Alexander Paulin 

Department of Mathematics
796 Evans Hall
University of California, Berkeley

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Linear Algebra and Differential Equations 54 (002 LEC) Spring 2018

Lectures: MWF, 11am-12pm, Wheeler Hall Auditorium.
Office hours : MWF 2pm-4pm, TT 3pm-5pm, 796 Evans Hall.
Discussion sections: Three, one hour sessions each week on MWF. Here is a link with further details. You may only attend the discussion section for which you are enrolled. Here is a link to GSI office hours. You may attend any office hour your please.

Welcome to Math 54! This fantastic course is an introduction to linear algebra and its applications to differential equations. At first glance linear algebra is just about solving systems of linear equations. However, after digging a little deeper, we'll discover a rich new language which will be applicable across all mathematical disciplines. This is something of a watershed course, opening up a whole branch of mathematics. It's going to be great!

Everything related to the course will be on this website. We will not be using bCourses. There will be weekly homework (posted below) which will be due every Friday in discussion section. In addition to this there will be weekly quizzes. I have office hours everyday of the week so there should always be an opportunity to get my help if you need it. If you can't make any office hours, e-mail me and we'll find another time to meet. In addition to this I will be posting my own lecture notes on this website at the end of each week. You'll be able to link to them directly from the detailed syllabus below. There will also be video recordings of the lectures posted at the end of Monday, Wednesday and Friday. Again you'll be able to link to them directly from the syllabus below.

Discussion sections will begin on Wednesday the 17th of January.

Make sure to read the course policy and the detailed syllabus below.

The first homework assignment will be due on Friday of week 2. The first quiz will also be on Friday of week 2.

Linear Algebra and Differential Equations (UC Berkeley Custom Edition), 3rd Edition, ISBN: 9781323720868.

This is a combination of two separate textbooks. These textbooks are

Linear Algebra and its Applications, Lay-Lay-Macdonald, 5th Edition.

Fundamentals of Differential Equations, Nagle-Saff-Snider, 9th Edition

I strongly advise you against buying these textbooks individually. They contain far more material than will be needed and will be substantially more expensive. We've negotiated a reduced price for the custom textbook if you buy it directly from the publisher. Here's the link:

Pearson Textbook Website Enter Username: algebra and Password: berkeley

You can also buy this textbook from the Cal Student Store for $95 new.

Homework 1 and Solutions 1

Homework 2 and Solutions 2

Homework 3 and Solutions 3

Homework 4 and Solutions 4

Homework 5 and Solutions 5

Homework 6 and Solutions 6

Homework 7 and Solutions 7

Homework 8 and Solutions 8

Homework 9 and Solutions 9

Homework 10 and Solutions 10

Homework 11 and Solutions 11

Homework 12 and Solutions 12

Homework 13 (Not to be submitted)

Homework assignments are due each Thursday in section. They will be posted here along with solutions and videos of me going through a selection of the more challenging problems. Your two lowest homework scores will be dropped. The homework corresponding to material covered during a given week is due in the following week's Thursday discussion session.

Assignments will be graded on a coarse scale based on spot checks for correctness and completeness. Your two lowest scores will be dropped. You may discuss the homework problems with your classmates, but you must write your solutions on your own. Doing the work yourself is crucial to learning the material properly. Make use of discussion sections, office hours, study groups, etc. if you need assistance, but in the end, you should still write up your own solutions.

I am aware that it is not hard to find solutions manuals on the internet. Copying said solutions on a homework assignment is illegal and will result in a negative grade for that assignment, and potentially in more serious consequences. (Also, it will not help you learn the material).

The homework load for this course is heavy at times, but it is essential for learning the material. Be organized, and don't leave things for the last moment. (You cannot complete the homework assignment if you start on the night before it is due.) Work in small installments, and ask questions in section and during office hours.

Quizzes will take place roughly every week in the Friday discussion section. They will last about 15 minutes, be of closely related to the homework problems for that week. Your two lowest scores will be dropped from your grade. Here is the quiz schedule:

1 Week 2
2 Week 3
3 Week 6
4 Week 7
5 Week 8
6 Week 9
7 Week 13
8 Week 14
9 Week 15

For more detailed information see the course policy

First Midterm (Practice 1) and solutions.

First Midterm (Practice 2) and solutions.

First Midterm (Practice 3) and solutions.

Midterm 1 Solutions and statistics.

Second Midterm (Practice 1) and solutions.

Second Midterm (Practice 2) and solutions.

Second Midterm (Practice 3) and solutions.

Midterm 2 Solutions and statistics.

Final(Practice 1) and solutions.

Final (Practice 2) and solutions.

Final (Practice 3) and solutions.

There will be two midterms and a final. There will be no make-up exams, unless there are truly exceptional circumstances. Because of the grading scheme, you can miss one midterm, for whatever reason, without penalty. On the other hand, missing both midterms or missing the final will seriously harm your grade and make it very difficult/impossible to pass the course. Please check the dates now to make sure that you have no unavoidable conflicts!

