Module Description
In this course we will discuss the basics of calculus that you will need throughout your entire studies. Many of the concepts that are covered in this course may already been known to you from school. We will revisit these concepts, but now we will cover them in more detail. In particular, we will discuss precise definitions and present mathematical theorems with their proofs in detail. This course will become more abstract and you will also see that intuition may sometimes trick you (by discussing meaningful examples and counter-examples)!
Content
- sequences and series, convergence,
- functions in one real variable, continuity,
- differentiability and derivatives, differentiation rules, Taylor's theorem,
- Riemann integrability, integration rules, fundamental theorem of calculus.
Contact
Lecturer: Prof. Dr. Matthias Voigt
Assistant: Dr. Nikolaos Tsipinakis
Course Organization
We will provide you with several different learning activities and formats:
- Lecture notes: They provide you with all the details that you need to know at the end of the semester. It is important that you read these notes regularly and try to understand everything.
- Video lectures: The video lectures will pick up on certain aspects of the topics covered in the lecture notes, but they will not go into the full level of detail. Still, it is highly recommended to watch the videos regularly.
- Weekly exercises session: We will do an exercise session in which will discuss problems that are mostly relevant for the homework assignments. Here you will also have the opportunity to ask live questions.
- Weekend meetings: Here we will first give you a summary of the main points of the course content of the previous weeks. Then we will discuss the homework assignments and you will have the chance to present your solutions to your fellow students.
- Forum: The forum is for discussions among yourselves, but we will also have a regular look there and support you in case you have problems.
Live exercise class: TBD.
Interactive lectures: TBD.
A tabular overview of the course schedule is as follows:
| Study week | Dates | Events |
|---|---|---|
| 1 | Feb. 3-Feb. 7 | Begin course |
| 2 | Feb. 10-Feb. 14 | Ex. sheet 1 online, Ex. session 1 |
| 3 | Feb. 17-Feb. 21 | Ex. sheet 2 online, Ex. sheet 1 due, Ex. session 2 |
| Feb. 22 | Lecture 1 | |
| 4 | Feb. 24-Feb. 28 | Ex. sheet 3 online, Ex. sheet 2 due, Ex. session 3 |
| 5 | Mar. 3-Mar. 7 | Ex. sheet 4 online, Ex. sheet 3 due, Ex. session 4 |
| 6 | Mar. 10-Mar. 14 | Study break (no exercise) |
| Mar. 15 | Lecture 2 | |
| 7 | Mar. 17-Mar. 21 | Ex. sheet 5 online, Ex. sheet 4 due, Ex. session 5 |
| 8 | Mar. 24-Mar. 28 | Ex. sheet 6 online, Ex. sheet 5 due, Ex. session 6 |
| 9 | Mar. 31-Apr. 4 | Ex. sheet 7 online, Ex. sheet 6 due, Ex. session 7 |
| Apr. 5 | Lecture 3 | |
| 10 | Apr. 7-Apr. 11 | Ex. sheet 8 online, Ex. sheet 7 due, Ex. session 8 |
| Apr. 14-Apr. 18 | Study break (no reading, no exercise) | |
| 11 | Apr. 21-Apr. 25 | Ex. sheet 9 online, Ex. sheet 8 due, Ex. session 9 |
| 12 | Apr. 28-May 2 | Ex. sheet 10 online, Ex. sheet 9 due, Ex. session 10 |
| May 3 | Lecture 4 | |
| 13 | May 5-May 9 | Ex. sheet 11 online, Ex. sheet 10 due, Ex. session 11 |
| 14 | May 12-May 16 | Ex. sheet 12 online, Ex. sheet 11 due, Ex. session 12 |
| 15 | May 19-May 23 | Ex. sheet 12 due |
| May 24 | Lecture 5 |
Grading & Exam
The total grade you will obtain is composed of different parts:
- Homework assignments (30%): You can only learn mathematics by doing mathematics. The homework assignments will give you the opportunity to do so. It is recommended to start early (at least to think about the problems or let your subconscious do it). You should plan for at least 6-8 hours per week to solve the homework problems. It is explicitly allowed that you work on the exercise sheets in teams - but everyone will have to hand in an individual solution. For your grade we will count the best 10 out of 12 exercise sheets The homework assignments are passed, if at least 100/200 possible points on the 10 best assignments were achieved.
- Final exam (70%): The final exam will be a 30 minutes oral exam. Here we will talk about different concepts provided in the lecture notes. Here it will be particularly important that you understand the theory. You have to be able to present the definitions and theorems and you should also be able to explain the proofs and give examples and counter-examples. Do not try to learn the notes by heart but try to understand them! Note that admission to the final exam is subject to passing the homework assignments.