Linear Algebra and Differential Equations

The present text consists of 130 pages of lecture notes, including numerous pictures and exercises, for a one-semester course in Linear Algebra and Differential Equations. The notes are reasonably self-contained. In particular, prior knowledge of Multivariable Calculus is not required. Calculators are of little use. Intelligent, hands-on reading is expected instead. The lecture notes correspond to the course “Linear Algebra and Differential Equations” taught to sophomore students at UC Berkeley. We accept the currently acting syllabus as an outer constraint and borrow from the official textbooks two examples, 1 but otherwise we stay rather far from conventional routes. In particular, at least half of the time (Chapters 1 and 2) is spent to present the entire agenda of linear algebra and its applications in the 2D environment; Gaussian elimination occupies a visible but supporting position (section 3.4); abstract vector spaces intervene only in the review section 3.7. Our eye is constantly kept on why?, and very few facts 2 are stated and discussed without proof. The notes were conceived with somewhat greater esteem for the subject, the teacher and the student than is traditionally anticipated. We hope that mathematics, when it bears some content, can be appreciated and eventually understood. We wish the reader to find some evidence in favor of this conjecture.