Course Syllabus

MATH 54 Linear Algebra and Differential Equations (Summer 2022)

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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

13954

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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: covers material from the entire course.

Quizzes

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

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 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

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 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:

• David Nadler's Fall 2017 Math 54.
• Nikhil Srivastava's Fall 2016 Math 54.
• David Nadler's Fall 2015 Math 54.
• David Nadler's Fall 2014 Math 54.
• Katrin Wehrheim's's Fall 2014 Math 54.
• Alberto Grunbaum's Fall 2013 Math 54.
• Alberto Grunbaum's Fall 2012 Math 54.
• Maciej Zworski's Spring 2012 Math 54.
• Olga Holtz's Fall 2010 Math 54.
• Peyam Tabrizian's Math 54 web page.
• George Melvin's Math 54 webpage.

Study help and tutoring:

• Study groups, reviews, and drop-in tutoring for Math 54 at the Student Learning Center.
• Math department list of tutors.

Some previous Math 54 exams:

• Math department archive
• Tau Beta Pi archive

Math 54 Worksheets.

Some online linear algebra:

• J. Strom, K. Astrom, and T. Akenine-Moller, Immersive Linear Algebra, "The world's first linear algebra book with fully interactive figures." (Thanks to Alven Wang for the link.)
• 3Blue1Brown, Essence of Linear Algebra, youtube videos. (Thanks to Carly de Frondeville for the link.)

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