Calculus 1

Description

The following subjects will be discussed in Calculus 1: limits and continuity, differentiating and integrating functions, inverse and transcendental functions, mean value theorem, sequences and series, linear differential equations. .

Knowledge and understanding

Calculus I offers an indispensable basis, in content as well as in method, for studying and applying exact sciences, which will be built on during the rest of the curriculum.

The main purpose of the course is to develop concrete quantitative skills in the framework of the most successful mathematical formalism in the history of science. At the end of the course, it should be possible for the student to formalize, analyze and solve (almost) any problem passable of description in standard (continuous) mathematics.

Making Judgements

Instead of being paralysed by a view of mathematics as something requiring either supernatural skills or a gifted memory for “recipes”, the student at the end of the course will have developed “mathematical common sense”. The latter will enable him to either solve a problem, or formulate an educated guess about its solution.

Communication

The material studied in Calculus I is essentially the grammar of mathematics. After successfully passing the exam, the student will be able to use it without hesitation in describing concrete problems, and will have developed enough trust in himself in order to be able to work on a problem without being restrained by mathematical insecurity.

Skills

After having passed the exam, the student will be able to tackle not only the standard type of problems (graph-drawing, calculation of maxima and minima of functions, etc.) studied at the high-school level, but also apply his knowledge to considerably more relevant problems, most prominent among these the description of dynamical systems with (linear) differential equations, the workhorse of physics and engineering since their beginnings as sciences in the 17th century.