**Math H54**

**Lecture:**Tuesday and Thursday from 9:30-11 in 310 Hearst Memorial Mining Building

**Office Hours:**Monday 2:30-4 and Tuesday 1-2:30,

**in my office, 735 Evans. During the week of December 4, I will have office hours on Tuesday and Thursday from 1-3. During the week of December 11, I will have office hours on Tuesday from 1-3 and on Wednesday from 3-4. I am also available by appointment during both of these weeks -- just send me an email.**

**GSI:**Jonny Gleason. Discussion will be held Monday, Wednesday, Friday 11-12 in 310 Hearst Memorial Mining Building. Jonny's office hours are Mondays, Wednesdays, and Fridays, 12-1 in 935 Evans.

**Textbook:**Lay, Nagle, Saff, & Snider,

__Linear Algebra and Differential Equations__(UC Berkeley custom edition). See the bookstore web site for exact details.

**Information for students:**

- The syllabus. Please read it carefully.
- DSP students should come see me as soon as possible, even if you do not have a letter yet.
- Guidelines on what to do if you think you have an extracurricular that interfere with this course. In particular, you must speak with me no later than the end of the second week of class.

**Course Goals:**The topics for the course will be:

- Basic linear algebra
- Matrix arithmetic and determinants
- Vectors in
**R**^2 and**R**^3 - Vector spaces and inner product spaces
- Eigenvalues and eigenvectors
- Linear transformations
- Homogeneous ordinary differential equations
- First-order differential equations with constant coefficients
- Fourier series and partial differential equations

Most of the course consists of a detailed study of linear algebra.

*Linear algebra*is, at its root, the study of systems of linear equations (you've probably encountered those before, both in high-school algebra courses and when doing partial fractions in Math 1B). Central to this study (for Math 54 and beyond) is the practice of putting the coefficients of a system of linear equations in the form of a matrix, and then doing operations on that matrix to better understand the system of equations. Math 54 goes quite a bit further, though, and looks at other things you can do with matrices. For example,

*recommendation systems*(“People who bought this item also bought...”) use matrices in their computations (but in ways that go beyond what we'll do in Math 54).

The last (approximately) six weeks of the course involve differential equations. You should already be somewhat familiar with differential equations from Math 1B, where second-order linear differential equations with constant coefficients were studied. Math 54 goes a bit further, by studying higher-order linear differential equations, as well as first-order linear differential equations in more than one variable, and partial differential equations. The latter involve vibrations of fixed strings (as on a guitar or violin), vibrations of air in an organ pipe, etc. In other words, in Math 54 we study more kinds of differential equations than in Math 1B, and see how they relate to physical phenomena in the world around us.

**Homework:**Homework will be assigned weekly and will be posted below (in the Course Calendar) no later than midnight on Tuesday. Homework is to be handed in to the GSI in discussion the following Wednesday. Homework will be graded on completion.

*Late homework will not be accepted under any circumstances.*In the case of extended illness, you must contact me as soon as possible. If you know you will miss a Wednesday discussion, you must arrange to turn your homework in to the GSI ahead of time.

You are encouraged to discuss the homework assignments with your classmates, but you must write up the solutions

*entirely*on your own. That is, your assignment should be your own work, written in you own words (i.e., by yourself without consulting someone else's solution). Plagiarism and copying (from other students, the internet, etc.) are not tolerated under any circumstances.

**Honors Course:**This course is aimed at students with a strong ability and interest in mathematics. I will follow the curriculum for Math 54 but will try to provide greater rigor (real proofs), greater insight, and more interesting exercises. I don't expect the grading scale to be either higher or lower than for regular Math 54, but you will have to do more thinking to get a good grade; I hope that you will enjoy this. If you start H54 but find in a few weeks that it is not the course for you, it should be possible to transfer to regular Math 54 and not be at a disadvantage.

For more information on honors courses in the math department, see the department's web page on honors courses.

