying the correct proofs from class after the homework has been graded, without turning in their own efforts. This tends to produce low grades on Part I of each test, because the student's own conceptual errors have not been turned in and thus have not been corrected. So please turn in every assignment!
Tests
These will be in-class closed book tests with no notes or communication devices allowed. Part I of each hour test will consist of a choice of 8 out of 12 short answer questions, and Part II will offer a choice of 2 out of 3 proofs. (The Final Exam will be equivalent to two hour tests.) The proofs will be very similar to the collected homework problems. The short questions will be small variations of homework problems---including those not collected---together with examples from the lectures and notes. Thus if you have done the homework conscientiously, you should be prepared well for all tests. If you must miss a test, it is your responsibility to speak to me as soon as possible to determine whether or not your excuse is acceptable.
Grades
We plan to have three hour tests, worth 100 points each, and a two hour final examination, worth 200 points. Your test average will be the sum of all your grades divided 5. Your Final Average will be the better of the two grades calculated by adjusting the average using either Adjustment #1 or Adjustment #2 described above under Homework. The minimum grade for each letter grade is as follows: A+, 97 A, 93 A-, 90 B+, 87 B, 83 B-, 80 C+, 77 C, 73 C-, 70 D+, 67 D, 63 D-, 60 F, below 60. You should save all your graded work for future study and in case you think your final grade is in error. You should save all your graded work for future study and in case you think your final grade is in error.
General Advice: Questions and Attendance
- Many students need help to learn how to write proofs. If you feel confused, it is important to see me for help as soon as possible. If you don't know how to start a homework problem, ask for a hint---either in class or in my office hours---or by email. I can guarantee you it is possible to learn to write sound proofs: Learning begins with your efforts and your persistence.
- Attend class and ask questions. The roll will be called at the beginning of each class. If you are not present you are greatly missed. Please come to class, unless you have a valid reason such as illness or a quarantining requirement! Non-attendance or lax attendance is usually the first sign of impending academic difficulty. Sometimes a student feels frustrated because of not understanding the classwork. If that is the case, it is necessary to ask more questions. Advanced calculus is a subject you can learn---but you must participate in this work.
- Come to class on time. However, anyone may need to arrive a bit late on some occasions for reasons beyond ones own control. If you are in that situation, just come right in and take your seat. You should not miss any more of the class time than is necessary for reasons beyond your control.
- Assignments are collected at the beginning of class. . If you need to be absent and turn it in directly to the grader by e-mail, do not turn it in later than that, because it is not fair to the graduate teaching assistant, who will be busy enough with the work of grading the assignments that are turned in at the proper time.
- LSU offers extensive academic support services to help students adjust to the demands of university studies: List of Frequently Used Services.
Remarks concerning emergency conditions
We have seen that sometimes there are emergency conditions that affect the Univeristy's operations. These include such emergencies as extreme weather events and/or pandemics. Please be aware that under emergency conditions the operation of courses may diverge from the description in this syllabus. But we will be sure to respond to the needs of every student in a fair and caring manner. Regardless of whether or not there is an emergency at hand, if you have any special needs, please let me know as soon as possible so I can do my best to help.
Homework Assignments and Downloads
We will update the list of assignments and tests below as the
semester progresses. You
will know an
assignment has been updated if
a due-date
appropriate to this
semester appears in the left-hand column. However,
sometimes we will assign a problem for a certain date and then
postpone it because we don't cover as much as planned in class.
So check regularly for updates as to what is due and when.