  • First midterm: February 12 in class
  • Second midterm: March 23 in class
  • Final exam: May 8 (7pm-10pm)

Calculators and notes will NOT be allowed for the exams.

To obtain full credit for an exam question, you must obtain the correct answer and give a correct and readable derivation or justification of the answer. Unjustified correct answers will be regarded very suspiciously and will receive little or no credit. The graders are looking for demonstration that you understand the material. To maximize credit, cross out incorrect work. We will be scanning all exams so you will get them back electronically.

After each midterm, there will be a brief window when you can request a regrade. In general, midterm exam grades cannot be changed. The only exception to this is then there has been a clerical error such as a mistake in adding the scores (if this is the case immediately inform your GSI) or if part of the solution has been accidentally overlooked by the grader. Regrade requests may result in a lowering of your grade. As per university policy, final exams cannot be regraded.

DSP students requiring accommodations for exams must submit to the instructor a "letter of accommodation" from the Disabled Students Program at least two weeks in advance. Due to delays in processing, you are encouraged to contact the DSP office before the start of the semester.

Cheating is unacceptable. Any student caught cheating will be reported to higher authorities for disciplinary action.

There will be two midterms, the first on Monday February 12 and the second on Friday March 23 . The final exam will be on Monday May 7 (7pm - 10pm).

For more detailed information see the course policy

WhenWhat Where
Week 1 (1/17 - 1/19) 1.1, 1.2
Week 2 (1/22 - 1/26) 1.3
1.4, 1.5
1.5, 1.7
Week 3 (1/29 - 2/2) 1.8, 1.9
Week 4 (2/5 - 2/9) 2.2, 2.3
3.1, 3.2
Week 5 (2/12 - 2/26)
4.1, 4.2
4.1, 4.3, 4.5
Week 6 (2/21 - 2/23) 4.3, 4.5, 4.6
4.4, 4.7
Week 7 (2/26 - 3/2) 5.1, 5.2
Week 8 (3/5 - 3/9) 5.4
Week 9 (3/12 - 3/16) 6.2
Week 10 (3/19 - 3/23) 6.5
Week 11 (3/26 - 3/30)
Week 12 (4/2 - 4/6) 7.1
Week 13 (4/9 - 4/13) 4.2, 4.3
4.4, 4.5
Week 14 (4/16 - 4/20) 9.1, 9.4
9.5, 9.6
Week 15 (4/23 - 4/27) 10.3, 10.4
10.3, 10.4
Week 16 (4/30 - 5/4)
Week 17 (5/7 - 5/11)

Grades are calculated as follows:

Homework 10%
Quizzes 10%
First Midterm 20%
Second Midterm 20%
Final Exam 40%

Each midterm and final score will first be curved into a number on a consistent scale. More precisely, I will assign a number to each exam (midterm 1, midterm 2 and the final) reflecting their relative position in the class. As an example, if you scored 70/120 on the first midterm and exactly 60 percent of the class got this score or below, you'd be assigned the scaled score of 60/100 for that midterm. These numbers are just a reflection of your relative performance. They do not correspond to letter grades in the usual sense. Section scores will be adjusted to account for differences between GSI's in quiz difficulty and grading standards. Your lowest scaled midterm score will be replaced by the scaled final exam score if it is higher. Finally, the scaled scores will be added up (with proportions outlined above) giving a final course score between 0 and 100. This score gives an extremely accurate description of your overall relative performance.

This is not high school. For example, you do not need to get 90 or above to get an A. Your final letter grade will ultimately be decided by your ability to demonstrate a crisp understanding of the material and the ability to apply it to a diverse set of problems. Broadly speaking I will be looking for the following criteria for each letter grade:

  • A-/A/A+: A clear demonstration that the central concepts have been fully understood; Computational techniques (and their many subtleties) have been mastered and can be applied accurately to a diverse problem set; A strong understanding of how the abstract concepts can be applied to many real world applications.
  • B-/B/B+: Demonstration that the central concepts have been reasonably understood, but perhaps with minor misunderstandings; Core computational techniques have been reaonably understood (but generally not key subtleties) and can be applied fairly accurately to a fairly large problem set; Reasonable understanding of how the abstract concepts can be applied to some real world applications.
  • C-/C/C+: Demonstration that the central concepts have been vaguely understood, but with major misunderstandings; Core computational techniques have been poorly understood and can be a applied accurately only in the most standard examples; Weak understanding of how the abstract concepts can be applied to even basic real world applications.

To be as fair as possible, I will also take into account the historic average of the class. This means that if I set an exam which is too difficult it will be taken into account in the final letter grades.

Please note: incomplete grades, according to university policy, can be given only if unanticipated events beyond your control (e.g. a medical emergency) make it impossible for you to complete the course, and if you are otherwise passing (with a C- or above).

Enrollment: For question about enrollment contact Jennifer Pinney.

The Student Learning Center provides support for this class, including full adjunct courses, review sessions for exams, and drop-in tutoring. This is a truly fantastic resource. I definitely recommend you take advantage of it.