Course Syllabus

Please note that this syllabus is subject to change and will be updated for the current semester.

MATH 54 Linear Algebra and Differential Equations

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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.


Math 1B or equivalent preparation.

Class number


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Required Text

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

Textbook at Cal student store [direct link pending]

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


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: covers material from the entire course.


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

Quizzes and 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.


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


Gradescope will be used for submission of the homework, some of the quizzes, and parts of the midterms and final exam. 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 policy: Based on homework (5%), quizzes (20%), two midterms and the final exam (75%).

We will drop your three lowest Tuesday quiz scores, your three lowest Thursday quiz scores, and your three 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.

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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 instructors and GSI through course email of the accommodations you would like to use.

UC Berkeley is committed to providing robust educational experiences for all learners. With this goal in mind, we have activated the ALLY tool for this course. You will now be able to download content in a format that best fits your learning preference. PDF, HTML, EPUB, and MP3 are now available for most content items. For more information visit the alternative formats link or watch the video entitled, "Ally in bCourses."

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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