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Linear Algebra and Multivariable Calculus (Math 290) — Fall 2019

Welcome to Math 290! This is a three-quarter sequence in linear algebra and (you guessed it) multivariable calculus. The goal of the course is to learn how to use mathematical tools to solve problems in multiple variables and to understand why they work. In particular, this is not a proof-based course—the proof-based equivalent is Math 291, and higher-level courses in mathematical analysis will also derive many of the results we use in this course.

In Math 290-1 (Fall quarter) we will focus on linear algebra. Algebraically speaking, a linear problem is one that can be expressed using polynomials of degree ≤ 1—that is, variables cannot be multiplied together or raised to a power, and they can only be scaled by constants. (For example, 3x + 2y = 4 is a linear equation, but xy + sin(x2) = ey is not.) The reason for the word ‘linear’ is that when you translate such a problem to a geometric problem, the equations and constraints define points, lines, planes, and higher-dimensional hyperplanes. This translation between algebra and geometry turns out to be very fruitful; for example, we can simplify systems of linear equations by transforming the lines and planes they describe into new lines and planes. Such transformations are called linear maps and can be described using grids of numbers, called matrices. This is where this course comes in—most of our time will be devoted to studying matrices, developing algebraic tools for manipulating matrix equations, and using matrices to mediate between algebra and geometry.

Most administrative aspects of the course will be handled using Canvas. There you can find the syllabus and information about homeworks, quizzes and examinations.

Time and place.

Examinations. There will be two midterm exams and a final exam. Locations TBA.

Handouts. What follows are the handouts from class and solutions to exercises. Handouts from last year are here.

  1. Linear systems — handoutsolutions