Math 54-001 - Linear Algebra and Differential Equations

 

Instructor: Katrin Wehrheim

Office: Evans 907

Email is not a sustainable form of communication in this course

Lectures: Mon/Wed 5 - 6:30pm in 155 Dwinelle

Contact: via Piazza or in person before class and in office hours

Office Hours: generally Mon/Wed 6:30pm onwards in or near the lecture hall, and Tue 8:30-9:30am in Evans 907, with updates on piazza




CONTENTS

Topics: Basic linear algebra, matrix arithmetic and determinants, vector spaces, eigenvalues and eigenvectors, linear transformations. Linear second-order differential equations; higher-order homogeneous differential equations; linear systems of ordinary differential equations; Fourier series and partial differential equations.

Textbook: Lay, Nagle, Saff and Snider, Linear Algebra and Differential Equations, second custom edition

PREREQUISITES / REVIEW

This course will build on a lot of the material from Berkeley's Calculus (1A-1B) sequence. In particular, if you are not comfortable with complex numbers and differential equations (or your calculus course did not cover much of them), then you should learn/review this material (Stewart, Calculus: Early Transcendentals, 7th Edition, Chapters 9 and 17, Appendix H) before the complex eigenvalues / differential equations parts of the course. A quick review of series (Chapter 11) is recommended before we discuss Fourier series.
If you did not take Multivariable Calculus (53), then you should get familiar with partial derivatives (Stewart, Multivariable Calculus for UCB, 7th Edition, Chapter 14) before the PDE part of the course. See the syllabus for concrete dates.

PROFESSIONALITY EXPECTATIONS AND COURSE STRUCTURE

If you take this course you are expected to attend lectures, enroll and participate in one of the discussion sections, enroll, participate, and pay attention to announcements in the Piazza online forum, and to be committed to learning the material (by e.g. reading the book and working through the practice problems) as well as to checking/demonstrating your learning in the common assignments (quizzes, midterms, final). In return you can expect your instructors full commitment to supporting your learning - by structuring the material towards main goals, providing constant opportunites to get questions answered (in sections, piazza, office hours), and giving you quick feedback on assignments - for exams usually within 24h via gradescope.
To take maximal advantage of what we can offer, you should in particular attend your section meetings regularly and well prepared to follow and contribute to the discussion, by having done the reading, attended lecture, and attempted some practice problems. Sections will not serve as introductory lectures, but as venues to clarify, deepen, and practice your understanding interactively. To further help you with staying current with the material, there will be no mandatory homework submission or grading; instead the course structure encourages and supports the following approximate weekly learning schedule:

2 x 0.5h reading before lecture
2 x 1.5h lecture
2 x 1h lecture/reading review and practice problems after lecture, before corresponding section
3 x 1h discussion section
3h review and further practice problems before weekly quiz resp. exam

To ensure that this course structure does not conflict with your other commitments, please make sure that you have no obstructions to attending lectures or sections, and check the exam dates on the syllabus before committing to this course. If you require accomodations for exams, please contact the Disabled Students Program before the start of the semester. For more details on course policy and structure see the logistics tab.

COMMUNICATION

If you have a logistical question, ask a fellow student, post in the forum (after checking whether this question was already answered), or ask in the discussion section. If you have a mathematical question, ask a fellow student, ask in the discussion section, post on the forum (after checking for posts on that topic), or come to office hours. If you have a personal question or issue, talk to your section leader (GSI - who may communicate your issue to the head instructor) or the head instructor in person in office hours.

We ask you to refrain from email so we can concentrate our time and energy on helping everyone with mastering the material. For that purpose we will monitor the online forum regularly - in our waking hours. However, since we're not necessarily awake when you are working, and there are a lot more students than instructors, the most efficient use of the forum is for all of you to rather ask ''silly'' questions or chance a ''wrong'' answer than to sit back and be confused. Between 500 eager minds, usually the truth will prevail; and if it doesn't, that's important feedback for us and a good learning opportunity.



REGISTRATION LOGISTICS

Anything involving registration, wait list, sections, etc: Sorry, most of this is outside of departmental control. See the forum for updates.

Concurrent Enrollment Program: As long as there is physical space, we will be happy to have you, however we need to wait for UCB registration to settle. So please start attending the lectures, find a discussion section with free seats in the classroom, and see one of our undergraduate advisor staff in the first week to pick up the Concurrent Enrollment form. I will make an announcement on the forum if/once I can start signing these.

Math 49 option: This enrollment option is not offered in this course since the topics are not sufficiently standard or separated. However, if you can demonstrate to your section leader (GSI) that attending lectures and sections on the linear algebra part will be a waste of your time, then they can allow you to miss all but the quizzes; determining your discussion grade for this part only from the quiz scores. You will still have to take all exams, and will get credit for math 54.