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# Analyse 1

Course
2021-2022

none

## Description

This course treats the principles of calculus for functions of one variable. You will become familiar with the fundamental concepts of the theory and get access to applications in other areas of Mathematics and beyond.

The following topics will be covered: limits; continuity and differentiability; curvature of a graph; linear approximation of functions; Taylor polynomials for functions of one variable; Landau's big-O notation; integration of functions of one variable; fundamental theorem of calculus; substitution rule; integration by parts; partial fractions; improper integrals; finding anti-derivatives; real series; convergence criteria for real series; real power series; differentiation and integration of power series; Taylor series.

## Course objectives

The student knows the theory of the topics mentioned and can apply the theory judiciously. The student can skillfully use the theory to solve concrete problems.

## Mode of instruction

During the semester there will two lectures in almost every week. Some lectures may be replaced by exercise classes. There will be weekly homework and a midterm exam.

## Assessment method

The final grade consists of homework (20%), a written midterm exam (24%), and a written (retake) exam (56%).
To pass the course, the grade for the (retake) exam should be at least 5 and the (unrounded) weighted average of the three partial grades at least 5.5. No minimum grade is required for the homework and midterm exam in order to take the exam or to pass the course. There will be no retakes for the homework and the midterm exam. The homework counts as a practical and it is expected to consists of 10 assignments, of which the lowest grade is dropped. The midterm exam counts as a constituent examination and its grade will be replaced by the grade of the (retake) exam if the latter is higher.

## Literature

Calculus - A Complete Course (8th or 9th or later edition) by Robert A. Adams en Christopher Essex, Pearson Education, 2013, ISBN 978-0-321-78107-9

There also exist combinations of the book with software packages. These are considerably more expensive and NOT needed for the course.

## Brightspace

Brightspace is essentially used, for instance to publish the homework.

## Contact

Onno van Gaans, Mathematical Institute, Snellius room 222,
Email: vangaans[at]math.leidenuniv.nl
Tel.: 071 527 7122.