20106 Infinitesimal Calculus I 1

Credits: 6 intermediate credits in Mathematics

Prerequisites: none

Recommended: Introduction to Mathematics

Structured along the lines of A Programmed Course in Calculus, by the Committee on Educational Media of the Mathematical Association of America (W.A. Benjamin, 1968), this course was developed by Daniela Leibowitz, Eli Levin, Naomi Shaked-Monderer and Shmuel Berger.

The course is compulsory for students majoring in Mathematics, in Computer Science and in all dual-disciplinary degrees that include Mathematics. It is also recommended for Physics students. It acquaints students with the basic concepts of calculus, emphasizing mathematical rigor.

Together with Infinitesimal Calculus II (20212), it corresponds to undergraduate calculus courses taken by Mathematics students in other Israeli universities. The topics covered here are also covered in Differential and Integral Calculus I (20406), but through a different approach. Beyond providing techniques and applications, this course strongly emphasizes the theoretical aspects of calculus, and provides complete and rigorous proofs for all the theorems presented. As a result, it is not easy. Therefore, although no specific prior Mathematics courses are required, it is not recommended as a studentís first encounter with university-level Mathematics.

Topics: Functions, limits and continuity; Bounded sets and bounded functions; Properties of continuous functions; The derivative; The definite integral; Methods of integration.

1There is some overlap in the content of this and other courses. For details, see Overlapping Courses.