Linear Algebra and Multivariable Calculus are two of the
widely used mathematical tools across all scientific disciplines. This
course seeks to develop background in both and highlight the ways in
which multivariable calculus can be naturally understood in terms of
By the end of this course, you should be able to:
- Solve and analyze systems of linear equations, and relate the solution set to properties of algebraic objects (matrix null space, column space) associated to the system.
- Analyze the rate of change of a multivariable function in coordinate directions via partial derivatives. Aggregate partial derivatives (derivative matrix, gradients) to get local information such as: tangent planes, linear approximation, and directional derivatives.
- Apply least squares and use differential calculus techniques such as critical points and Lagrange multipliers to solve for constrained local and global extrema.
For a detailed syllabus see
the Syllabus page.
Math 51 students attend lectures on MWF, starting January 4, and discussion sections on TTh,
starting January 5.
You will enroll in lectures on Axess, and discussion sections via Coursework.
This quarter we are offering both
a "traditional" and "active-learning" (or flipped) format for the lectures.
Please see the enrollment tab for more information.
If you are in the active-learning sections, please familiarize yourself with the policies for the active-learning sections that are listed at
the enrollment tab. .
The textbook is a special combined edition of Levandosky's Linear
Algebra Book and parts of Colley's Vector Calculus. (We will use Chapter 2 and 4 from the 4th edition of Colley.)
Hard-copy versions of the text should be available at the campus bookstore.
An electronic version is also available. If you are interested in one, read these instructions and then go to the publisher's site.
If you are in an active-learning lecture, you should purchase
an "iClicker2" from the bookstore or online or used. You should then register your clicker on Coursework.
Calculators are neither required
nor recommended for Math 51.
Your grade will be based on the following components:
- 16% homework and class participation:
There will be weekly written homework assignments. Both traditional and active-learning
lectures have the same weekly written homework. However, the active learning sections split the 16% as 12% weekly written homework,
2% CourseWork questionnaire assignments, 2% clicker participation; for the traditional sections, the 16% is solely based on weekly written homework.
84% Exams: there will be two midterm exams and a final
exam; see exams page for dates, policies, and previous exams. The breakdown
the 84% amongst exams will be approximately 24% for both midterms and 36% for the final.
Things you need to check right away and tell us
- Students with exam conflicts: Except in case of emergency, you must inform us at least two weeks prior to the exam,
together with a valid reason for the conflict.
For midterm exams, the allowable reasons are course-related or competition-related schedule.
The time of the final exam is set by the University, and all students must take the exam then.
- Students with documented disabilities:
See registrar's page on academic accomodations. You must provide an accomodation letter, dated in the current quarter, at least two weeks prior to
an exam, to provide us adequate time to arrange the accomodations.
You are encouraged to attend the office
hours provided by the
instructors and teaching assistants. You
may attend the office hours of any teaching staff member, and no appointment is ever necessary.
The office hours page also lists some other help resources.