Linear Algebra and Calculus

Short Bio Born in 1949 in Ljubljana. Attended the University of Ljubljana, graduated in mathematics in 1972. PhD in 1982. Employment: Biotechnical faculty in Ljubljana, starting in 1972 as teaching assistant, retired in 2008 as associate professor. Research work: Institute of mathematics, physics and mechanics in Ljubljana. Teaching courses: mostly undergraduate mathematics for technicians. Author of four books and 25 scientific papers. Speciality: mathematics / algebra and functional analysis / non-associative algebras. Prerequisite knowledge Note from the Academic Convenors to prospective participants: by registering to this course, you certify that you possess the prerequisite knowledge that is requested to be able to follow this course. The instructor will not teach again these prerequisite items. If you doubt whether you possess that knowledge to a sufficient extent, we suggest you contact the instructor before you proceed to your registration. The mathematics of the secondary school. No specific prerequisite knowledge is requested. Short course outline The contents of this refresher course are supposed to facilitate the participation in mathematically coloured main courses. However, since it is not possible to know in advance, which main courses will be selected by the future participants of this refresher course, the suggested program is merely an initial proposal and is subject to changes and amendments. It is therefore recommended that in the middle of July 2015, the candidates communicate by e-mail with the instructor whether they fully agree with the contents or they would wish to substitute some chapter(s) with new one(s) (such as: formal logic, set theory, functions of several variables and partial derivation, linear and nonlinear regression, linear programming, facts from the probability theory, etc.) The first part of the course consists of topics in linear algebra: • matrix calculations, • systems of linear equations, • basic facts of eigenvalues and eigenvectors, • Euclidean space. The second part is devoted to the notion and properties of real functions: • basic definitions, • sequences and series, • descriptions of elementary functions, • properties of functions. The rest of the course is the calculus: • differentiation and derivative, • applications of the derivative, • indefinite integral, • definite integral.