If you email me about a pending assignment, I may send a hint to
the whole class in answer to your question, not giving
your name of course! OUR TESTS WILL BE CLOSED BOOK, IN-CLASS EXAMS. |
| Academic Honesty |
The University has clear policies requiring academic honesty. If you email me about a pending assignment, I may send a hint to the whole class in answer to your question, not giving your name of course! If on the other hand you get a good idea from another book, or from talking with a friend, academic honesty requires that you acknowledge your sources openly. Above all, never copy directly from another person's written work as though it were your own. Remember that your own good name is irreplaceable. This is a sound principle which will serve you well throughout your life. Moreover, on a practical level, it is very foolish claim as your own an argument from a former student in this class or from a textbook. The arguments which are copied can be recognized very easily as not coming from the student, and often the precise source can be identified readily. This means that the honorable course of action is also the practical one. |
| Due Date |
Assignments: Hand in problems in red for grading. The problems in red are required. Assignments must be written neatly so that the grader can read them. But there is also a class of optional problems, called Bonus Problems. These are worth up to 20 extra homework points per problem. Bonus problems need to be turned in directly to me on a separate sheet from the regular homework, clearly marked Bonus Problems at the top. Bonus problems are due, if you choose to do one of them, one full week after the date listed, unlike normal graded homework, which is due the date listed. Bonus problems will be graded more strictly for logical rigor than the required homework. Bonus problems are more challenging than the required problems. |
| August 25 |
Today is the first day of class. You should have your texts for your classes and be ready for work.
|
| August |
Today only, my office hours will be a half hour earlier: 12:30 PM -- 1:30 PM. |
| August |
Read Pp. 245 -- 246, through Example 8.1. Be sure to practice reading with a pencil!
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August
|
Today only, my office hours will be earlier: 12:00 PM -- 1:00 PM.
|
| August |
Read Pp. 246 -- 249. Be sure to practice reading with a pencil! Do problems 8.1 -- 8.4; 8.6 -- 8.8; 8.10. These are not to hand in, but you should write your solutions on paper in order to learn from the work. In this section, 8.1, we use Definition 2.5.3 (page 63) of convergence in a normed vector space and of a Cauchy sequence in a normed vector space.
|
| September |
|
| September |
Do problems 8.9, 8.11, 8.14(a)--(c) and turn them in to me at class time!
Mr. Sandvik will grade your homework. Please be sure to write your solutions neatly, so that he can read them!
The first Bonus Problem B1 is 8.14(d). If you choose to do it, turn it in to me--NOT to the grader-- one week from today, separately from the regular homework. I grade Bonus problems strictly for rigorous reasoning.
|
| September |
8.16-17; 8.21-23. Terminology: A set is called closed if and only if its complement is open. |
| September |
|
| September |
8.18-19; 8.24-25; 8.30--31; 8.33. |
| September |
8.20, 8.26, 8.28. The Bonus Problem B2 is 8.32. If you choose to do it, turn it in to me one week from today, separately from the regular homework. Bonus problems are graded strictly for rigorous reasoning.
I may be late for my office hours today. If I am not there when you visit via Zoom, please email me and I will arrange a meeting for you when I return. Thank you. |
| September |
8.34 --8.38; 8.42. |
| September |
8.39, 8.40, 8.41. (Hint for problem 39: You need not suppose false. Just follow the rest of the stated hint in the book to show that the complement of E must be open if E is compact.)
If you get an idea from a friend, acknowledge your sources openly. Above all, never copy directly from another person's work as though it were your own. I am sorry to report that there are already two cases of students copying from a third student. If you are one of the three involved, please don't let it happen again. |
| September |
First Hour Test today! For practice, please download Hour Test #1, 2011, Solution Sketches and Class Statistics. |
| |
Please download Hour Test #1, 2021, Solution Sketches and Class Statistics. |
October |
8.44, 8.46, 8.48 -- 8.53. |
| October |
8.45, 8.47, 8.54. |
| October |
The next Bonus Problem B3 is 9.11, due one week from October 8 if you do it. Turn it in separately from the other homework. In one direction, 9.11 is quite easy, so that bonus credit requires both directions. Here is another Bonus problem, suggested by a student. I will call it B2.5. You have a week from October 8 to turn it in if you like. Suppose A and B are disjoint connected sets, but suppose A-closure intersect B-closure is nonempty. Prove that A-closure union B-closure is connected. |
| October |
9.2, 9.3, 9.6, 9.7. |
| October |
9.4, 9.5. |
| October |
|
| October |
9.12, 9.14--9.15, 9.19--9.26. |
| October |
9.13, 9.16, 9.28.