**Course Calendar:**I will post the sections of the textbook covered each day, all homework assignments, as well as any handouts distributed in class here.

- Thursday, 8/24: We covered sections 1.1-1.3. Homework #1 is due on Wednesday, 8/30.
- Tuesday, 8/29: We covered sections 1.5 and 1.7.
- Thursday, 8/31: We covered sections 1.8-1.9. Homework #2 is due on Wednesday, 9/6. Update: Optional proof-based problems now added to HW#2. You do not need to turn these in, but you should try them!
- Tuesday, 9/5: We covered sections 2.1 and 2.2.
- Thursday, 9/7: We covered section 2.3 and 3.1. Homework #3 is due on Wednesday, 9/13.
- Tuesday, 9/12: We covered sections 3.2 and 3.3.
- Thursday, 9/14: We covered sections 4.1 and 4.2. Homework #4 is due on Wednesday, 9/20. Here is a solution to Homework#4 Additional Problem #2.
- Tuesday, 9/19: We covered sections 4.3 and 4.4.
- Thursday, 9/21: We covered sections 4.5 and 4.6. Homework #5 is due on Wednesday, 9/27.
- Tuesday, 9/26: We covered sections 4.7 and 5.1.
- Thursday, 9/28: We covered sections 5.2 and 5.3. Homework #6 is due on Wednesday, 10/4. Review Sheet for Midterm 1 (updated on 9/29). Solutions to the review sheet: File 1 and File 2. (corrected 10/3)
- Tuesday, 10/3: We covered sections 5.4 and 5.5.
- Thursday 10/5: Review for midterm. There is no homework due next week, and no quiz, due to the midterm.
- Tuesday 10/10: Midterm #1, covers all sections listed above, through 5.5. Solutions to Midterm #1.
- Thursday, 10/12: We covered sections 6.7, 6.1, and 6.2. Homework #7 is due on Wednesday 10/18.
- Tuesday, 10/17: We covered section 6.3.
- Thursday, 10/19: We cover sections 6.4 and 6.5. Homework #8 is due on Wednesday 10/25.
- Tuesday, 10/24: We covered section 7.1. This is the end of the linear algebra portion of the course.
- Thursday, 10/26: We covered sections 4.2 and 4.3 of PART TWO of the textbook. Homework #9 is due on THURSDAY 11/2 IN LECTURE!!. The quiz is rescheduled for FRIDAY.
- Tuesday, 10/31: We covered sections 4.4 and 4.5. No homework due next week, and no quiz, due to the midterm.
- Thursday, 11/2: We covered sections 4.6 and 6.2. Review sheet for Midterm 2 (typos corrected 11/3). Solutions for the review sheet. This review sheet is approximately twice as long as the exam will be, so it should take you around 2 hours and 40 minutes to complete (if you want to time yourself).
- Tuesday, 11/7: Review for midterm #2.
- Thursday, 11/9: Midterm #2
- Tuesday, 11/14: We will cover sections 9.1, 9.4-9.6. Homework #10 is due on Monday, 11/20. Quiz #10 will also be given on Monday, 11/20.
- Thursday, 11/16: We will cover sections 9.7 and 9.8.
- Tuesday, 11/22: We will cover sections 10.3 and 10.4. Homework #11 is due on Friday, 12/1. Quiz #11 will also be given on Friday, 12/1.
- Tuesday, 11/28: We will cover sections 10.1 and 10.2.
- Thursday, 11/30: We will cover section 10.6.
- Wednesday, 12/13:
**Final Exam from 11:30-2:30, in 310 HMMB (our usual classroom). Final exam covers sections Part I, Sections 1.1-1.9, 2.1-2.7, 3.1-3.3, 4.1-4.7, 5.1-5.5, 6.1-6.5, 6.7, 7.1, and Part II, Sections 4.2-4.6, 6.1-6.2, 9.4-9.8, and 10.1-10.6. Review sheet for the final exam. Part 1 and Part 2 of solutions to the review sheet.**