Course Syllabus

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MATH W54 Linear Algebra and Differential Equations (Summer 2023)

Please note that there will be NO synchronous/live lectures in this course. All the lecture content has been pre-recorded and is available via the module pages. The synchronous components of this course are the discussion sections and office hours, which are listed on the Synchronous Activities page.
Before you begin this course: please take our one-minute enrollment survey.

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Course Description

Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; linear transformations, symmetric matrices. Linear ordinary differential equations (ODE); systems of linear ODE. Fourier series.

Prerequisites

Math 1B or equivalent preparation.

Class number

14085

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Required Text

Lay and Nagle, Saff & Snider, Linear Algebra and Differential Equations, combined Berkeley custom edition.

The textbook is available in several forms (including electronic) at the Cal student store: textbook options.

The ebook is also available through the library on UC Bears (UC Berkeley Electronic and Accessible Reserves System): Linear Algebra and Differential Equations | MATH 54. The loan period is two hours, and can be renewed if another patron hasn’t checked it out after the two-hour loan period expires. See the UC Bears User Guide for more information.

We will cover the following sections of the textbook:

Part 1: Linear algebra (Lay)

  • Chapter 1: Linear equations in linear algebra
    Sections 1.1-1.5, 1.7-1.9
  • Chapter 2: Matrix algebra
    Sections 2.1-2.3
  • Chapter 3: Determinants
    Sections 3.1-3.3
  • Chapter 4: Vector spaces
    Sections 4.1-4.7
  • Chapter 5: Eigenvalues and eigenvectors
    Sections 5.1-5.5 and Appendix B
  • Chapter 6: Orthogonality and least squares
    Sections 6.1-6.7
  • Chapter 7: Symmetric matrices and quadratic forms
    Sections 7.1-7.2, 7.4

Part 2: Differential Equations (NS&S)

  • Chapter 4: Linear second-order ODE
    Sections 4.2-4.5
  • Chapter 9: Systems of linear ODE
    Sections 9.1, 9.4-9.6
  • Chapter 10: Fourier Series, application to PDE
    Sections 10.3, 10.4

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Exams, Quizzes, and Homework

Exams

Midterm 1: covers material up to and including Lay Ch. 2.3.

Midterm 2: covers material up to and including Lay Ch. 6.4.

Final Exam (in-person): covers material from the entire course.

The final exam will take place on Thursday, August 10, 2023, from 10am to 1pm Pacific Time, in-person (the location on campus will be announced). This will be a paper exam—you will need pens and/or pencils. You may also bring one page of notes, written (handwritten or typed) on both sides of a single regular sheet of paper (letter size or A4). Other notes, books, or electronic devices of any kind are not permitted.

If you need to take the final exam off-campus, remember to review the Proctor Information page for guidelines on how to find a proctor and the process and deadlines for approval. Off-site proctor applications must be submitted prior to Wednesday July 19, 2023. It is important to begin this process as early as possible to ensure you are able to schedule the final exam at the allowed date and time.

All students need to complete the Confirm Final Exam Date and Time survey. This survey lets your GSI know if you are taking the exam on campus or off-site with a proctor, and if you are taking it off-site, what date and time you have scheduled. You will not be able to access the last two weeks of course material until you have completed this survey.

Quizzes

There will be quizzes each week. They will be modeled on the sample quizzes contained in the modules.

Quizzes and midterm exams become available at 12:01 am Pacific Time on the day that they are due. They are due at 11:59 pm Pacific Time.

Homework

Each week contains homework. You are encouraged to discuss ideas with other students. However, you must write and submit your solutions independently.

Gradescope

Gradescope will be used for submission of the homework. All Gradescope assignments are linked in bCourses. For instructions on how to scan and upload on Gradescope, see this video on submitting PDF homework and this handout with recommended scanning apps.

 

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Grading

Grading policy: Based on homework (5%), quizzes (20%), two midterms and the final exam (75%).

We will drop your three lowest quiz scores and your five lowest homework scores.

Each midterm will be worth 25% and the final exam will be worth 50% = 2 x 25%.
Of these four 25% scores, we will drop the lowest and keep your best three to arrive at 75%.

Example: Alice's scores are Midterm 1: 90, Midterm 2: 82, Final exam: 94.
So her four 25% scores are 90, 82, 94, 94.
We will drop 82 and average 90, 94, 94 to arrive at 92 2/3.

Example: Bob's scores are Midterm 1: 91, Midterm 2: 93, Final exam 88.
So his four 25% scores are 91, 93, 88, 88.
We will drop one 88 and average 91, 93, 88 to arrive at 90 2/3.

Final grades will roughly follow historical distributions as recorded at berkeleytime.

Extra Credit: Course Evaluation

Please take a few minutes to participate in our course evaluation, available for the last two weeks of class (until Friday of Week 8). To access the course evaluation, click on the Course Evaluations link in left navigation.

Once you have submitted the evaluation, confirm your Completion of Course Evaluation for the opportunity to receive extra credit added to your final grade. When the grade totals are calculated at the end of class, if you are on the cusp between two grades, we will lean toward the higher grade.

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Course Policies

Academic honesty: You are expected to rely on your own knowledge and ability, and not use unauthorized materials or represent the work of others as your own. Protect your integrity and follow the honor code: "As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others."

There will be no make-up exams or quizzes. No late homework will be accepted.

Grades of Incomplete will be granted only for dire medical or personal emergencies that cause you to miss the final, and only if your work up to that point has been satisfactory.

Students with Disabilities

If you require course accommodations due to a physical, emotional, or learning disability, contact UC Berkeley's Disabled Students' Program (DSP). Notify the instructor and GSI through course email of the accommodations you would like to use. You must have a Letter of Accommodation on file with UC Berkeley to have accommodations made in the course.

UC Berkeley is committed to providing robust educational experiences for all learners. With this goal in mind, we have enabled the ALLY tool for this course. You can now automatically generate “Alternative Formats” for course files and bCourses Pages. Depending on the context, these formats can include Tagged PDF, HTML, BeeLine Reader, Electronic Braille, ePub, Immersive Reader, MP3, and translated versions. For more information, watch the video entitled, "Ally Tutorial for Students at UC Berkeley.”

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Useful Resources

Academic Resources

Some previous Math 54 course web pages:

Study help and tutoring:

Some previous Math 54 exams:

Math 54 Worksheets.

Some online linear algebra:

Course Summary:

Date Details Due