|
| October |
9.29 -- 9.32, 9.35, 9.36, 9.38. Note: In 9.36, there is a missing letter "t" in the argument of a function. Also: Remember to turn in today the problems that were "due" on the virtual class day, October 22! |
| October |
9.33, 39, 41. |
|
October 29
|
9.44 -- 9.48 The next Bonus Problem B4 is 9.42. Due one week from today if you decide to do it.
|
| |
9.43, 9.49, 9.50 |
| October |
Second Hour Test today! |
| November |
10.1--10.3, 10.5--10.7, 10.12. |
| November |
10.4, 10.8, 10.16, 10.20. |
|
November 9
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| November |
10.25 -- 10.29, 10.31, 10.37, 10.42. Typos: In 10.31 E3 should be E2. In 10.42, the domain of the mapping is incorrectly stated. It should read D : En --> Em. |
| November |
10.30, 10.32, 10.38, 10.39. |
| November |
10.56. Second Hour Test Today. This test will cover everything we have done since the first hour test. |
| November 21 |
Please download Hour Test #2, fall 2021, Solution Sketches and Class Statistics. |
| November |
10.44, 10.46 -- 10.49, 10.51. |
| November |
10.45, 10.50, 10.52. |
| November |
10.59 . Hint for 10.59: For a linear transformation T: En --> Em, compare the dimension of the image of T with the dimension of the domain of T. Also: 10.56--10.59. |
| November |
. Third Hour Test Today. This test will cover everything we have done since the seond hour test. |
|
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10.61 . Hint for 10.61: If the claim were false, show that there is a problem at some local extreme point. |
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| December 1 |
10.60--10.66. |
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10.62, 10.64. (Be sure to prove that your example has the specified properties!) |
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10.69 -- 10.71. |
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10.72 -- 10.74, 10.77. |
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10.76, 10.81, and 10.82(b,d, and e only) . For 10.82(e), you may use either equation (10.8) or (10.10) |
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11.48, 11.49, 11.50, 11.52, 11.54ab. |
| December |
Bring questions to review for the Final Exam! Don't forget to review from the beginning of the course! Also, please remember to fill out the end-of-course evaluation form that is available to you online! Your anonymous feedback is very important: It helps your teacher and the University to serve your needs to the best of our ability. Remember: Your opinion matters: You are the reason we are here! Thank you. |
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December --
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Exam Week Office Hours TBA I am available at many other times. Email first to make sure I'm able meet with you. I answer email many times daily---usually quickly.
|
| | 11.57bc. In 11.57c, you are not expected to prove the Riemann integrability statement, since we do not have time for that topic this semester. Use the Jacobian theorem to transform the integral under the given change of variables. See the small typo on page 357 in the errata list linked at the top of this page. Bring questions to review for the Final Exam. |
| December 12 |
Final Exam: The final exam will be Friday, Dec. 12, 12:30-2:30 PM.
The Final Exam will have a choice of 12 out of 18 short questions for 96 points and 4 out of 6 proofs for 104 points. At least one of the proofs and 3 of the short questions will come from the hour tests. There will be two proofs and 6 short questions from each one-third of the semester.
Advice: Be sure to review the first two-thirds of the course. Often students who are doing well overlook the need for this review. Safety Net Policy: Each student is guaranteed at least the grade determined by the methods explained above. However, as an incentive to do well on the final exam, no final grade will be worse than one letter below the final exam grade. As an extreme example, one might have a failing final average and an A on the final exam, earning a B in the course. (The safety net helps some students each semester, but I have never seen an instance of the extreme example just given.)
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Please download Final Exam, Fall 2021, Solution Sketches and Class Statistics. |
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